# Analysis of the Spatiotemporal Changes of Ice Sheet Mass and Driving Factors in Greenland

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}from 2003 to 2015. This mass loss was relatively stable in the two years after 2012, and then continued a decreasing trend; (2) in terms of space, the mass loss areas of the Greenland ice sheet mainly concentrates in the southeastern, southwestern, and northwestern regions, and the southeastern region mass losses have a maximum rate of more than 27 cm/yr (equivalent water height), while the northeastern region show a minimum rate of less than 3 cm/yr, showing significant changes as a whole. In addition, using spatial distribution and the time coefficients of the first two models obtained by EOF decomposition, ice sheet quality in the southeastern and northwestern regions of Greenland show different significant changes in different periods from 2003 to 2015, while the other regions showed relatively stable changes; (3) in terms of driving factors temperature, there is an anti-phase relationship between ice sheet mass change and land surface temperature by the mean XWT-based semblance value of −0.34 in a significant oscillation period variation of 12 months. Meanwhile, XWT-based semblance values have the largest relative change in 2005 and 2012, and the smallest relative change in 2009 and 2010, indicating that the influence of land surface temperature on ice sheet mass significantly varies in different years.

## 1. Introduction

^{3}/a, and an acceleration of −30 ± 11 Gt/yr

^{2}; Ramilli et al. [29] estimated that the melting rate of the Greenland ice sheet was −109 ± 9 Gt/a from 2002 to 2005; Slobbe et al. [30] used GRACE post-processing data to compare Greenland ice sheet mass changes from four different organizations. The results indicated that the different data sources caused different results; Baur et al. [31] explored the annual average Greenland ice sheet melting with a rate of 162 ± 11 km

^{3}/a through GRACE RL04 data during 2002–2008; Joodaki et al. [32] found that the mass of the Greenland ice sheet melted at the rate of −166 ± 20 Gt/a and the acceleration of melting was −32 ± 6 Gt/a by GRACE RL04 data from 2002 to 2011; Lu Fei et al. [33] found that the melting speed and acceleration of the ice sheet were −157.8 ± 11.3 Gt/a and −17.7 ± 4.5 Gt/a

^{2}, respectively, through GRACE RL05 data from 2003 to 2012. In addition, the melting rate significantly increased after 2010, from −132.2 Gt/a in 2003–2009 to −252.5 Gt/a in 2010–2012; Forsberg et al. [34] concluded that the mass change rate of the Greenland ice sheet was 265 ± 25 Gt/a, and the correlation coefficient was 0.72 with the global mean sea level change. In addition, some scholars studied ice sheet mass trends in different regions of Greenland. Chen et al. [35,36] reported that the mass change rate of Greenland ice sheet was −239 ± 23 km

^{3}/yr from April 2002 to November 2005. In addition, its decrease rate increased in the northwest and tended to be balanced in the southeast between 2007 and 2009; Wouter et al. [37] found that the overall mass change rate of the Greenland ice sheet was −179 ± 25 km3/yr on a smaller scale from February 2003 to January 2008 and the greatest mass loss occurred in the southeastern coast (279 Gt) and the northwest coast (328 Gt) in the summer of 2005 and 2007; Zhu Chuandong et al. [38] found that the annual total melting amount of the Greenland ice sheet was 188 ± 10 km

^{3}/a during 2002–2011, and the melting area mainly concentrated in the southeast and northwest of the ice sheet; Shamshiri et al. [39] used GRACE RL05 data to conclude that the peak loss of ice mass was −15 cm/yr in the southeast and northwest of Greenland, and loss acceleration was −2.5 cm/yr

^{2}in the southwest during 2003–2014.

## 2. Study Area and Data

#### 2.1. Study Area

^{2}(836,330 sq mi). Among them, the Greenland ice sheet has a volume of about 2,850,000 km

^{3}(680,000 cu mi) and covers 1,755,637 km

^{2}(677,855 sq mi) (81%) [41].

#### 2.2. GRACE Data

^{3}), latitudes, longitudes, love numbers of degree l with ${l}_{\mathrm{max}}$ = 60 [44,45], and coefficients changes of the normalized complex spherical harmonic (Stokes’ coefficients), respectively. Meanwhile, ${\tilde{P}}_{lm}(\mathrm{sin}(\theta ))$ is the fully normalized Legendre function of degree l and order m.

^{3}kg/m

^{3}). The ice sheet mass variation $\Delta m$ of Greenland can thus be given as [4]

#### 2.3. Land Surface Temperature data

## 3. Methods

#### 3.1. Theil–Sen Median Trend Analysis

#### 3.2. Mann–Kendall (MK) Trend Test

_{j}and x

_{i}are values at jth and ith points, and sign is a sign function. Then, the M–K statistic, Z, is calculated as

#### 3.3. Rotated EOF Method

**C**of time series is obtained and orthogonally decomposed as

**EOF**value can then be obtained by normalizing the decomposition. In addition, the principal component

**Z**can be calculated in the time series.

#### 3.4. Continuous and Cross Wavelet Transform

_{n}, n = 1, 2, ⋯, N) is [59]

_{n}and Y

_{n}is given as [60,61,62]

^{Y*}denotes a complex conjugation of W

^{Y}. The cross wavelet power spectrum is defined as

**|**W

^{XY}

**|**, and the complex argument of W

^{XY}can be seen as the local relative phase between X

_{n}and Y

_{n}in time–frequency domain. While the larger the

**|**W

^{XY}

**|**value, indicating that X

_{n}and Y

_{n}have a common high-energy region, which significantly correlates them with each other. More details about Cross Wavelet Power Spectrum test and phase difference calculation are given by Grinsted et al. [59] and are not repeated here.

_{i}, i = 1, 2, …, N) is defined as

## 4. Results and Discussion

#### 4.1. Time Variation Analysis

#### 4.1.1. Time Series and Change Trends

^{2}in 2003–2015, as was done in most previous studies. We use a quadratic form to obtain a trend of −195 ± 21 Gt/yr for the Greenland ice sheet between 2003 and 2015. The uncertainties of the data results (±12, ±2, and ±21) include contributions from the gravity field error, signal leakage effects, truncation error, GIA correction, and the statistical uncertainty of the fit. Mass loss increases with time in a relatively consistent pattern from 2003 to 2012, and a sudden decline in the time series could be observed in 2012. This was followed by a relatively stable mass loss in the next two years after 2012, and then continued in a decreasing trend. The above results are basically consistent with those obtained by researchers using GRACE data in recent years [27,28,33,36,39,64]. However, the time series of the results of this study are longer than those of previous studies, especially the trend of change in 2015 relative to 2014, and their different values are due to different data sources, time series, and post-processing methods.

#### 4.1.2. Monthly Mean and Seasonal Change

#### 4.2. Spatial Change Analysis

#### 4.3. EOF Analysis

#### 4.4. Relationship between Temperature and Ice Sheet Mass

#### 4.4.1. Spatiotemporal Contrastive Analysis

#### 4.4.2. Wavelet Transform Analysis

## 5. Conclusions

^{2}, which was relatively stable for the two years after 2012, and then continues to show a downward trend. However, in terms of monthly and seasonal variations, the change of ice sheet mass in the whole study area slowly increases between October and April, but decreases between May and September.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Monthly mass change of Greenland from January 2003 to December 2015 estimated based on the GRACE solution of the CSR processing center. The blue line, green line and red curve represent the mass change of the time series, and the best fitting of linear and quadratic trend, respectively.

**Figure 3.**(

**a**) and (

**b**) represented monthly and seasonal changes in the mass of the Greenland ice sheet from January 2003 to December 2015, respectively.

**Figure 4.**Spatial distribution of annual change trend of GRACE ice sheet mass in Greenland from 2003 to 2015. Note: Lattice point representation has passed the M–K test of 95% confidence interval.

**Figure 5.**Spatial distribution (

**a**,

**b**) and time coefficient (

**c**,

**d**) change of the first and second EOF modes. Note: The time coefficients and EOF variables in the figure indicate relative size and are dimensionless.

**Figure 6.**Annual changes of GRACE ice sheet mass and land surface temperature in Greenland from 2003 to 2015.

**Figure 7.**Spatial distribution of annual change trend of GHCN CAMS land surface temperature in Greenland from 2003 to 2015. Note: Lattice point representation passed the M–K test of 95% confidence interval.

**Figure 8.**Continuous wavelet transform with average mass and land surface temperature represented by (

**a**) and (

**b**) from 2003 to 2015.

**Figure 9.**Cross wavelet transform of ice sheet mass and land surface temperature fluctuations. Arrows indicate relative phase relations, where straight-up arrows represent ice sheet changes, and land surface temperature shows an anti-phase relationship.

**Figure 10.**XWT-based semblance value is the closest to one cpy outside the COI. Red dashed lines represent the COI, which limits the region not affected by edge effects.

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**MDPI and ACS Style**

Bian, Y.; Yue, J.; Gao, W.; Li, Z.; Lu, D.; Xiang, Y.; Chen, J.
Analysis of the Spatiotemporal Changes of Ice Sheet Mass and Driving Factors in Greenland. *Remote Sens.* **2019**, *11*, 862.
https://doi.org/10.3390/rs11070862

**AMA Style**

Bian Y, Yue J, Gao W, Li Z, Lu D, Xiang Y, Chen J.
Analysis of the Spatiotemporal Changes of Ice Sheet Mass and Driving Factors in Greenland. *Remote Sensing*. 2019; 11(7):862.
https://doi.org/10.3390/rs11070862

**Chicago/Turabian Style**

Bian, Yankai, Jianping Yue, Wei Gao, Zhen Li, Dekai Lu, Yunfei Xiang, and Jian Chen.
2019. "Analysis of the Spatiotemporal Changes of Ice Sheet Mass and Driving Factors in Greenland" *Remote Sensing* 11, no. 7: 862.
https://doi.org/10.3390/rs11070862