Changes in the design and operational wind due to climate change at the Indian offshore sites

Marine Structures 37 (2014) 33–53

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Changes in the design and operational wind due to climate change at the Indian offshore sites Sumeet Kulkarni, M.C. Deo*, Subimal Ghosh Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 February 2014 Accepted 13 February 2014

The increasing global warming is most likely to affect the magnitude and pattern of wind at a regional level and such an effect may or not follow the trend predicted at the global scale. Regional level exercises are therefore necessary while making decisions related to engineering infrastructure. In this paper an attempt is made to know the extent of change in design as well as operational wind conditions at two offshore locations along the west coast of India. The design wind speeds with return periods of 10, 50 and 100 years derived for two 30-year time slices in the past and future are compared. In two separate exercises the past and future wind at the local level is simulated by empirical downscaling as well as by interpolation of the general circulation model (GCM) output. Both sets of past and future data are fitted to the Generalized Pareto as well as Weibull distributions using the peak over threshold method to extract long term wind speeds with a specified return. It is noticed that at the given locations the operational and design wind may undergo an increase of around 11%–14% when no downscaling is adopted and 14%–17% when the GCM data are downscaled. Although these figures may suffer from a certain level of statistical uncertainty the study points out to take a relook into the safety margins kept in the design and operation of ocean structures in the light of global warming. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Offshore structures Operational wind Design wind Climate change impact Neural networks

* Corresponding author. E-mail address: [email protected] (M.C. Deo). http://dx.doi.org/10.1016/j.marstruc.2014.02.005 0951-8339/Ó 2014 Elsevier Ltd. All rights reserved.

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1. Introduction The inter-governmental panel on climate change (IPCC), based on sophisticated modeling tools and observations of average air and ocean temperatures over the earth, had confirmed existence of global warming that is most likely due to human interference with the atmosphere [1]. Due to dependency of air pressure on temperature changes in wind speed and its pattern of flow can only be expected as a consequence. An increase in wind could affect other coastal processes as well. For example as per DHI [2] a 10% rise in wind can give rise to 26% higher waves and 40%–100% jump in the rate of sediment transport in general. The stated increase in wave heights may possibly result in case of wind of around 20 m/s generating fully developed seas. A quantitative prediction of such changes with respect to operational and design wind speeds would go a long way in ascertaining safety of various coastal, harbor and offshore structures installed in the sea. The present study is oriented in this direction and it predicts the change in values of daily mean wind speeds corresponding to return periods of 10, 50 and 100 years, typically used in operation and design exercises. The changes are worked out for two offshore locations along the western Indian coastline. Such station-specific studies are necessary because ocean structures are built with local conditions and the regional change may or not follow global trends due to the influence of a variety of local factors like coastal geomorphology, shifting of storm tracks and surface roughness. The procedure to evaluate the changed wind conditions normally involves use of a general circulation model (GCM) which is a mathematical description of circulations in atmosphere, ocean, and at land boundaries. Based on concepts of mass, momentum and energy balance, it simulates response of climate systems to increasing global temperatures arising out of the rise in green house gas emissions. A GCM typically gives predicted values of climate variables including wind speeds and directions over large spatial grids and time steps. Investigators over the world are continuously experimenting with a variety of GCMs with a view to come up with more and more accurate and reliable versions. Those working under the US based World Climate Research Program have conducted a state of the art modeling exercise called Coupled Model Inter-comparison Project (CMIP) that deals with analysis of coupled atmosphere and ocean general circulation models. The 5-th phase of this experiment called CMIP5 is one of the latest and it involves several multi-model exercises for reliable impact assessments [3]. A GCM is run for possible future scenarios of temperature rise due to a certain increase in greenhouse gas emissions together with world’s response to reduce such emissions. The Fourth assessment report, AR4, of IPCC lists six families of warming scenarios, including the high warming scenario: A2. The revised scenarios in the latest Fifth assessment report, AR5, are called Representative Concentration Pathways (RCPs) and these are specified as per their warming potential and societal response encapsulated into a certain radiative forcing, like 4.5 or 6.5 W/m2, that drives the GCMs. More information regarding the GCMs can be found out in textbooks by Donnor et al. [4] and Randall [5]. The outputs of GCMs are available over large spatial grids and hence may need conversion through a process called downscaling to apply to a specific region. There are basically two alternatives to downscale GCM data, namely, dynamical and statistical. In dynamical downscaling the knowledge of the underlying physical process is utilized while the statistical alternative exploits regression capabilities of various statistical and other approaches like artificial neural networks and genetic programming. The various downscaling models are presented in Prudhomme et al. [6] and Wilby et al. [7]. The standard for downscaling could be observed data or reanalysis data available over a long term. The reanalysis data result from assimilation of observations into GCM predictions, making the latter more reliable. The reanalysis data called ERA-40 of European Centre for Medium-Range Weather Forecasts (ECMWF) is available over a period of more than 40 years in the past. The National Center for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) have created historical wind records of more than 50 years. Owing to an incomplete knowledge of the physics underlying various atmospheric processes and also due to the application of numerical schemes to solve the governing differential equations, GCM data contains bias or a systematic error. There are various ways to remove such a bias and most of these involve comparison of statistical properties of a given GCM with those of a more reliable long term dataset obtained by other means like observed or reanalysis data.

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Some more information on GCMs RCPs and datasets is given in Appendix I. 2. Past studies The impact of climate change on regional design wind speeds was assessed in the recent past by Debernard et al. [8] over the northeast of Atlantic based on a control climate of 1980–2000 and projected climate of 2030–2050. Certain areas in Barents Sea, northern North Sea and some portions of Atlantic Ocean were found to undergo noticeable increase in wind speeds. Grabmann and Weiss [9] analyzed extreme wind conditions in North Sea and noted increased wind intensity and frequency. The 99-percentile of the long term distribution of hourly mean wind speeds in North Sea was predicted to increase by 7%. Merryfield et al. [10] analyzed data of surface marine winds off Canada. The projected wind over two intervals, 2030–2049 and 2080–2099, were compared to the 1976–1995 baseline period. An increase of 5%–10% in average summer wind speeds was noticed. For various locations in The Netherlands, Steenbergen et al. [11] found a change of 0.8%–2.3% in the 50-year return hourly wind, while Tank et al. [12] predicted a change of
1% to 4% in the annual maximum of daily mean wind speeds by 2050. Cheng et al. [13] studied potential changes in hourly and daily gust wind with the help of gust simulation models and statistical downscaling over Ontario, Canada. The results showed an increase up to 15% and 25% for annual mean wind exceeding 28 kmph and 70 kmph, respectively, and further that these changes were greater than those due to uncertainties associated with the GCM’s and scenarios. Over the North Sea Winter et al. [14] used an ensemble of 12 CMIP-5 GCM’s that were run for two climate scenarios of rcp-4.5 and rcp-8.5 to know changes in annual maximum and long term wind speeds. Authors however failed to notice any firm change in magnitudes but observed increased frequencies of occurrence. Another example of a decreasing trend is due to Najac et al. [15] who worked over the Mediterranean region using downscaled projections of 14 GCMs of CMIP-3 multi-model data and found a decrease rather than an increase in wind conditions. It is thus clear that the nature as well as magnitudes of changes in the future wind is strongly region-specific and needs to be individually addressed to while designing and operating ocean structures. One such attempt at an Indian location was due to Deepthi and Deo [16] who considered 7 years daily measurements made at a location off the west coast of India as well as future projections of the daily wind at the same location corresponding to the Canadian GCM – version 3 (CGCM3) run for the worst global warming scenario: A2. This study however suffers from the use of a small sample size and also that of less sophisticated data as well as fitting procedures. The present work addresses these issues and further confirms the findings at one more location in the same region. It considers a large sample of 30 years to represent the past wind and incorporates statistically more appropriate distribution of Generalized Pareto type fitted to data using the peak-over-threshold technique [17–21] in place of the total sample method that neglects data independency. An alternative to the downscaling in the form of interpolation of the GCM data has been additionally attempted in this work to confirm the nature and magnitude of the change. The two locations in the present study are along the west coast of India and code named DS1 and DS2 which are off Goa and Lakshadweep, respectively (Fig. 1). The site: DS1 has the depth of 3800 m and the latitude and longitudes of 15.447 N and 69.236 E, respectively. For the other location: DS2 the water depth is 1850 m and the latitude, longitude values are 10.651 N and 72.525 E, respectively. 3. The assessment based on downscaled GCM data The first exercise consisted of downscaling the GCM data and carrying out its statistical analysis. It involved five different types of datasets as follows: (i) Wave rider buoy data: Wind measurements made by National Institute of Ocean Technology at Chennai, India over a period of 8 years from 1998 to 2006 at both the locations were used to train the downscaling model as described subsequently. The sensor had an accuracy of 1.5% in speed and 3.6 in direction and could measure the wind speed up to 60 m/s. Specific loss of accuracy at extreme values was not reported From the 3-hourly observations made at 3 m from the water

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Fig. 1. The location of study around the Indian coastline.

level the daily mean wind speed at the 10 m height (referred to as wind speed only hereinafter) were derived. The use of the usual 1/7-the power law was made to convert the 3 m wind to the 10 m height. (ii) CGCM-RCP-4.5 data: The wind data resulting from the Canadian General Circulation Model (CGCM), version 4, run for the Representative Concentration Pathway (RCP)-4.5 waring and response scenario for future 30 years from the current year provided the projected values (http://www.cccma.ec.gc.ca/data/cgcm4). For the location DS1 the current year was assumed as 2000, consistent with the earlier work on the same site while for the location: DS2 the same was presumed to be 2005. These GCM models were earlier developed as a part of Coupled Model Inter-comparison Project Phase 5 (CMIP-5) exercise under the World Climate Research Program. The program combines results from more than twenty major global climate models that incorporated large sets of experiments with the latest coupled climate models. The RCP-4.5 is a scenario that restricts radiative forcing due to green house gas emissions to 4.5 W/m2 till the year 2100. It includes long-term, global emissions of greenhouse gases, short-lived species, and landuse-land-cover in a global economic framework [22]. The wind speed data at 25 grid points (5  5) around the locations of interest were extracted. Data at many locations around the site of interest were preferred over just one location because of the possible influence of nearby wind over wind speed at the actual site. The size of each grid was 2.81  2.81 or 313 km  313 km, approximately. (iii) The Canadian General Circulation Model corresponding to the 20th Century, 3-rd version model experiment (CGCM-20C3M) data: The output of wind speed obtained by running the CGCM20C3M experiment under CMIP5 over the historical time slice of 30 years as mentioned above was used, in view of its accurate and reliable nature, to make correction in the bias of future data (using the quantile mapping technique referred to later and described in Appendix II) and make it consistent with the historical data. The quantile mapping is regarded as more appropriate in applications that involve extreme value analysis since it matches the upper quantiles of both empirical (data) and theoretical (GPD) distributions. The CGCM-20C3M data were used for this purpose in view of their accuracy (http://www.cccma.ec.gc.ca/data/cgcm4/CanCM4/historical/ index.shtml). These data were extracted over the same locations as that of the CGCM-RCP-4.5 data. (iv) ERA-40 re-analysis wind data: The ERA-40 project of European Centre for Medium-Range Weather Forecast (ECMWF) provides atmospheric data for over 40 years in the past (from 1957 to 2002) obtained by running sophisticated and high resolution global atmospheric models with the help of enormous observations from various direct and indirect sources. The data sets are quality controlled and expected to be free from spurious trends [23]. This information was used to simulate historical wind at location: DS1, while the same at site: DS2 was done on the basis of the National Centre for Environmental Prediction/National Centre for Atmospheric

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Research (NCEP/NCAR) data mentioned below due to the unavailability of ERA-40 outcome beyond 2002. The wind speeds obtained as a result and over 4  4 grid points around DS1 for the period of 30 years in the past from 1971 to 2000 were extracted from the web site: http://dataportal.ecmwf.int/. Each of the grids was of size: 2.5  2.5 . (v) NCEP/NCAR reanalysis wind data: This information along with the wave buoy observations was used as input to train the downscaling model and also to simulate historical wind at the site: DS2. As mentioned in the subsequent section the downscaling model training was achieved through an artificial neural network, whose input was NCEP/NCAR data over the period of 8 years from 1998 to 2006 and whose output was the wave rider buoy observations in the same period. The duration for calibration data pertained to 8 years from 1998 to 2006. The duration of the historical data at site: DS2 was of 30 years from 1976 to 2005. The size of each grid involved was 2.5  2.5 (http://www.esrl.noaa.gov/psd/data/reanalysis/reanalysis.shtml). The extracted wind data as above were in two components: meridional (North-South) and zonal (East-West), which represent the two orthogonal components of the resultant wind speed. Further, in order to be consistent with the peak-over-threshold method of analysis only monsoon data of four months (June to September) every year was considered since the fair weather data would not contain peaks to extract. The dimensionality associated with these data was high (typically: 2 components  30 days  4 months  30 years  16 grids) representing highly noisy data that would be difficult to model. A principal component analysis (PCA) was therefore made as mentioned later to reduce the dimensionality before using the data for developing the downscaling model.

3.1. The methodology The procedure followed to arrive at the long term wind speed values was as follows: 1. Re-grid the past CGCM-20C3M and future CGCM-RCP4.5 data to match the grid size of the ERA-40 and NCEP/NCAR data using the bilinear interpolation scheme that involves linear interpolation along both horizontal and vertical directions. 2. Obtain unbiased GCM data by minimizing the bias in future values through the quantile mapping technique introduced by Li et al. [24] in which probability distribution functions of both observed and GCM data are derived and the distribution function of simulated GCM series is matched with that of the observed series. More details of the quantile mapping are given in Appendix II. 3. Standardize all data (GCM’s, NCEP/NCAR and ERA-40) by subtracting the mean and dividing by the standard deviation, for facilitating the PCA. 4. Reduce the dimensionality of the past ERA-40, NCEP/NCAR and future CGCM3-RCP4.5 data by carrying out the PCA as mentioned earlier and retaining only those Principal Components (PC’s) that typically explain 95% of data variance (See Appendix II for a few details of the PCA). More information can be seen in Jolliffe [25] and Shlens [26]. 5. Develop an artificial neural network (ANN) model for downscaling future data of the GCM. ANN’s have been abundantly used for such a mapping purpose due to their fitting flexibility. Appendix II gives the expressions that were used to arrive at the output from an ANN (Reference is made to Rojas [27] and Gershenson [28] for details on the ANN methodology). 6. Generate wind speed values for the future 30 years’ period using the above ANN. 7. Fit the Generalized Pareto Distribution (GPD) to both past as well as projected future wind with the help of peak-over-threshold method. The GPD is given by the following expression:

P ½ðW  Ws ÞjðW  uÞ ¼ 1
½1 þ ðaðWs
mÞ=sÞ
a

1

(1)

where, P ( ) ¼ probability distribution function of ( ); W ¼ the variable of daily mean wind speed; Ws ¼ given value of the daily mean wind speed; u ¼ selected threshold; m ¼ location parameter, s ¼ scale parameter; a ¼ shape parameter.

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Obtain the probability distribution function, P(W), corresponding to a given return period Tr in years, using:

PðWÞ ¼ 1


1

b$Tr

(2)

where, b is the mean rate of extreme events obtained by dividing the total number of extreme events crossing a given threshold by the number of years of data collection. Substitute the P(W) value so obtained, in the left side of Eq. (1) and obtain the unknown wind speed Ws corresponding to Tr. The above procedure of evaluating the operational and design wind at the specified stations has the advantage that it tags the GCM data with in-situ measurements by making it more reliable and thereafter fits the statistical distributions. Sailor et al. [29] found the above procedure as more satisfactory than the one that uses GCM data directly. 3.2. The results at site: DS1 The network was trained using the input of initial six years (1998–2004) of the NCEP/NCAR data and tested for the remaining two years of measurements. The network output during training pertained to the corresponding buoy observations. A study of how the explained variance changed with increasing number of PCs, typically shown in Fig. 2(a) and (b), enabled selection of the appropriate number of PCs as input to the ANN. Generally the first four PC’s explained 95% variance of data and hence formed the input to the ANN. The ANN (Fig. 3) was of 3-layered feed forward type with 4 input nodes, 3 hidden nodes and 1 output node. During training the output belonged to the observed daily mean wind speed. The network was trained using the conjugate gradient algorithm and it involved the Sigmoid Axon transfer function.

Fig. 2. (a) and (b): Cumulative explained variance versus principal components for past and future dataset at DS1.

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Fig. 3. Typical feed forward neural network used (P1, P2, P3, P4: Input principle components for wind speeds).

Table 1 shows the basic statistics (mean, standard deviation, skewness and kurtosis) of the training and testing data. It may be seen that both training as well as testing data had comparable statistics indicating sufficiency of the range of the testing values involved. Fig. 4(a) and (b) shows the testing exercise of the network done with the help of 2 years of the last segment of the observations in terms of time history plots and scatter diagrams. The closeness between the observed and network-derived values of the daily mean wind may be noted. This is further confirmed quantitatively through the corresponding error statistics of the correlation coefficient, R ¼ 0.81, root mean square error, RMSE ¼ 0.63 m/s and mean absolute error, MAE ¼ 1.89 m/s. The MAE thus seen in the network testing is high. However it was desirable to use the technique of soft computing tools like ANN for downscaling as done in this work in preference to other conventional statistical tools since many studies in the past [30,31] had indicated that they usually perform better than other ‘fixed model’ approaches like statistical regressions. Hence the use of alternative statistical methods was not attempted. Further, since each error statistic has its strength as well as limitations one has to simultaneously consider a few other measures as well. Typically here the correlation coefficient, R, is 0.81 which should be regarded as good for simulation of such natural phenomena. The MAE depends on the entire range of values of the predicted property whereas R gets severely affected by extreme differences; hence a good value of R is indicative of less number of extreme errors. Another such statistic, working like R is RMSE, whose value is 0.63 m/s, much lower than that of the MAE. After the ANN model was so established, it was applied to simulate historical and future wind.

Table 1 (a), (b): Statistics of training and testing data at locations: DS1 and DS2. Statistic (Training)

Modeled wind speed (m/s)

(a): Location: DS1 Mean 7.22 Std. dev. 3.07 Skewness
0.37 Kurtosis
0.76 (b): Location: DS2 Mean 6.45 Std. dev. 2.66 Skewness 0.75 Kurtosis 1.33

Target(Buoy) output (m/s)

Statistic (Testing)

Modeled wind speed (m/s)

Target(Buoy) output (m/s)

7.10 2.93
0.50
0.72

Mean Std. dev. Skewness Kurtosis

8.25 2.26
0.44
0.68

7.78 1.84
0.38
0.71

6.27 2.22 0.56 0.19

Mean Std. dev. Skewness Kurtosis

6.50 3.17 0.65 1.05

6.37 2.97 0.59 0.99

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Fig. 4. (a). Testing of the ANN: Network-yielded versus target wind speed (Site: DS1). (b). Testing of the ANN: Network-yielded versus target wind speed (Site: DS1).

The selection of the threshold consisted of experimenting with a very large number of its values, deriving the GPD distribution for each value and assessing its fit with the empirical (un-fitted) distribution by the KS test at 5%–10% significance level. That threshold value which satisfied the test and also had the largest number of values above it was finally selected. The thresholds so resulted were 1.61 m/s and 5.08 m/s for past and projected data, respectively. The number of data values above these were 2000 and 1490, respectively. The location, scale and shape parameters of the GPD were m ¼ 1.605, s ¼ 5.470, a ¼
0.339, respectively for the historical data fitting and m ¼ 5.081, s ¼ 16.380, a ¼
0.967, respectively for the fit to the projected data. In a separate exercise the threshold values for the past and projected data were kept nearly the same. This brought the number of data values above the threshold, of both past and future data closer to each other. The extraction of the long term (return-period) wind speeds based on the resulting fit of the GPD however showed little difference with respect to the same wind speeds derived on the basis of the earlier exercise with unequal thresholds, indicating less sensitivity of the threshold changes once the threshold satisfied the KS test. The long term wind speed values used for operational and design purposes obtained as above and derived for both past as well as future projected data are shown in Table 2. The Table shows that for all return periods the daily mean wind speed would increase in future. Such an increase would be 15.31%– 16.99% for the various return periods. A slight reduction in the percentage increase from operational to design level may mean that the changes may happen more intensely in the earlier period. The Table shows that the change with respect to past conditions is significant and remains more or less same over both operational as well as the design conditions.

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Table 2 Change in the long term wind speed at location: DS1. Return period (yr)

Wind speed based on past climate (m/s)

Wind speed based on projected climate (m/s)

% Increase

10 50 100

15.97 16.38 16.40

18.68 18.91 18.92

16.99 15.42 15.31

In an earlier study by Deepthi and Deo [16] that was based on (i) comparison with the past 7 years’ observed data unlike the present 30 years’ GCM data, (ii) fitting of the Weibull distribution and (iii) use of the total sample method, an increase of 55%–59% was seen at the same site for similar return periods. While the deviations could be attributed to the difference in data used, methods of comparison and fitting tools, it can be said that the present work involves (i) a larger sample size for the past data, (ii) more reliable form of projected data due to the state of the art bias correction applied, (iii) statistically more acceptable fitting tools (GPD and peak-over-threshold method) than the earlier work and hence the present results may be viewed as improved and more reliable predictions of the effect of climate change at the given location. In terms of the magnitudes it is also more consistent with the past studies at other locations over the world mentioned earlier. In order to further confirm above results the trend of the annual maximum daily wind speed for the entire 60 years’ period under consideration was studied. The fitted linear trend line is shown in Fig. 5. This exercise confirms the rising trend with the slope of the fit as 0.016 m/s per year or 1.6 m/s per 100 yr. This transforms to 10.22% over the 100-year wind extracted from the past data as indicated in Table 2. The statistical significance of the slope value was ascertained with the help of Kendall’s test [32]. In this exercise the Kendall’s statistic s was
0.21583 and its variance was 0.01569. Based on these statistical parameters the standard statistic, Z, was found to be
1.723. Because this value is in the range of (
1.96, 1.96) it was concluded that the slope is statistically significant. This exercise thus shows some amount of consistency in the change in the annual maximum wind and the 100-year return value of the daily mean wind (15.31%) evaluated earlier by the rigorous statistical procedures. Another exercise to confirm the increasing wind intensity at the given location consisted of comparing the probability distribution functions of the past and future wind across the underlying 30yr time slices. This is shown in Fig. 6. It may be noticed that the lower winds may visit less frequently but the higher wind would occur more often in future, raising thereby the long term wind speed. In order to quantitatively understand the differences in the probability distributions the values of mean, standard deviation, skewness and kurtosis were derived for both past and projected data. It was found that the mean increased from 8.78 m/s to 13.11 m/s and so also the standard deviation from 3.24 m/s to 3.93 m/s indicating higher levels of wind with somewhat larger spread over the mean. Further the skewness changed from 0.47 to
0.23 suggesting a shift from the right skewed to the left skewed

Fig. 5. Trend in the long term wind of 60 years period (1970–2030) (Site: DS1).

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Fig. 6. Probability distribution functions of past and future wind (Site: DS1).

distribution with tendency of most of the values to lay on the higher side of the mean. The kurtosis (excess) that measures peakedness of the distribution was found to change from
0.915 to
1.230 in future indicating a flatter distribution with a possibility of smaller spread around the mean. The statistical distribution of wind in future may thus undergo some change at the given location.

3.3. Results at site: DS2 The downscaling network at this location was trained for the eight years of the NCEP/NCAR data (1998–2006) as in the earlier case using the initial six years for training purpose and remaining two years for the testing purpose. Like DS1 here also the first four PC’s explained around 95% of data variance and hence formed the input to the ANN which in turn was of 3-layered feed forward type with 4 input nodes, 5 hidden nodes and 1 output node. In this exercise it was found that the Levenberg– Marquardt algorithm provided more satisfactory training than other schemes and hence the same was adopted. The transfer function however was the same as earlier, namely, Sigmoid Axon. Fig. 7(a) and (b) shows the testing of the network over a period of the last segment of two years of data in terms of time history and scatter plot-based comparisons. A satisfactory match between the target and the estimated wind speed may be seen. This was further confirmed by a fair value of the correlation coefficient, R, between the two time series, namely, 0.73, and low values of RMSE and MAE of 0.478 m/s and 1.38 m/s, respectively. When compared with the site: DS1 in this case the R value is relatively low, but RMSE and MAE are also lower. Having tested the network the projected values were thereafter generated and the long term distribution of GPD was fitted to both past and projected data. The GPD fitting involved selection of the threshold value of wind speed by trials aimed at satisfying the KS test at 5%–10% significance level with the largest number of data values lying above the threshold. The thresholds so resulted were 9.46 m/s and 9.80 m/s for past and projected data, respectively. The number of data values above the thresholds were 820 for the past and 775 for the future datasets. With these thresholds the location, scale and shape parameters of the fitted GPD were m ¼ 9.47, s ¼ 10.2, a ¼
1.29, respectively, for the historical data fitting and were m ¼ 9.81, s ¼ 11.96, a ¼
1.18, for the fit to the projected data. Table 3 presents the long term wind speeds so derived for both historical as well as future data. It is apparent that like the earlier site: DS1 the daily mean wind speed at DS2 would also increase in the future for both operational as well as design conditions. Such an increase would range from 14.24% to 14.61% for design and operational return periods. Unlike the previous location of DS1, here the change

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Fig. 7. (a). Testing of the trained network at location: DS2. (b). Testing of the ANN: Network-yielded versus target wind speed (Site: DS2).

is more or less same over various return periods, meaning thereby that the changes would mostly happen in the near future and would remain same later. When compared with the corresponding wind speeds at the previous location: DS1 these percentage increases are generally of similar order, but somewhat lower. DS1 is at around 400 km northward than DS2 and may face more cyclones than DS2 due to typical paths followed by them. The noted increase of the long term wind as above was further confirmed by fitting a linear trend to the entire 60 years’ data of yearly maximum wind as shown in Fig. 8. The increasing trend seen in this Figure is associated with the slope of 0.015 m/s per year or 1.5 m/s over 100 yr. This means an 8.74% rise in 100 years over the 100-year wind extracted from the past data indicated in Table 3. The application of Kendall’s test to confirm the statistical significance of the slope indicated that the statistic s was
0.20226 and its variance was 0.015694 and based on these statistical parameters the standard statistic, Z, was
1.6145, i. e., in between the range of (
1.96, 1.96) confirming that the slope of the fitted trend line was statistically significant. Thus like DS1 at this location as well certain consistency with the increase projected by the earlier rigorous statistical procedures was noticed. The rising trend in the wind speed was again confirmed by comparing the probability distribution functions of the historical and projected wind over the two 30-yr time slices as in Fig. 9. Like DS1 here as well it was seen that although the peak value may occur less frequently the higher wind speeds would have more frequent visits and this may raise the long term wind speed in future. With respect to

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Table 3 Change in the long term wind speed at location: DS2. Return period (yr)

Wind speed based on past climate (m/s)

Wind speed based on projected climate (m/s)

% Increase

10 50 100

17.35 17.35 17.36

19.82 19.89 19.89

14.24 14.59 14.61

Fig. 8. Trend in the long term wind of 60 years period (1976–2035) (Site: DS2).

these distributions it was found that the mean wind speed would increase from 13.91 m/s to 15.28 m/s in the future while the standard deviation would rise from 2.38 m/s to 2.99 m/s indicating higher wind energy associated with more turbulence. The skewness of the past data was
0.213 while the same for the projected one was
0.156 showing the asymmetric or left skewed nature of both distributions. The kurtosis was
1.23 for the past and
1.42 for the future data indicating somewhat lower spread over the mean in the future. The study described above shows a need to relook into the operational and design wind speed values traditionally worked out at given offshore locations and decide if an increase in the safety margin is necessary. The above work has limitations arising out of uncertainties in the statistical methods and downscaling procedures and can always be refined when more state of the art GCM data as well as statistical fitting methods becomes available from the works of climate scientists and statisticians. 4. The assessment based on data derived by GCM interpolations The second exercise now involved the use of GCM data without any downscaling and with bilinear interpolation only. This may appear workable at offshore locations where complexity arising out of sea–air interface can be less severe than the one at the land-air boundary. It was additionally thought to be interesting to see how such an effort compares with the one described earlier that involved the downscaling, appearing more attractive due involvement of the in-situ wind observations. The methodology, explained later, involved collecting past as well as future GCM output around the sites of interest and interpolating them at the specified offshore locations. The interpolated data were thereafter subjected to the long term statistical analysis to extract operational and design wind speeds. Before interpolation however bias correction for both past and projected data was necessary and this was done using the more accurate NCEP/NCAR data. 4.1. The datasets used (i) CGCM-RCP-4.5 data: This information was used to obtain the projected climate over the years: 2006–2035 and pertained to wind resulting from the Canadian General Circulation Model:

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45

Fig. 9. Comparison of past and projected probability distribution functions at DS2.

(CGCM)-4 run for the RCP-4.5 scenario for future 30 years. The grid size was 2.81  2.81. The information of meridional and zonal wind over a 3  3 grid points centered over DS1 and DS2 was extracted. The use of nine grid points facilitated interpolation at a four grid points of NCEP/ NCAR described later. (ii) 20C3M data: The outcome of the Canadian GCM called 20C3M experiment was extracted from the web site as mentioned in the preceding downscaling work and used to simulate the past wind conditions over the years: 1976–2005 at both the sites. The information over the same nine grids (of size: 2.81  2.81 ) as above was extracted.

Fig. 10. Comparison of NCEP/NCAR data with wave buoy observations. (a) at site: DS1; (b) at site: DS2.

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(iii) NCEP/NCAR reanalysis wind data: These data, being more accurate and reliable than a general GCM output, were used to remove bias in the above referred GCM data. The information over the years: 1976–2005 and at a 2  2 grid points each surrounding DS1 and DS2 was extracted. The grid size here was 2.5  2.5 . In summary the usage of various datasets in this work is clarified as below: A. The downscaling experiment Past dataset: downscaled ERA-40 at site: DS1; NCEP/NCAR at site: DS2 Future dataset: downscaled and bias removed CGCM-RCP4.5 Bias removal in future data: NCEP/NCAR and CGCM-20C3M Downscaling model training: input: NCEP/NCAR; output: wave buoy observations B. The interpolation experiment Past dataset: CGCM-20C3M Future dataset: CGCM-RCP4.5 Bias removal in past and future data: NCEP/NCAR and CGCM-20C3M 4.2. The methodology The procedure to arrive at the operational and design wind speeds at the selected locations using the above mentioned datasets was as follows: (i) Interpolate the NCEP/NCAR data at DS1 and DS2 using the bi-linear interpolation method for those eight years for which the buoy records were available. Compare the resulting interpolated wind speed with the buoy measurements and ensure compatibility. (ii) Re-grid the CGCM-RCP-4.5 data (from 2.81  2.81 ) to the NCEP/NCAR grid size (2.5  2.5 ) using the bi-linear interpolation method. (iii) Perform quantile mapping for CGCM-RCP-4.5 and 20C3M datasets with respect to the NCEP/ NCAR data as explained in Appendix II. At the end of the quantile mapping RCP-4.5 and 20C3M datasets got corrected for the bias at the resolution of 2.5  2.5 . Unlike the earlier downscaling based procedure in this interpolation based method the bias was required to be removed from both past as well as future data of the GCM. (iv) Perform a bi-linear interpolation for the above unbiased data to the buoy location levels. (v) Having generated the bias-free and interpolated GCM data as above for past as well as future, carry out the statistical analysis to obtain the wind speed with varying return periods as follows: (It was noted that unlike the preceding exercise here the Generalized Pareto Distribution was not found to provide good fit to data (as determined by the Kolmogorov–Smirnov test) and hence the Weibull distribution was fitted as an alternative.) Obtain the probability distribution function, P(Ws), corresponding to a given return period Tr in years, using the Weibull distribution function in Eq. (3) fitted with the help of peak-over-threshold method.


W
ma  s PðWs Þ ¼ 1
e
b

(3)

where, P ( ) ¼ probability distribution function of ( ); Ws ¼ daily mean wind speed above the threshold “m”, m ¼ location parameter (selected threshold), b ¼ scale parameter; a ¼ shape parameter. Obtain the P(Ws), corresponding to a given return period Tr in years, using Eq. (2). Substitute P(Ws) value so obtained in the left side of Eq. (3) and obtain the unknown wind speed Ws corresponding to Tr.

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4.3. Results for sites: DS1 and DS2 As stated earlier, for removal of the bias on the GCM datasets the NCEP/NCAR data were used. The adequacy of the NCEP/NCAR data was ascertained by comparing the same with the wave buoy measurements. Fig. 10 shows this exercise in the form of a scatter plot for both the sites. It may be seen that the reanalysis data are fairly close to the wave buoy observations and the same can be used for removal of the bias in GCM data. Like the preceding exercise that involved a downscaling process here as well the threshold value of wind speed for use in the Weibull distribution was selected by trials made such that the distribution fit satisfied the Kolmogorov–Smirnov (KS) goodness of fit test at the significance level of 0.05–0.10 and also has the largest number of data values above the threshold. The values of distribution parameters at both sites is given in Table 4. As examples, comparisons of resulting Weibull (fitted) and empirical (sample) cumulative distribution function (CDF)’s for past as well as future data at both DS1 and DS2 locations are shown in Fig. 11. Fig. 11(a)–(d) shows how in this interpolation based study the sample cumulative distribution matched with the fitted one in case of past and projected data at the locations: DS1 and DS2. A close match may be noticed, indicating adequacy of the Weibull distribution fit, based on the selected thresholds. The long term wind speed values used for operational and design purposes obtained by following the methodology discussed above and applied for both past as well as future data are shown in Table 5 for location: DS1 and in Table 6 for the site: DS2. The Tables show that for all return periods the daily mean wind speed would increase in future for both the sites and that such an increase would be 11.41%–12.21% at DS1 and 11.20%–14.17% at DS2 over the various return periods. These changes are somewhat smaller in magnitudes compared to the earlier ones worked out for the downscaled data, namely, 15.31%–16.99% at DS1 and 14.24%–14.61% at DS2, respectively. The effect of downscaling was thus to predict slightly higher changes. As mentioned earlier however the downscaling based analysis needs more attention due to its higher reliability. If we compare Table 2 with Table 5 for location DS1 and Table 3 with Table 6 for site: DS2 we find that the numerical values of long term wind speeds evaluated through downscaling were lower at DS1 and higher at DS2 than the interpolated ones, which might be due to the site-specificity but both methods predict significant increase in the operational as well as design wind speeds. 5. Limitations This study was focused on knowing what happens when projected data which explicitly account for climate change are used in place of past data at given locations. The study employed daily mean wind as unit of analysis in order to have compatibility between the past information and future GCM based data. For certain applications such as effects on waves and wave loads, storm surges, analysis with shorter interval values may be necessary. The locations considered in this study are those where India’s National Institute of Ocean Technology carries out data collection through wave rider buoys. Intensive research is presently going on in oil companies operating in Indian offshore locations to explore and exploit oil and gas in very deep waters and at the end of continental slopes where high gas potential has been strongly detected. Floating production systems like Floating Production Storage and Offloading (FPSO) and many others are getting deployed in very deep waters. Although majority of ocean structures are installed in much shallower waters the study nonetheless demonstrates a methodology to assess the effect of climate Table 4 Weibull distribution parameters values at DS1 and DS2. DS1

DS2

Parameters

20C3M

GCM-RCP 4.5

20C3M

GCM-RCP 4.5

a b m

1.417 2.129 10.899

1.410 2.516 11.598

1.399 1.284 8.254

1.272 1.492 8.141

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Fig. 11. (a) and (b): Comparison of empirical (sample) and Weibull cumulative distribution functions for past (20C3M) and future (RCP 4.5) wind data at DS1 – Interpolation based study. (c) and (d): Comparison of empirical (sample) and Weibull cumulative distribution functions for past (20C3M) and future (RCP 4.5) wind data at DS2 – Interpolation based study.

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Table 5 Long term wind speeds at DS1 based on GCM interpolations. Return period (yr)

Wind speed based on past climate (m/s)

Wind speed based on projected climate (m/s)

% Increase

10 50 100

18.71 19.57 20.14

20.25 21.92 22.60

11.41 11.99 12.21

Table 6 Long term wind speeds at DS2 based on GCM interpolations. Return period (yr)

Wind speed based on past climate (m/s)

Wind speed based on projected climate (m/s)

% Increase

10 50 100

12.91 13.79 14.14

14.36 15.74 16.15

11.20 14.13 14.17

change on design and operational parameters applicable for any marine structure and can be replicated at other offshore and coastal sites. 6. Conclusions Analysis of wind speeds projected using state of the art GCM data and statistical fitting procedures at two offshore locations along the west coast of India showed that the operational and design wind corresponding to 10 and 100 years’ return may increase by around 11% to 15% due to the climate change induced by global warming. Such an increasing tendency based on a rigorous analysis with the downscaled data was further confirmed by fitting of linear trend lines to the past and projected data and studying their probability distribution function variations. Simulation of past and future wind conditions based on statistical downscaling indicated somewhat higher changes in operational and design winds than the conditions determined on the basis of GCM interpolations. The analysis involving the downscaling however can be viewed as more reliable owing to the incorporation of in-situ observations. At both locations along the west coast of India it was found that the average speed as well as fluctuations over it would increase, and further, higher wind speeds would occur more frequently. Thus the intensified long term wind conditions would be caused more by the moderate speeds and increased frequencies of the extreme winds. The trend equations derived in this study can be of help in knowing how annual mean wind speed at the two locations would vary over different years in future. The study thus points out to the necessity of increasing safety margins in the design and operation of ocean structures at specified locations in the light of global warming. The procedures and tools adopted to assess the effect of climate change have effect on the magnitude of the final outcome and hence continuous re-working of the effect is necessary as and when more accurate and latest data and analysis procedures become available. Appendix I. General Information on Climate Change Assessment For more details readers are referred to standard text books [4–7]. General Circulation Models (GCMs) The GCMs are mathematical models representing the physical process of circulations in atmosphere, ocean, and at the land interface. They are based on principles of conservation of mass, energy, momentum and solved using numerical methods. There are atmospheric, oceanic and coupled models. The GCMs have been traditionally used to simulate response of climate systems to the increasing global temperature arising out of the rise in green house gas emissions. Their outcome is in the form of climate variables such as temperature, humidity, air pressure, wind speeds and directions – all at a

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certain temporal and spatial resolution. One of the limitations of the GCMs is that they provide information over a very wide spatial grid size, typically, 200 km  200 km. Certain regional phenomena like local cloud formations may not therefore be satisfactorily represented in the original GCMs and may need approximate modeling by parameterizations. Many countries like the US, Canada, Australia, Japan have developed their own GCMs. The US based Working Group of Coupled Modeling came together under the World Climate Research Program and initiated Coupled Model Inter-comparison Project (CMIP) in 1995 to systematize the study of coupled atmospheric-ocean GCMs and improvise the same. Several climate modeling groups of the world carried this lead further and in 2008 jointly initiated a new set of climate modeling experiments called CMIP-Phase 5 (CMIP5) that was aimed at improving gaps in knowledge; for example, better accounting of model sub-components and improving decadal scale predictions, among others (http://cmip-pcmdi.llnl.gov/cmip5/index.html). CMIP5 involves four scenario runs based on future population growth, technological development, societal responses and using climate simulations with more than 50 different climate models. Scenarios and Representative Concentration Pathways (RCPs) The GCMs mentioned above are run for possible future scenarios of temperature rise due to a certain increase in greenhouse gas emissions together with world’s response to reduce such emissions. The Fourth assessment report, AR4, of Inter Governmental Panel for Climate Change (IPCC) lists six families of scenarios, namely, A1F1, A1B, A1T, A2, B1 and B2. The A2 scenario typically considers a rise in global temperature from 2  C to 5.4  C by the year: 2100 along with the highest carbon emission rate and fast population growth. The revised scenarios in the latest Fifth assessment report, AR5, are called Representative Concentration Pathways (RCPs). Four RCPs are specified as per their warming potential and societal response encapsulated into a radiative forcing to a GCM. Such forcing has peak values of 8.5 W/m2 and less by the year: 2100. Reanalysis Datasets Normally the most reliable data to use in an application would be in the form of actual in-situ observations of the required variable. However this is possible only at some sites and over short durations, owing to general expensiveness of the collection exercise. Hence observational data are many times integrated into GCM based predictions (that may have impurities like bias and spurious trends) through a suitable data assimilation technique giving rise to reanalysis data. The reanalysis data thus enhance accuracy as well as reliability of model predictions. The reanalysis data called ERA-40 of ECMWF covers a period of more than 40 years in the past; from September 1957 to August 2002. The NCEP and NCAR have similarly come up with wind records of more than 50 years: from 1948 to present. These global reanalysis products are of high quality over regions of large data availability; but could be of low quality when insufficient observations are available to correct the predictions. Appendix II. PCA, ANN and Quantile Mapping Principal component analysis This consists of first computing the covariance matrix of the normalized variables. The eigen values and eigen vectors are computed from the covariance matrix. The computed eigenvectors are orthogonal and the indices are arranged so that the first eigenvector corresponds to the largest eigen value and in general the nth eigen vector corresponded to the nth largest eigen value. The percentage of total variance explained by the nth Principal Component (PC) is given by

ln

Total variance of nth PC ¼ Pm

i ¼ 1 li

where, m ¼ number of grid points in the domain; ln ¼ nth eigen vector

(4)

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Artificial Neural Network Mathematically the four-step procedure followed in obtaining the network output is as given below: 1. Sum up weighted inputs, i.e.

Nodj ¼

NIN  X  Wij xi þ bj

(5)

i¼1

where, Nodj ¼ summation for the jth hidden node; NIN ¼ total number of input nodes; Wij ¼ connection weight ith input and jth hidden node; xi ¼ normalized input at the ith input node; and bj ¼ bias value at the jth hidden node. 2. Transform the weighted input:

i h Outj ¼ 1= 1 þ e
Nodj

(6)

where, Outj ¼ output from the jth hidden node. 3. Sum up the hidden node outputs:

Nodk ¼

NHN X

 Wjk Outj þ qk

(7)

j¼1

where, Nodk ¼ summation for the kth output node; NHN ¼ total number of hidden nodes; Wjk ¼ connection weight between the jth hidden and kth output node; and qk ¼ bias at the kth output node. 4. Transform the weighted sum:

i h Outk ¼ 1= 1 þ e
Nodj

(8)

where, Outk ¼ output at the kth output node. The objective of any training is to reduce the global error, E; defined below:

E ¼

P 1X Ep P 1

(9)

where P is the total number of training patterns. Ep is given by

Ep ¼

N 1 X ðOk
tk Þ2 2

(10)

k¼1

where N is the total number of output nodes, Ok is network output at the k-th output; node, and tk is target output at the k-th output node. Quantile Mapping The procedure to perform quantile mapping given 3 datasets: ‘a’, ‘b’ and ‘c’ is as follows: Typically let ‘a’ represent relatively accurate NCEP/NCAR, ‘b’ denote CGCM-20C3M and ‘c’ indicate CGCM-CMIP-5 datasets.

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(i) Establish theoretical cumulative distribution function (CDF), say of Weibull type, for datasets: a and b. (ii) Replace/overlap the CDF (values) of b with that of a removing bias in b. (iii) Derive CDF of c and subtract these CDF (values) from those of CDF of b, generating ‘shift’ representing effect of climate change. (iv) Overlap the values of CDF of c and CDF of a and add the above shift to the overlapped values. Note that generation of the shift and adding it to the overlapped values is necessary only when the time of realization of b and c are not same (as in case of the later exercise of GCM-CGCM-CMIP-5 but not in the former exercise of CGCM-20C3M).

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