This document details the step-by-step revised methodology for ingesting the seasonal forecast in Fuel Consumption Model (FCM). Previously we already had climatology and anomaly data prepared by B-Open, but in this revised methodology, we have to compute the anomaly for forecast of 2019 using hindcast of (1993-2016) ourselves before ingesting in FCM along with the climatology already computed by BOpen. The steps are outlined below (following guidelines given by CNR and B-Open).
1. We have two main datasets, Hindcast / Forecast and Reanalysis
a. Forecast/ Hindcast data is daily forecast for first seven months (i.e. Jan to July) with 25 ensemble members (i.e. realization) of each year (1996-2015); forecast of 2019 has 51 ensemble members.
b. Reanalysis data is also daily observations but for 12 months of each year (1993-2017)
2. Data processing procedure:
a. Anomaly computation:
• Monthly mean is computed for both, forecast of 2019 anjd Hindcast (1996-2011) data. The reason of selecting this time range for Hindcast monthly climatology is mentioned in RPS computation section. Output, forecast (time: 7 months, realizations: 51), Hindcast (time: 7 months, realizations:25)
• Hindcast climatology for u and v are subtracted from u and v of forecast, which results in u and v anomaly of 2019. Subtract function of CDSTools library is used for this operation which also handles the different no. of realizations of both datasets automatically (51 and 25 realizations for forecast and Hindcast respectively); results were verified manually. Output:
anomaly (time: 7 months, realization: 25)
(anom = monthly_mean(for) – monthly_mean(hind)
Fig. 1: Near Surface Wind anomalies computed for the month of January using 2019 forecast. Left panel shows the northward wind anomaly for Jan., 2019 and right panel shows the eastward wind anomaly for Jan., 2019.
b. Anomaly Calibration (Absolute values computation):
• Anomalies computed above are calibrated by adding the monthly climatology (already computed by B-Open for the time range of 1979-2017). Output: time: 7 months, realization:25
seas = anom + monthly_climatology
Fig. 2: Near Surface Wind absolute values (calibrated anomalies) values computed for the month of January using 2019 forecast. Left panel shows the eastward absolute wind for Jan., 2019 and right panel shows the northward absolute wind for Jan., 2019.
c. Shaft Power Climatology
• For Shaft power climatology, climatology of uas, vas, swh, pp1d, mwd, and currents are used. B-Open have already shared climatology of these variables which have been used for this process.
d. Shaft Power Seasonal
• For Shaft power seasonal data, calibrated wind anomalies (absolute values) of 2019 have been used, which have time and realization dimensions. As we need to compute Shaft power on monthly basis instead of realization, so mean over the realizations (25 ensemble members) has been taken for each month before computing the shaft power. For rest of the required variables, climatology values are used.
Note: Mean is taken over the realizations for each month and then shaft power is calculated over this mean. An alternate approach could have been to calculate shaft power over each of the 25 realizations, and then take mean of that shaft power set of values. However, this alternate procedure is not consistently feasible for the set of operational indicators, e.g. it does not make sense to calculate 25 realizations of the optimized route with seasonal data, and then take their mean.
Fig. 3: Comparison of shaft power computed on seasonal forecast and Reanalysis climatology of wind. Left panel shows shaft power computed for the month of January and right panel shows shaft power computed for the month of June. The difference in behavior can be seen between both months
SKILL CALCULATION FOR FCM USING HINDCAST DATA – ASSESSMENT OF RANKED PROBABILITY SKILL
(RPS) AND RANKED PROBABILITY SKILL SCORE (RPSS)
Given below are steps to calculate the skill of FCM while utilizing Hindcast and Reanalysis data for the period 1996-2011 (suggested is 1993-2016); the Ranked Probability Skill (RPS) and Ranked Probability Skill
Score (RPSS) statistical parameters are being used for skill calculation (as recommended by CNR in D2.4.2).
RPS Computation
- For each month of Hindcast, compute shaft power using Hindcast of wind for the time span of 1996-2011, and climatology of swh, pp1d, mwd (climatology from Reanalysis) and currents for the standard route. Output, obs (way points of the route):11, time:7 x years, realization:25 Note: While processing the Hindcast shaft power, it has been found that vas component data (2012-14) has some issue with time information stored in dataset. Year mentioned in file name is not matching to the time information provided with the actual data stored in respective files. This could be handled by replacing time of affected files by time of the u component files so that process can be completed. Vas component of 2016 is also missing from FTP folder. After discussion with B-Open, it has come to light that vas component for 2014 was also missing but created by replacing the name of another file. So processing for skill assessment and seasonal forecast ingestion process is limited to 1996-2011.
- Compute shaft power for Reanalysis data for wind from reanalysis and pp1d, swh, mwd, currents from climatology. Wind data from reanalysis will selected for the same time range used for Hindcast. Output, obs:11, time:12 x No. of Years.
- Add frequency variable to insert the "day of the year" using date information already available in both datasets. Output, dayofyear coordinate is inserted. See the highlighted text in the figure below as an example.
- Compute quantiles for fuel_cons_hind (on time and realization dimension) and fuel_cons_rean (on time dimension) using quantile frequency function available in seasonal.py provided by BOpen. Output, Obs: 11, quantiles for each month of the Year.
- Compute cumulative probability and categories using tercile_cum_prob function for both Hindcast and Reanalysis data. Output, Obs:11, 3 categories for both datasets, forecast (time:7 x No. of Years, realization:25) and Reanalysis (time:12 x No. of Years)
Fig. 4: Cumulative probabilities graph for all three categories of Hindcast and Reanalysis data of January. Left column of grid is showing cumulative probability of Hindcast and Right is showing cumulative probability of Reanalysis data. Probabilities for both datasets will vary along time. This figure does not represent results, but is just a combination of plots to check the correct functioning of the method.
7. Compute Annual RPS by taking the sum of the square of difference between cumulative probabilities of Hindcast and Reanalysis. Output, annual RPS value for first seven months of each year (e.g. Jan. 1996, … Jan. 2011, Feb. 1996, … Feb. 2011, …. …, Jul. 1996 … July 2011) at each way point (obs: 11).
8. Compute overall average RPS over the Hindcast data for each month (i.e. mean RPS for Jan, Feb, and so on for (1996-2011). Output, obs:11, RPS of 7 months.
Fig. 4: Ranked Probability Skill (RPS) computed using Hindcast and Reanalysis data for time span of 1997-2011. Left: Showing RPS of January and Right: showing RPS for June.
RPS_clim
- Compute Shaft power for climatology after computing the climatology of Reanalysis data of same time span 1996-2011.
- Add frequency variable to insert the 'day of year' in Reanalysis shaft power output. (as performed for shaft power Hindcast and shaft power Reanalysis in RPS Section).
- Compute quantiles for shaft power Reanalysis (on time dimension) using quantile frequency function available in seasonal.py provided by B-Open.
- Compute cumulative probability and categories using tercile_cum_prob function for both climatology and Reanalysis data. Graphs were plotted for both datasets (climatology and Reanalysis) to see how the graphs appear, just for verification. Output, Obs:11, categories:3 for both datasets, time: 12 x No. of Years.
- Compute Annual RPS by taking the sum of the square of difference between cumulative probabilities of climatology and Reanalysis. Output, Obs:11, annual RPS value for 12 months of each year (e.g. Jan. 1996, … Jan. 2011, Feb. 1996, … Feb. 2011, …. …, Dec. 1996 … Dec 2011).
- Compute overall average RPS over the climatology data for each month (i.e. mean RPS for Jan, Feb, and so on for (1996-2011). Output, Obs:11, months: 12.
Fig. 5: This is the graph of Ranked Probability Skill (RPS) computed using climatology of 1970-2017 and Reanalysis of 1997-2011. Left: Showing RPS_clim of January and Right: showing RPS_clim for June.
RPSS
1. Use the following equation to compute RPSS. Output, Obs:11, months:7.
\[ RPSS = 1 - \frac{\overline{RPS}}{\overline{RPS\_clim}} \]
Fig. 6: Graphs are representing RPSS computed against climatology and Reanalysis data for all seven months. Months are mentioned in legend and caption of each graph.
Note: Skill score is computed using shaft power results from Hindcast, Reanalysis and climatology data which results in RPSS on each way point. Same method can be applied on fuel consumption output of said datasets which will result in cumulative skill score along the route. Cumulative skill score can be generated by integrating the shaft power along the route.
Results for Different Routes
RPS, RPS_clim and RPSS results are presented here for the routes suggested by Jorgen. There were 20 routes, 8 of them are selected to perform RPS, RPS_Clim and RPSS to compare and analyze results by the team, whereas rest of the routes were eliminated because of two reasons, 1st is, unavailability of routes in standard route folder of BOPen and 2nd is, routes are covering more region than hindcast coverage e.g. route covering the region of Pacific and Atlantic Oceans.
Missing values in the following graphs indicating that routes are not overlaying to hindcast data.
Results are presented for the month of Jan and June to see the variations in winter and summer.
1.Bishop Rock to Panama
2. Panama to Bishop Rock
3. New York to Cape of Good Hope
4. Cape of Good Hope to New York
5. Cape of Good Hope to Sunda Strait
6. Sunda Strait to Cape of Good Hope
7. Cape of Good Hope to Bombay
8. Bombay to Cape of Good Hope
