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Iceberg Drift Forecasting Using Machine Learning


Abstract and Figures

A machine learning approach has been developed to improve iceberg drift forecasting on a tactical timescale to mitigate potential impacts between icebergs and offshore facilities in the North Atlantic. The problem of iceberg forecasting involves many uncertain terms. Although iceberg drift trajectories can be measured with sufficient accuracy, the iceberg shapes are generally unknown. Moreover, the corresponding metocean forecasts, in particular ocean current forecasts, carry their own uncertainties. The forecasting error for this highly uncertain drift process can be minimized using a hybrid approach that calculates Coriolis acceleration explicitly and estimates combined hydrodynamic and wind drag accelerations using machine learning. The latter is an implementation of gradient boosted trees algorithm that predicts and integrates the unknown accelerations. The training dataset consists of iceberg GPS tracks obtained during 2019 iceberg data collection campaign offshore Labrador. The trained model is cross-validated using the k-folds approach. The evolution of the average error between the observed and forecast tracks is used as the measure of performance. The resulting error curve is promising and can be improved even further if more, and more accurate in-situ data are collected. The trained model can be used operationally, together with conventional dynamic approach, as an additional source of information in order to determine an adequate response to iceberg threat.
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Iceberg Drift Forecasting Using Machine Learning
Renat Yulmetov1
1C-CORE, St. John’s, Newfoundland and Labrador, Canada
A machine learning approach has been developed to improve iceberg drift forecasting on a
tactical timescale to mitigate potential impacts between icebergs and offshore facilities in the
North Atlantic. The problem of iceberg forecasting involves many uncertain terms. Although
iceberg drift trajectories can be measured with sufficient accuracy, the iceberg shapes are
generally unknown. Moreover, the corresponding metocean forecasts, in particular ocean
current forecasts, carry their own uncertainties. The forecasting error for this highly uncertain
drift process can be minimized using a hybrid approach that calculates Coriolis acceleration
explicitly and estimates combined hydrodynamic and wind drag accelerations using machine
learning. The latter is an implementation of gradient boosted trees algorithm that predicts and
integrates the unknown accelerations. The training dataset consists of iceberg GPS tracks
obtained during 2019 iceberg data collection campaign offshore Labrador. The trained model
is cross-validated using the k-folds approach. The evolution of the average error between the
observed and forecast tracks is used as the measure of performance. The resulting error curve
is promising and can be improved even further if more, and more accurate in-situ data are
collected. The trained model can be used operationally, together with conventional dynamic
approach, as an additional source of information in order to determine an adequate response to
iceberg threat.
KEYWORDS: Icebergs, machine learning, forecasting, Newfoundland, iceberg management
The 2019 iceberg season was busy for the offshore industry and tourism in Newfoundland, with
1515 reported icebergs crossing 48° latitude (International Ice Patrol, 2019). Based on previous
years’ statistics, the 2019 iceberg season severity was characterized as “extreme”. The oil and
gas industry relied on extensive iceberg management operations near offshore facilities on the
Grand Banks.
Iceberg management operations on the Grand Banks usually include, but are not limited to,
iceberg surveillance, tracking and drift forecasting. Surveillance is performed by means of
reconnaissance flights, satellite imagery analysis and on-site vessel observations. The tracking
is done from the radar-equipped vessels and offshore facilities, however, GPS tracking may be
involved in special cases. The iceberg tracks are usually logged in a table containing
information on iceberg locations, size, towing attempts, and associated weather conditions.
Operational drift forecasting for the observed icebergs is carried out using International Ice
Patrol (IIP) and Canadian Ice Service (CIS) drift models (Murphy and Carrieres, 2010). One is
usually better at estimating distance and the other at estimating direction of iceberg drift tracks.
These models use large-scale gridded ocean and atmosphere circulation products for wind and
current input data. The input data carry high level of uncertainty, yet they are often the only
Proceedings of the 26th International Conference on
Port and Ocean Engineering under Arctic Conditions
June 14-18, 2021, Moscow, Russia
source of data, because local Acoustic Doppler Current Profiler (ADCP) or other local
metocean measurements are unavailable.
Several models have been recently developed to deal with these uncertain metocean inputs and
to generally advance short-term iceberg drift forecasting. Some of the approaches are based on
the use of inferred currents (Turnbull et al., 2015), ocean current statistics (Andersson et al.,
2019), state-estimation and filtering (Andersson et al., 2016), and machine learning (Yulmetov
and Ralph, 2019).
The initial attempt to apply machine learning (ML) to iceberg drift prediction was based on a
neural network (NN) approach (Yulmetov and Ralph, 2019). It was a purely statistical model
that predicted new iceberg velocities using observed iceberg velocities and additional metocean
inputs. The NN approach is prone to input normalization issues, and is inferior in performance
to modern ML regression algorithms.
This study presents the next generation of the approach undertaken in Yulmetov and Ralph
(2019). The major improvements are: implementation of gradient-boosted trees instead of NN,
and a hybrid approach instead of a “black box” model. In addition, the model is trained on new
GPS iceberg tracks collected during an iceberg tagging campaign off the coast of Labrador in
2019 (Briggs et al., 2020).
The paper starts with a short description of the approach and the setup of the forecasting model.
It is followed by the input data description. The forecasting performance is presented in the
next section and discussed afterwards. A short conclusion is given in the final section.
Iceberg drift prediction can be approached using dynamics-based models that integrate the
equation of motion for an iceberg, or using statistical models that fit the iceberg motion based
on local currents, winds and waves. There are several hybrid models that are able to deal with
uncertain inputs statistically while still relying on the equation of motion to ensure physical
validity. The resulting performance for those models tend to be superior (Andersson et al.,
A hybrid model is presented here. The drift model predicts uncertain drag accelerations using
ML while the Coriolis acceleration is calculated accurately using iceberg location and velocity
according to:
  
 
 
 
 
is iceberg velocity, is Coriolis parameter,
is an outward unit normal vector to the
Earth surface, is acceleration caused by hydrodynamic force acting from water and air drag,
is wind velocity, and
is ocean current velocity. The ML part of the model uses observed
iceberg velocities, predicted wind velocity and predicted ocean current velocity to predict the
combined hydrodynamic and wind drag acceleration.
Machine learning is a term that covers a wide range of algorithms and methods aiming to
classify, regress, predict, or analyze data. An approach called supervised learning is used in this
model. In supervised learning a function that maps a set of inputs onto the set of outputs is
determined based on the known data. For each known input/output pair the function predicts
the output and is adjusted depending on the error metric between the known and predicted
outputs. This adjustment process is called “training”. In this case the model is trained to predict
the unknown acceleration based on iceberg velocity, wind velocity and ocean velocity. A
sufficient amount of accurate data is the key to ML performance.
Neural networks were used in the first generation of the drift model, but generally better-
performing algorithms were discovered. The gradient boosting (GB) technique was chosen
based on better performance for general regression problems and a lack of normalization issues
to which NNs are prone. In GB the algorithm combines multiple decision trees, improving
prediction. The original work combining multiple regression trees into an optimal regression
function was published by Friedman (2001). An open-source implementation called Catboost
was used here (Prokhorenkova et al., 2018). It supports GPU architecture, has a wide range of
optimization parameters and tools to perform cross-validation routines.
Depending on the discretization of (1), two mathematical formulations were implemented. An
explicit form can be written as:
  
 
 
  
  
 
where the upper index denotes the time step, and the lower index denotes the projection. In the
training process the model is trained to estimate the acceleration projections 
 
known iceberg velocities at time steps (    , wind velocity at time step and ocean
current velocity at time step . In the actual prediction process, the algorithm calculates the
unknown acceleration using the trained model, and then finds an unknown position of the
iceberg at time step   .
The implicit form can be written as:
  
 
 
  
  
 
  
  
In the implicit case the training and prediction processes require wind velocity and ocean
current velocities at time step   , instead of as in the explicit case.
Thus, a total of eight inputs are required at each time step to make a prediction: two velocity
vectors, wind velocity, and ocean current velocity, each having two projections. The model is
currently trained to make single-step predictions and integrate multiple single-step predictions
iteratively. The drift forecast duration does not exceed the tactical timescale, which is 24 hours
long in this study.
The iceberg GPS tracks were collected during a tagging campaign offshore Newfoundland and
Labrador in 2019. Unmanned Aerial Vehicles (UAVs) were used to deliver the GPS trackers
from the vessel to the icebergs (Briggs et al., 2020). Each of the trackers consisted of a GPS
unit attached to a rubber mat with toothed metal plates. This maximized friction, preventing
the trackers from sliding down the icy surface when placed on a slope or as it tilts during a
partial iceberg roll.
After the UAV with the payload reached an iceberg, the deployment process consisted of two
stages in which the tracker would be first released free-hanging on a short tether, and then it
would be released completely when the tracker was suitably positioned on an iceberg. The two-
stage release was developed to avoid risks of crashing associated with the UAV’s landing and
to provide the sense of depth to the pilot because of the bright white iceberg surface.
Figure 1. Iceberg drift tracks used for the model training
The trackers were set to transmit the GPS location every 30 minutes. At total of 119 GPS
trackers were deployed, however many of the trackers got lost within just a few hours, because
of waves washing over some of the smaller icebergs and frequent iceberg rolling over in warm
weather. Multiple icebergs were excluded from consideration because they were grounded or
scouring, which would affect the training of the model. Finally only 77 iceberg tracks were left,
and used for the model training (Figure 1). The average track duration was approximately 2
days, while the longest track lasted more than two weeks.
It is worth noting that the icebergs were profiled using multibeam echosounder for keels, and
laser scanner for sails (Bruce et al., 2021). The majority of the icebergs that were tagged can
be classified as small/medium size, however, there were a few larger tabular icebergs. The
smallest iceberg was less than 30 m waterline length, while the largest was longer than 300 m.
The wind data were taken from the CFSv2 operational analysis (Saha et al., 2014), which is a
gridded global-scale circulation model. Its spatial resolution is 0.2°, and its temporal resolution
is one hour. The ocean current data were taken from HYCOM (Chassignet et al., 2007), which
is a gridded global-scale ocean model. It has 0.08° spatial resolution, 32 vertical layers in the
water column and three-hourly temporal resolution. The ocean currents were averaged for the
top 50 m, which was characteristic of the tracked icebergs’ keel depth. The gridded metocean
data have been linearly interpolated over the iceberg trajectories (Figure 2).
Figure 2. An example of iceberg velocity and corresponding wind velocity and 50m-average
ocean current velocity
Large scale gridded models are generally considered insufficiently accurate for reliable iceberg
drift modelling, however those are often the only data sources available. Current operational
models are using gridded metocean products as inputs. Local current profiles are required for
accurate drift hindcasts, and it is expected that real-time access to ADCP and weather station
data would help to correct the gridded products, and thus deliver more accurate drift forecasts.
The model has been used to forecast every 24 hour trajectory span starting every hour of drift
data for each of the icebergs in the database. Shorter forecasts were issued where remaining
measured track duration was shorter than 24 hours. An example of measured and predicted
iceberg tracks is shown in Figure 3a. The corresponding drift velocity and metocean data are
shown in Figure 2. It can be seen that in the first 12 hours, the predicted iceberg drifted with
approximately same speed, but then it slowed down significantly, while the real iceberg
accelerated northwest. An increasing eastward ocean current component provided by HYCOM
model likely decelerated the forecasted iceberg.
The forecasting error is characterized by the evolution of distance between actual and predicted
iceberg locations in time for a single forecast. A more accurate forecast would result in lower
error curve. The corresponding forecast error curve for this particular example is shown in
Figure 3b. The error stayed below 3 km in the first 12 hours, while the forecasted iceberg was
able to catch up. But then the error jumped up to 12 km in 24 hours, when the forecasted iceberg
Figure 3. a) An example of observed and predicted iceberg tracks; b) the corresponding
forecast error.
Error curves averaged between all of the available forecasts indicate model performance. The
average forecasting error curve for the explicit model given by equation (2) trained using the
whole dataset shows approximately 11.2 km error at 24 hours of forecast (Figure 4). The
corresponding standard deviation is 7.2 km. The 24 hour error for the implicit model is
10.1±6.6 km. For the implicit implementation the minimal 24 hour forecast error achieved is
79 m, the worst forecast has been 35.6 km off. These numbers, however, are biased because of
the same data used for training and testing the forecasting performance.
Figure 4. Average error curves compared for various iceberg drift forecasting models.
K-folds cross-validation is a statistical method that allows to estimate model performance on
new ‘unfamiliar’ data. In the k-folds cross-validation, the data is divided into k blocks of equal
size. By iterating over the blocks, the model is trained using the corresponding remaining k-1
blocks, and its performance is measured using that ‘unfamiliar’ k-th block. The average
performance calculated between the k blocks can be considered a more accurate estimate of
expected model performance, than pure training performance. The cross-validated implicit
model’s average error is about 11.5±7.3 km error at 24 hours.
It is hard to compare various models’ performance on different data sources because, although
iceberg tracks can be measured with rather consistent accuracy, the metocean input data
accuracy varies. Figure 4 compares average error curves calculated for various drift models.
The operational IIP/CIS models deliver more than 17 km of error at 24 hours on the Grand
Banks (Murphy and Carrieres, 2010). A purely statistical drift model with ocean currents
predicted using vector-autoregression achieves less than 10 km error (Andersson et al., 2019).
The inferred current approach applied to 18 profiled icebergs offshore Labrador resulted in 13
km average error (Turnbull et al., 2018). Based on historical data from Labrador exploratory
drilling sites in 1980s, the currents and winds measured locally provided more accurate drift
forecasts (Yulmetov and Ralph, 2019). Due to this local data it was possible to achieve less
than 9 km error at 24 hours using the previous generation of the ML model.
This model offers competitive performance, achieving 10.1 km error when using full dataset
for training and about 11.5 km error when cross-validated. The model uses only iceberg
velocities, gridded winds and currents and no additional information on size and shape so far.
It should be noted that the performance for all of the studies mentioned above was determined
using different sets of iceberg tracks. Nevertheless, accurate data is the key to ML model
performance. It is expected that a real-time stream of accurate local metocean data will
significantly improve the reliability for iceberg management applications.
It is possible to further expand the model and formulate it using iceberg velocity relatively
water to include water accelerations into account. As seen in Figure 2, the water accelerations
are on the order of iceberg accelerations and will contribute in the form of the Froude-Krylov
hydrodynamic force (Turnbull et al., 2015, Marchenko et al, 2019). In this case equations (2)
and (3) will include an additional term related to water acceleration that will be determined
from the ocean current forecast data.
In addition to the metocean inputs, size and shape information can be used in the ML part of
the model. The 2019 dataset contained accurate information on size (measured by laser scanner
and multibeam), and the iceberg waterline length will be used in the next generation of the
model. The shape, however, has been hard to characterize. There have always been long
discussions and disagreements whether a particular iceberg is wedged or blocky, pinnacled or
dry dock. It is simply hard to describe the above water shape of and iceberg in one word.
The approach to forecasting performance metrics is nor trivial either. The forecasting error
measured as distance between the forecasted and actual iceberg positions is not always a fair
measure. For example, faster icebergs cover larger distances, and the corresponding forecasting
error might become larger as a result. At the same time, the forecast usually predicts the
direction for faster icebergs much better than for slower drifting icebergs. To tackle this effect,
the forecasting error may be considered in relation to the distance traveled by the iceberg,
similar to the relative performance index used by Andersson et al. (2018). But minimizing the
average relative performance index will result in non-optimal forecasting error. Thus, the
choice of the performance metric is determined by the priority for the forecast: more accurate
drift direction or more accurate drift distance.
The model can be reformulated for longer-term forecasting too. It is expected that the
RADARSAT Constellation Mission (RCM) will provide consistent twice-daily coverage of the
region of interest. There is possibility to constantly track icebergs and generate a significant
amount of data using automated satellite imagery analysis. A large number of iceberg tracks is
a perfect case for ML application, even though those tracks are of low temporal resolution.
Twelve hour resolution iceberg tracks are not able to capture the higher-frequency iceberg
dynamics, but may be well correlated with lower-resolution circulation model inputs. Machine
learning applied to satellite data may be used for longer-term forecasts exceeding short-term
tactical scale and setting a bridge to upstream and seasonal forecasting time-scales.
Finally, the next step in the ML model development is reprogramming it into the form that will
use the integral of the multi-step forecasting error during training instead of the single-step
error. It is expected that it will significantly improve the model performance. Additional
improvements will be the introduction of iceberg size to the training database, and further
expansion of the training database via data collection and assimilation.
This study presents the next generation of ML iceberg drift model. The model is a hybrid that
predicts combined acceleration caused by hydrodynamic force and wind drag based on iceberg
velocities and metocean inputs from large-scale circulation models. A gradient-boosted trees
implementation was used in the ML part of the model. The model was trained and tested using
new iceberg track data collected during an iceberg tagging program offshore Labrador in 2019.
The training performance of the implicit implementation is 10.1±6.6 km of forecasting error in
24 hours. The cross-validated performance is 11.5±7.3 km of error for the same forecasting
period. This is significantly lower than the average error level of the models that are currently
operational for the Grand Banks (e.g. Murphy and Carrieres (2010) curve in Figure 4).
The model requires minimal data and no additional optimization once trained. This makes it a
perfect candidate for operational applications. The model can be further developed in a number
of ways including the addition of iceberg size information to the training data, switching to the
multi-step cost function, and extending the forecast duration using satellite data products for
training. Obviously, the model will benefit from expansion of the training database through
data collection. Simultaneous measurements of drift tracks and local metocean data would be
the most valuable.
The author is grateful to the United States Department of Homeland Security Office of Science
and Technology under an Interagency Agreement with the United States Army Combat
Capabilities Development Command C5ISR Center NVESD for permission to use the data.
Additional thanks to current and former colleagues at C-CORE for supporting this work during
all stages, from data collection to internal review.
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Short-term iceberg drift prediction is challenging. Large uncertainties in the driving forces – current, wind and waves – usually prevent accurate forecasts. Recently several statistical iceberg forecast models have been proposed by the authors, which use iceberg position measurements to improve the short-term drift forecast. In this article these statistical forecast methods and models are briefly reviewed. An extensive comparison between the statistical models, in addition to a dynamic iceberg forecast model, is performed on several iceberg drift trajectories. Based on this comparison a new statistical forecast scheme is proposed that combines some of the advantages of the other methods.
Iceberg drift forecasting is challenging. Large uncertainties in iceberg geometry and in iceberg driving forces – current, wind and waves – make accurate forecasts difficult. In this work, a new estimation-forecast scheme is proposed that improves iceberg drift forecasts by using past iceberg drift information to reduce uncertainties. Which of the most uncertain parameters to adjust in order to reduce uncertainties, is guided by simple criteria that are introduced and explained. These criteria are applied to different iceberg drift estimation models and a new parameter estimation process is proposed and implemented in the form of a moving horizon estimator. Different performance indices are introduced to evaluate estimation and forecast performance of the proposed set-up. The set-up is tested in a case study on two iceberg drift trajectories surveyed during a research expedition offshore Newfoundland in 2015. The results indicate that the quality of iceberg drift forecasts improve significantly for short-term forecasts, whereas the improvements are smaller for longer forecasts. Moreover, it is demonstrated that the proposed set-up is superior to solutions based on adjustments of the drag coefficients.
Function estimation/approximation is viewed from the perspective of numerical optimization iti function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent "boosting" paradigm is developed for additive expansions based on any fitting criterion. Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for interpreting such "TreeBoost" models are presented. Gradient boosting of regression trees produces competitives highly robust, interpretable procedures for both regression and classification, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire and Friedman, Hastie and Tibshirani are discussed.
An operational iceberg drift forecast model was developed and used in 2012 to support Shell Greenland A/S, which was leading a consortium of companies to conduct a scientific coring campaign offshore northwest Greenland. The nine-week program took place in August–October 2012 in Melville Bay where there is a very high spatial density of icebergs. In order to increase operational safety and efficiency, the iceberg drift model presented here was fully integrated within the ice management strategy and its decision protocols. The model was optimized to fulfill the operational requirements in terms of (1) the format and content of the input/output, (2) the calculation of the iceberg alert zones, and (3) the derivation of the associated Closest Point of Approach (CPA) and time to CPA (T-CPA). To achieve this, the iceberg drift forecast model used as near real-time input: in-situ measured metocean parameters, observed iceberg drift and size data, tidal currents, and weather forecasts. The model forecast the 24-hour iceberg drift trajectory including the CPA and T-CPA. It also derived the T-Time (e.g., Total Time, or the time necessary to lift the coring pipe to 50 m below the seabed) alert zones based on the observed mean iceberg drift speed. The iceberg trajectory forecast was optimized by running a hindcast simulation of the observed iceberg trajectory. In this simulation, the air and water iceberg form drag coefficients were tuned to minimize the difference between the hindcast and the observed iceberg drift trajectories. The forecast iceberg track, beginning at the end of the observed iceberg record, was subsequently generated using the air and water form drag coefficients derived from the hindcast simulation. The model also incorporated a method to correct for the lack of robust near real-time in-situ ocean current measurements. During this campaign, the model was used to forecast the drift of 73 icebergs and exhibited good performances in locations with strong and persistent non-tidal currents. However, further offshore where the ocean currents were dominated by tidal and inertial forcings, the model exhibited poorer performance. Nevertheless, as shown for two icebergs in this paper whose drift was dominated by tidal and inertial oscillations, model performance could be significantly improved in the hindcast mode by using the vessel's wind data and the ocean current data retrieved from a mooring deployed in the area. This illustrated the importance of using adequate near real-time ocean current and wind measured and forecast input data.