# Detailed Lacustrine Calving Iceberg Inventory from Very High Resolution Optical Imagery and Object-Based Image Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}where many icebergs were missed. A section of the lagoon with ice melange was not reliably mapped due to uniformity of the area in the imagery and DEM. The precision of the DEM limited the scaling effort to icebergs taller than 1.7 m and larger than 99 m

^{2}, despite the inventory containing icebergs as small as 4 m

^{2}. The work demonstrates viability of object-based analysis for lacustrine iceberg detection and shows that the statistical properties of iceberg population at San Quintín glacier match those of populations produced by tidewater glaciers.

## 1. Introduction

## 2. Study Area

^{2}and has an extensive tongue that forms much of the ablation area of the icefield [26].

^{2}between 1979 and 2013 together with the glacier’s retreat of 4.5 km [30]. The lagoon into which the glacier terminates is surrounded by push moraines created during the glacier’s advance in the second half of the 20th century [27]. The lake is drained to the Pacific Ocean by a narrow, meandering stream which prevents iceberg evacuation. Consequently, icebergs calved off San Quintín’s snout have no means of escaping the lagoon and remain in the lake for their entire life cycle. Melting of sediment-laden icebergs and influx of meltwater drive large amounts of sediment to the lagoon changing the water’s color. The terminal lagoon of San Quintín increased in area between 1947 and 2011 and is the largest of the proglacial lagoons surrounding NPI [4]. In such environment, OBIA promises better classification results than a pixel-based study thanks to its ability to classify objects by analyzing features other than just spectral response in four bands. The dirty icebergs blend with the dirty water, but they differ from water with their elevation, image texture or contrast between pixels, properties which can only be analyzed within groups of pixels.

## 3. Data and Methods

#### 3.1. Datasets Used and Imagery Preprocessing

#### 3.2. DEM Preprocessing

_{0}where all ${Z}_{rel}<0$ values are replaced by 0.

#### 3.3. DEM Uncertainty Assessment

#### 3.4. Iceberg Map Creation

^{2}were cut. The division workflow starts with a conversion of the iceberg vector polygon to a binary raster image where the value of “1” corresponds to iceberg presence and “0” to iceberg absence. With morphological erosion, thin “isthmuses” between icebergs were deleted, leading to disconnection of iceberg kernels. The watershed algorithm filled the space between the kernels, leaving pixel-lines in places where contours of recreated iceberg polygons met. These lines were vectorized and used to cut the initial vector iceberg polygon, dividing a shape of connected icebergs into several smaller polygons.

^{3}) is the iceberg’s entire (under- and overwater) volume, $\mu {Z}_{rel}$ (m) is the mean elevation above the water table and S (m

^{2})—the surface area of the waterline cross-section. We assumed ice density ${\rho}_{i}=900$ kg m

^{−3}and water density ${\rho}_{w}=1000$ kg m

^{−3}, as the lagoon is filled with fresh water. This amounts to an assumption that 90% of iceberg volume is submerged.

#### 3.5. Iceberg Map Uncertainty Assessment

#### 3.6. Data Filtering

- We used k-nearest neighbors (knn) clustering algorithm to discard outlying data points. All items which had fewer than four neighbors within radius of 0.2 in the log area–log volume space were considered outliers.
- All icebergs with $\mu {Z}_{rel}<{\sigma}_{DEM}$ were discarded. We assumed objects to be unreliable when their elevation measurements are below the precision of the DREM.
- We filtered out icebergs which were unrealistically high with respect to their width. We used a formula proposed in [48] (Equation (6)) for the critical width/height ratio at which an iceberg capsizes. We assumed that any iceberg with width/height below the critical ratio should capsize and thus the elevation measurement is not realistic.$${\u03f5}_{c}=\sqrt{6\xb7\frac{{\rho}_{i}}{{\rho}_{w}}(1-\frac{{\rho}_{i}}{{\rho}_{w}})}$$

_{var}) in this signal by dividing the signal into two parts at many candidate points and choosing the one at which the sum of deviations from the mean within each section is minimal.

#### 3.7. Area and Volume Distribution

^{2}(corresponding to 1 pixel on the 2 m/pixel DEM, smallest available size). We assessed the quality of fit of the curves with Kolmogorov–Smirnov (K-S) measure provided by the power law [49]. In addition, normal distribution curves were fitted to histograms of logarithm of area and volume of filtered dataset with the least squares method in MATLAB. Only icebergs larger than 1 m

^{2}were used for the fitting effort.

#### 3.8. Area–Volume Scaling

_{0}. We fitted power law model to the entire unfiltered inventory, to the unfiltered sections on the two sides of the V

_{var}threshold and to the fully filtered dataset. In addition, a linear model was fitted to the log area–log volume filtered data. The fits were performed with non-linear least squares method in case of power law fitting and linear least squares for log-log model fitting. We used two measures to assess the quality of fitted models:

- ${R}^{2}$ of the fit; and
- $C{V}_{10f}$—the product of k-fold cross-validation (CV) of a model. We divided the area–volume dataset into 10 subsets (folds) and performed the fitting with 9 subsets leaving one of them out for verification. ${R}^{2}$ of the volumes computed with the fitted line vs. the measured volumes was computed at each of the repetitions and the mean of these ${R}^{2}$s is reported as $C{V}_{10f}$.

## 4. Results

#### 4.1. DEM Accuracy Assessment

#### 4.2. Dataset and Filtering

^{2}of area with just around 24% of cases outside these bounds. The largest icebergs ($S>{10}^{4}$ m

^{2}) contribute only under 1% of the unfiltered dataset.

#### 4.3. Classification Accuracy Assessment

^{2}range. This is the size band in which the majority (247) of false negatives are found. A sizeable group of undetected icebergs (151) is also present among the smallest growlers (0–5 m

^{2}). These two groups account for the underestimation of iceberg count in these bands on the histogram. The remaining 96 false positives are all below 300 m

^{2}.

#### 4.4. Area and Volume Distribution

_{0}-based data where the ${R}^{2}$ of the Gaussian distribution fitted to the area and volume histogram are $0.87$ and $0.77$.

#### 4.5. Area–Volume Scaling

_{0}distorts the log-normality of the volume distribution by introducing to the population a large number of small icebergs. This is manifested by a slightly lower ${R}^{2}$ of the Gaussian distribution fitted to the histogram of the modified volumes and over-representation of low-volume cases. (compare Figure 13 and Figure 14). The number of icebergs with $\mu {Z}_{rel}=0$ is also higher when the modified DREM is used, showing large population of icebergs which did not contain any positive DREM values within their outlines. On the other hand, the population of $\mu {Z}_{rel}>0$ icebergs (green box plots in Figure 13 and Figure 14) has also increased, hinting at presence of cases where the negative values over-weighed positives on DREM, but the positive values shifted the mean above 0 in DREM

_{0}. Apparently, certain number of such individuals is found even in the filtered dataset, among the fairly large ($S>99$ m

^{2}) icebergs, as evidenced by lowering of median iceberg area in the filtered dataset used for fitting (Figure 13 and Figure 14). The imperfections introduced to the dataset and uncertain status of the negative ${Z}_{rel}$ measurements led us to assume the unmodified DREM as the basis for further analyzes.

^{2}of area. A model fitted to the whole dataset with the scaling formula $V=0.36\pm 0.04\xb7{S}^{1.51\pm 0.01}$ sports similar ${R}^{2}=0.84$, but much worse $C{V}_{10f}=0.49$.

^{2}) performed very poorly (${R}^{2}=0.10,C{V}_{10f}=0.07$), its scores lowest of all fits. The model based on the large icebergs, in turn, has identical formula to the model fitted to the entirety of the dataset, albeit with wider fitting confidence intervals ($V=0.36\pm 0.10\xb7{S}^{1.51\pm 0.03}$). Its ${R}^{2}$ is also identical, while $C{V}_{10f}=0.53$ differs in favor of the more limited model.

## 5. Discussion

#### 5.1. Iceberg Classification

#### 5.2. Iceberg Inventory

^{2}to several tens of thousands m

^{2}, means that a single, very large iceberg will contribute more ice to the lake than even several hundred smaller ones. The relationship is even more pronounced when ice volume is considered, a property which has higher order of magnitudes, and thus higher absolute differences between largest and smallest cases. Despite the very restrictive filtering imposed upon our iceberg inventory, resulting low fraction of reliable records accounts for nearly 80% of the ice in the lagoon. This value might, however, be inaccurate due to the uncertainty of height of the icebergs. Fitting of a power law model to the subset of small icebergs showed very little correlation between their areas and volumes. This lack of relationship is an argument for their exclusion from the scaling law determination. In the realm of small areas and low freeboards, the 1.7 m of DEM uncertainty introduces noise much stronger than the actual signal.

#### 5.3. Volume Assessment

^{2}of waterline cross-section area assuming perfectly cylindrical model of iceberg. Any smaller iceberg taller than the 1.7 m would be forced to capsize. Thus, 99 m

^{2}is a theoretical lower limit of iceberg area about which meaningful elevation information can be obtained from our DREM. Despite the availability of icebergs as small as 4 m

^{2}in our inventory, the precision of the DEM (1.7 m as compared to TanDEM-X DEM) limited our fitting effort to just the icebergs taller than the precision limit and larger than 99 m

^{2}. In the case of large icebergs, the very large number of pixels and high general elevation diminishes the impact of elevation uncertainty on the volume estimate. Moreover, large icebergs tend to have rich texture which lends more potential tie-points to the stereo correlation algorithm used to produce DEM. The elevations detected on highly crevassed or multi-colored icebergs can thus be considered more reliable than those computed from uniformly colored ones, particularly dark ones easily blending with surrounding water.

#### 5.4. Area–Volume Scaling and Distributions

^{2}of waterline cross-sectional area [15], while our dataset extends the range of sizes down to 4 m

^{2}hinting at universality of the physical processes that lead to the log-normal size distribution of older icebergs. Not only does the law hold in smaller sizes, it is also possible to find it in a lacustrine setting in temperate climate zone where conditions for iceberg decay are drastically different than in an Arctic fjord.

^{2}) with the least squares method. This fitting technique minimizes squares of residuals between the observed and modeled values. In a multi-scale study such as iceberg size analysis, the residuals in the heavy tail of the population (where absolute values of areas and volumes are very high) are much higher than in the lower orders of magnitude. Therefore, an algorithm intended to minimize these residuals will always favor fits that perform well in the region of very big icebergs and will neglect smaller ones. This approach is not necessarily bad when one tries to model the overall volume of ice because, as briefly shown above, the largest icebergs contribute the majority of ice volume in the set. This behavior of least squares is also highlighted by identical formulas of the power law model fitted to the entire population of icebergs and just the $S>211$ m

^{2}part (Figure 13). The weight of the largest icebergs is so great that the addition of a large, uncorrelated subset to the fitting did not change the course of the line. The specifics of least-squares fitting may be the reason why fitting a linear model to log-log data performed better. In this case the least squares algorithm operates on a range of values within a single order of magnitude (from $-4$ to $+8$ in our dataset), which does not involve the scale problems and leads to a more robust fit.

## 6. Conclusions

^{2}), leaves open a question of whether the power law is the best model of the scaling. More work with more precise elevation models would be needed to accurately constrain the model and extend it to smaller icebergs and growlers.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

Processing Step | Tool | Input Data | Flowchart |
---|---|---|---|

WV-2 imagery preprocessing | ENVI 5 | WV-2 raw images | Figure 2 |

DREM creation | QGIS 3.10 | WV-2 DEM | Figure 3 |

DREM uncertainty assessment | QGIS 3.10, SAGA, MATLAB | WV-2 DEM, TanDEM-X DEM | Figure 4 |

Image segmentation and classification | eCognition 9.3 | WV-2 processed images, DREM | Figure 5 |

Watershed cutting | Python 3 | Shapefile map of icebergs | Figure 6 |

Iceberg detection quality assessment | MATLAB | Cut shapefile map of icebergs | - |

Iceberg properties extraction | eCognition 9.3 | Cut shapefile map of icebergs | Figure 5 |

Statistical analysis | MATLAB | Table of iceberg properties | - |

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**Figure 1.**Map of the study area: (

**A**) location of the Northern Patagonia Icefield within the South America; (

**B**) location of the San Quintín terminus and lagoon in the region; and (

**C**) WV-2 image of the study area. Coordinates of (

**C**) in UTM 18S coordinate system.

**Figure 5.**Entire procedure of iceberg inventory creation. Steps enclosed in white-brown rectangular boxes are shown in detail on other figures.

**Figure 7.**Results of the accuracy assessment of the WV-2 DEM as compared to the TanDEM-X 90 m/pixel DEM: (

**A**) histogram of the values of the WV-2 DEM-TanDEM-X DEM difference map, where the orange line represents the normal distribution fitted to the histograml and (

**B**) empirical (blue dots) and fitted (orange line) semivariogram of the same difference map with parameters of the fitted synthetic variogram, where the green line indicates the correlation range.

**Figure 8.**Final result of the iceberg map creation process: (

**A**) example of iceberg map in the lagoon area; (

**B**) example of iceberg map in the ice melange area; and (

**C**) the overview of the classification over the whole lagoon and its surroundings. Coordinates in UTM 18S coordinate system.

**Figure 9.**Subsets of the area–volume dataset produced by applying different filters. Discarded data points shown in green: (

**A**) outliers removal with knn clustering; (

**B**) icebergs with $\mu {Z}_{rel}<1.7$ m removed; (

**C**) icebergs with width/height ratio below 0.73 removed; and (

**D**) all filters applied together. Discarded points shown in green, and the accepted ones in blue.

**Figure 10.**Results of quality assessment of iceberg map: (

**A**,

**B**) histograms of frequency of iceberg areas; and (

**C**,

**D**) 2D histograms of unsigned relative error of manually digitized icebergs compared to automatically mapped ones. Plots (

**A**,

**C**) relate to the lagoon, while (

**B**,

**D**) to the fields of ice melange. Dashed lines show the lines of 100% relative error. Values within each column add up to 100%. Relative differences were computed as $\frac{{S}_{man}-{S}_{cla}}{{S}_{man}}$. X-axis divisions spaced by equal ${log}_{10}S$ for histogram readability.

**Figure 11.**Fitting of heavy-tailed distributions (green lines) to logarithmically binned area data (blue dots): (

**A**) log-normal $P(S=x)=\frac{1}{x\sigma \sqrt{2\pi}}exp(-\frac{{(lnx-\mu )}^{2}}{2{\sigma}^{2}})$; (

**B**) power law $P(S=x)={x}^{\alpha}$; (

**C**) exponentially truncated power law $P(S=x)={x}^{\alpha}{e}^{\lambda x}$; and (

**D**) exponential $P(S=x)={e}^{\lambda x}$.

**Figure 12.**Fitting of heavy-tailed distributions (green lines) to logarithmically binned volume data (blue dots): (

**A**) log-normal $P(V=x)=\frac{1}{x\sigma \sqrt{2\pi}}exp(-\frac{{(lnx-\mu )}^{2}}{2{\sigma}^{2}})$; (

**B**) power law $P(V=x)={x}^{\alpha}$; (

**C**) exponentially truncated power law $P(V=x)={x}^{\alpha}{e}^{\lambda x}$; and (

**D**) exponential $P(V=x)={e}^{\lambda x}$.

**Figure 13.**Results of filtering and model fitting to the area–volume data. Unmodified DREM with negative values used: (

**A**) area distributions of iceberg classes selected by $\mu {Z}_{rel}$; (

**B**) histograms of iceberg area; (

**C**) histograms of iceberg volume; and (

**D**) power law relationship fitted to the area/volume data. Green fields indicate whole $\mu {Z}_{rel}>0$ dataset, blue—data filtered. Green lines are models (Gaussian distributions in (

**B**,

**C**), power law models in (

**D**)) fitted to unfiltered data, blue—to the filtered data. Orange line is a linear model fitted to the log-log data. Dashed lines indicate 95% confidence intervals of fitting.

**Figure 14.**Results of filtering and model fitting to the area–volume data. DREM

_{0}with negative values replaced with 0 used: (

**A**) area distributions of iceberg classes selected by $\mu {Z}_{rel}$; (

**B**) histograms of iceberg area; (

**C**) histograms of iceberg volume; and (

**D**) power law relationship fitted to the area/volume data. Green fields indicate whole $\mu {Z}_{rel}>0$ dataset, blue—data filtered. Green lines are models (Gaussian distributions in (

**B**,

**C**), power law models in (

**D**)) fitted to unfiltered data, blue—to the filtered data. Orange line is a linear model fitted to the log-log data. Dashed lines indicate 95% confidence intervals of fitting.

Band | Wavelength | Original Resolution | Date | Source |
---|---|---|---|---|

Blue | 450–510 nm | 2 m/pixel | 17 February 2017 | [35] |

Green | 510–580 nm | |||

Red | 630–690 nm | |||

NIR | 770–895 nm | |||

Panchromatic | 450–800 nm | 0.5 m/pixel | ||

WV-2 DEM | Elevation | 2 m/pixel | 17 February 2017 | |

TanDEM-X DEM | Elevation | 90 m/pixel | 22 January 2011–8 September 2014 | [33,34] |

Class | Interpretation | Visible Brightness | Relative Elevation | Texture | Comments |
---|---|---|---|---|---|

Clear Ice | Ice without debris cover | Very bright | Positive | Uniform to moderately grainy | — |

Dirty Ice | Icebergs or their sections covered with debris | Low, moderately variable | Positive | Non-uniform due to variable amount of debris | Easily mistaken for brash ice |

Brash Ice | Fields of icebergs too small to be resolved individually | Moderately bright | Close to 0 | Very highly textured | Easily mistaken for dirty ice due to similar brightness |

Shadow | Areas in deep shadow cast by an iceberg or glacier | Extremely low | Variable, depends on location | Very uniform | “Technical” class, merged with other classes in postprocessing |

Water | Open water area, without ice | Narrow band of brightness | 0 | Very uniform | Brightness values within range of Dirty and Brash Ice |

Big Iceberg | Tabular icebergs trapped in tightly packed ice melange | Variable, from clear ice to very dark | Very high | Variable, mostly uniform | Only used to reclassify the ice melange region |

Small Iceberg | Small icebergs trapped in tightly packed melange | Moderately bright, with very bright pieces of clear ice | Variable, positive, close to 0 | Uniform within small objects | Only used to reclassify the ice melange region |

**Table 3.**List of properties of image objects used as variables during the Random Forest classification and results of PCA analysis of their importance. “RF imp.” stands for “Random Forest Importance”, as returned by eCognition. Columns 3–6 list loadings of properties in the four Principal Components with largest explained variance in the classified objects dataset. Absolute loadings higher than 0.25 and properties carrying them are shown in bold. All minima, maxima, means and standard deviations are computed from pixels within a single object.

Image Object Property | RF imp. | Parameter Loadings | |||
---|---|---|---|---|---|

PC1 | PC2 | PC3 | PC4 | ||

Border contrast Panchromatic band | 0.024 | 0.08 | 0.07 | 0.68 | 0.17 |

GLCM Contrast | 0.030 | 0.06 | −0.27 | 0.22 | 0.77 |

GLCM Entropy | 0.032 | 0.00 | 0.00 | 0.00 | 0.00 |

GLCM Homogeneity | 0.029 | 0.00 | 0.00 | 0.00 | 0.00 |

GLCM Mean | 0.047 | 0.03 | 0.01 | 0.01 | −0.02 |

Max. relative elevation | 0.031 | 0.00 | 0.00 | 0.00 | −0.01 |

Max. Green band reflectance | 0.053 | 0.29 | −0.29 | −0.20 | −0.04 |

Max. Panchromatic band reflectance | 0.052 | 0.42 | −0.38 | −0.11 | 0.00 |

Max. Red band reflectance | 0.045 | 0.28 | −0.27 | −0.14 | −0.02 |

Max. NDSI value | 0.025 | 0.00 | 0.00 | 0.00 | 0.00 |

Max. Blue band reflectance | 0.052 | 0.28 | −0.27 | −0.21 | −0.03 |

Mean Blue band reflectance | 0.069 | 0.26 | 0.08 | 0.12 | −0.13 |

Mean relative elevation | 0.044 | 0.00 | 0.00 | 0.00 | −0.01 |

Mean Green band reflectance | 0.066 | 0.28 | 0.07 | 0.13 | −0.14 |

Mean NDSI value | 0.027 | 0.00 | 0.00 | 0.00 | 0.00 |

Mean NIR band reflectance | 0.027 | 0.17 | 0.09 | 0.20 | −0.17 |

Mean Panchromatic band reflectance | 0.023 | 0.40 | 0.14 | 0.29 | −0.20 |

Mean Red band reflectance | 0.035 | 0.27 | 0.11 | 0.21 | −0.13 |

Min. NDSI value | 0.024 | 0.00 | 0.00 | 0.00 | 0.00 |

Min. Panchromatic band reflectance | 0.028 | 0.27 | 0.46 | −0.17 | 0.22 |

Min. relative elevation | 0.024 | 0.00 | 0.00 | 0.00 | 0.00 |

Min. Blue band reflectance | 0.032 | 0.16 | 0.27 | −0.23 | 0.20 |

Min. Red band reflectance | 0.027 | 0.16 | 0.31 | −0.16 | 0.25 |

Min. Green band reflectance | 0.037 | 0.18 | 0.28 | −0.23 | 0.22 |

Std. NIR band reflectance | 0.030 | 0.02 | −0.07 | 0.04 | 0.04 |

Std. of Panchromatic band reflectance | 0.029 | 0.04 | −0.18 | 0.11 | 0.22 |

Std. of Relative elevation | 0.034 | 0.00 | 0.00 | 0.00 | 0.00 |

Std. of NDSI value | 0.024 | 0.00 | 0.00 | 0.00 | 0.00 |

% of explained variance | — | 83.84 | 10.42 | 1.89 | 1.19 |

Filter | Whole Dataset | Only V > 0 | knn Outliers Removal | DEM Error | Iceberg Height | All Filters |
---|---|---|---|---|---|---|

N of records | 38,781 | 20,170 | 20,110 | 6441 | 11,688 | 933 |

% of volume | 100 | 100 | 93.06 | 93.66 | 93.56 | 80.99 |

Iceberg area percentages | ||||||

S<4 | 18.43 | 15.26 | 15.21 | 20.43 | 5.31 | 0.00 |

10 < S < 100 | 53.36 | 44.25 | 44.34 | 43.81 | 38.07 | 0.00 |

100 < S < 1000 | 21.22 | 28.94 | 28.98 | 21.32 | 38.61 | 18.76 |

1000 < S < 10,000 | 4.93 | 9.03 | 9.01 | 9.39 | 14.50 | 51.34 |

S > 10,000 | 0.91 | 1.75 | 1.70 | 4.38 | 3.01 | 29.90 |

**Table 5.**Quantities of icebergs used in classification quality assessment. N

_{cla}stands for number of classified icebergs, N

_{man}– number of manually digitized icebergs and VF – Verification Fields.

Area | N_{cla} Whole Set | N_{cla} within VF | N_{man} within VF | Detected Icebergs | Icebergs within VF | False Positives | False Negatives |
---|---|---|---|---|---|---|---|

Lagoon | 38781 | 3184 | 3213 | 99.10% | 8.21% | 137 | 494 |

Ice melange | 9275 | 1702 | 535 | 318.13% | 18.35% | 303 | 55 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Podgórski, J.; Pętlicki, M. Detailed Lacustrine Calving Iceberg Inventory from Very High Resolution Optical Imagery and Object-Based Image Analysis. *Remote Sens.* **2020**, *12*, 1807.
https://doi.org/10.3390/rs12111807

**AMA Style**

Podgórski J, Pętlicki M. Detailed Lacustrine Calving Iceberg Inventory from Very High Resolution Optical Imagery and Object-Based Image Analysis. *Remote Sensing*. 2020; 12(11):1807.
https://doi.org/10.3390/rs12111807

**Chicago/Turabian Style**

Podgórski, Julian, and Michał Pętlicki. 2020. "Detailed Lacustrine Calving Iceberg Inventory from Very High Resolution Optical Imagery and Object-Based Image Analysis" *Remote Sensing* 12, no. 11: 1807.
https://doi.org/10.3390/rs12111807