Satellite Radar and Laser Altimetry for Monitoring of Lake Water Level And

Satellite Radar and Laser Altimetry for Monitoring of Lake Water

Level and Snow Accumulation in Arctic Regions

A dissertation submitted to the

Graduate School

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

in the Department of Geography & Geographic Information Science

of the College of Arts and Sciences

Song Shu

B.S., Physical Geography, East China Normal University, China, 2010 M.A., GIS, East China Normal University, China, 2013

Committee Chair: Hongxing Liu, Ph.D.

March 2019

ABSTRACT

Thermokarst lakes are the most conspicuous features in the Arctic coastal regions that

cover roughly 15% - 40 % percent of the area. Those lakes play as a critical niche in the local

environment system and provide habitats for a great number of species. In the context of global

warming, lakes are experiencing dramatic changes in recent decades. The lake water level and the

snow cover atop the ice in the winter are two sensitive indicators of the local and global climate

change. Monitoring the variations in lake water level and snow accumulation in Arctic regions

could provide more insights of the global climate change and facilitate our understanding of their

influences on local hydrological and ecological systems. However, there are very rare in situ

observations of lake water levels and lake snow accumulations for the Arctic regions due to the

remote locations and also the harsh environmental conditions. Satellite radar and laser altimetry

measures elevation profiles of Earth’s surface at the global scale and offers an alternative to

achieve the purpose. Most previous studies have focused on the application of satellite radar and

laser altimetry on lakes at low or middle latitudes, with few of them discussing the applicability of

these data to high-latitude lakes. In this research, I explored the capability of satellite radar and

laser altimetry missions to monitor lake water levels and snow accumulation on frozen lakes in the

Arctic coastal regions. The performances of Sentinel-3, the most recent satellite radar altimetry,

on the retrieval of lake water levels were assessed particularly for high-latitude ice-covered lakes.

The results showed that lake ice can greatly reduce the accuracy of Sentinel-3 observations. I

developed a new empirical retracking algorithm that significantly improves the measurements and

provide more reliable and consistent water level estimates for the ice-covered lakes. I examined

the performances of ICESat/GLAS, the first satellite laser altimetry mission, on the retrieval of lake surface elevations in Arctic regions. A novel probabilistic relaxation algorithm was then

developed to correct and improve the laser altimetry measurements that were affected by the thin

clouds, ice fogs and blowing snow in Arctic regions. The snow accumulations on frozen lake

surfaces in the winter were then derived using the corrected ICESat repeat observations. As

compared to the point-based in situ snow depth data, these relatively dense ICESat-derived snow

accumulation estimates enable us to investigate its spatio-temporal variations across the Arctic

coastal regions.

Keywords: Satellite radar and laser altimetry, water levels, snow accumulation, Sentinel-3,

ICESat/GLAS, altimetry waveform retracking.

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ACKNOWLEDGMENTS

I would like to express my enormous gratitude to my advisor, Dr. Hongxing Liu, for his

guidance over the past six years. Under his supervision, I learned how to define a research question,

approach the question, find a solution, write a paper and finally publish the results. I could never

push my way through the numerous obstacles and achieve this point without his encouragement

and support. He not only teaches me how to do high-quality researches but also how to face the

life difficulties with active and positive attitudes.

I am so grateful to my dissertation committee members, Dr. Richard Beck, Dr. Kenneth

Hinkel, Dr. Tomasz Stepinski and Dr. Emily Lei Kang for their valuable advices and insightful comments on my dissertation research. Special thanks should be given to Dr. Beck for his help and support during my last year at University of Cincinnati. I want to thank all the department faculties and staffs for making my study at University of Cincinnati a great unforgettable experience.

I would also like to acknowledge some of my colleagues. I want to thank Lei Wang for his technical support on the processing of ICESat level-1 and level-2 data. Qiusheng Wu and Bo Yang provided valuable sources of experienced knowledge on the issues I met in my study and daily life in Cincinnati. Special thanks are extended to my friends in Remote Sensing Lab at UC: Shujie

Wang, Min Xu, Yan Huang, Zuoqi Chen, Bin Wu, Yang Liu and Minxuan Lan for the wonderful time we spent together.

Last, but not least, I want to thank my family for their patience, understanding and support.

In particular, I would like to thank my beloved wife. Without her love, trust and encouragement the completion of this work could not have been possible.

CONTENTS

ABSTRACT ...... ii ACKNOWLEDGMENTS ...... v CONTENTS ...... vi LIST OF FIGURES ...... viii LIST OF TABLES ...... xi Chapter1: Introduction ...... 12 Chapter 2: Analysis of Sentinel-3 SAR Altimetry Waveform Retracking Algorithms for Deriving Temporally Consistent Water Levels over Inland Lakes ...... 18 2.1 Introduction ...... 18 2.2 Case study lakes and in situ water level measurements ...... 22 2.2.1 Case study lakes and their winter ice conditions ...... 22 2.2.2 In situ water level and ice thickness measurements from gauge stations ...... 25 2.3 Derivation of Sentinel-3 SRAL SAR lake water level estimates ...... 27 2.3.1 SRAL data products ...... 27 2.3.2 SRAL SAR waveform and SAR retrackers ...... 30 2.3.3 A new bimodal retracker for the retrieval of water-equivalent lake surface elevation over ice- covered lakes ...... 33 2.3.4 Estimation of lake water level using SRAL SAR elevation measurements ...... 36 2.4 Results and Discussions ...... 38 2.4.1 Lake surface profiles retrieved by different SAR retrackers ...... 38 2.4.2 SAR retracker performances over the lakes with different ice cover conditions ...... 41 2.4.3 Detection of lake ice with simultaneous Sentinel-3 MWR measurements ...... 49 2.4.4 Influence of lake ice on SAR altimetry waveform ...... 51 2.4.5 Application of bimodal retracker for the retrieval of water-equivalent lake levels ...... 57 2.5 Conclusions ...... 59 Chapter 3: Improving Satellite Waveform Altimetry Measurements with a Probabilistic Relaxation Algorithm...... 61 3.1 Introduction ...... 61 3.2 Datasets ...... 65 3.3 ICESat/GLAS standard retracking methods ...... 66

3.4 New probabilistic relaxation retracking method ...... 69 3.4.1 Spatial contextual information along the satellite track ...... 70 3.4.2 Decomposition of the returned waveform...... 71 3.4.3 Identification of the true signal-peak using the probabilistic relaxation method ...... 72 3.5 Application examples ...... 79 3.5.1 The snow surface of Lake Teshekpuk in Arctic Coastal Plain ...... 80 3.5.2 Tundra surface in the Arctic coastal plain...... 85 3.5.3 Ice sheet surface of Greenland ...... 88 3.5.4 Sand dune surface in an arid desert ...... 89 3.6 Discussion ...... 91 3.7 Conclusion ...... 95 Chapter 4: Estimation of snow accumulation over frozen Arctic lakes using repeat ICESat laser altimetry observations – A case study in northern Alaska...... 97 4.1 Introduction ...... 97 4.2 Study area and data sources ...... 102 4.3 Methods ...... 105 4.3.1 Data preprocessing through filtering of the contaminated measurements ...... 107 4.3.2 Derivation of reliable surface elevation measurements with max-amplitude-peak retracking method...... 109 4.3.3 Derivation of true surface elevation changes by correcting inter-campaign biases ...... 115 4.3.4 Derivation of snow depth by excluding surface elevation change contributed by lake ice growth ...... 117 4.4 Results and Discussion ...... 121 4.4.1 ICESat-derived snow accumulation over Alaskan ACP ...... 121 4.4.2 Validation of the ICESat-derived snow accumulation ...... 125 4.4.3 Spatio-temporal variation of snow accumulation over Alaskan ACP ...... 128 4.4.4 Discussion ...... 129 4.5 Conclusions ...... 133 BIBLIOGRAPHY ...... 136

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LIST OF FIGURES Figure 2.1 Geographic distribution of the case study lakes ...... 25 Figure 2.2 Radar altimetry waveforms echoed from the open water surface of Great Slave Lake in Canada. (a) SAR waveform acquired by Sentinel-3 SRAL on August 23, 2016; (b) Conventional pulse-limited altimetry waveform acquired by Envisat on August 11, 2002...... 31 Figure 2.3 The removal of spurious measurements from lake surface profile using robust statistical analysis. The orange points are the measurements excluded and the blue points are the retained measurements. The dashed line represents the in situ gauge water level on July 4, 2017. The profile runs from south to north...... 37 Figure 2.4 Sentinel-3 ground tracks (a) over Great Slave Lake and (b) over Lake Erie...... 39 Figure 2.5 Lake surface profile produced by different SRAL SAR retrackers; (a) along Track 576 over Lake Erie on June 22, 2016, (b) along Track 681 over Great Slave Lake on August 18, 2016, (c) along Track 681 over Great Slave Lake on February 23, 2017. The black dashed line in each plot represents the in situ gauge water level for each lake on the corresponding date. The profile runs from south to north...... 40 Figure 2.6 Comparison of water level estimates from Sentinel-3 retrackers and the in situ gauge measurements over Lake Erie during 2016-2017. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The date is in the format of MM/DD/YYYY...... 43 Figure 2.7 The scatter plots of water level estimates from SRAL SAR retrackers against in situ gauge measurements over Lake Erie. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The dashed line in each plot is the regression line of SRAL SAR water level estimates against concurrent in situ gauge measurements...... 44 Figure 2.8 Comparison of water level estimates from Sentinel-3 retrackers and the in situ gauge measurements over Great Slave Lake during 2016-2017. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The date is in the format of MM/DD/YYYY...... 44 Figure 2.9 The scatter plots of water level estimates from SRAL SAR retrackers against in situ gauge measurements over Great Slave Lake. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The SRAL SAR water level estimates have been excluded from the scatter plots. The dashed line in each plot is the regression line of SRAL SAR water level estimates against concurrent in situ gauge measurements...... 45 Figure 2.10 Coincidence between the sudden increase of brightness temperature and the deviation of lake level estimates from in situ observations over Great Slave Lake during 2016- 2017. (a) Brightness temperature from Sentinel-3 MWR channels at 23.8 GHz and 36.5 GHz. (b) Lake level estimates given by Sentinel-3 Ice-Sheet retracker. (c) Daily air temperature at the gauge station Yellowknife...... 50 Figure 2.11 The time series of SRAL SAR waveforms over Great Slave Lake during the 2016- 2017 winter. The epochs (τ) are produced by SAMOSA-3 retracker. The date is in the format MM/DD/YYYY...... 53 Figure 2.12 Weekly-mean ice thickness on Great Slave Lake and Lake Inarijarvi from 2010 to 2016. The dates of the first and of the last bimodal waveform in Figure 2.11 are denoted by the red arrows...... 55

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Figure 2.13 The time series of SRAL SAR waveforms over Lake Inarijarvi during the 2016- 2017 winter. The epochs (τ) are produced by SAMOSA-3 retracker. The date is in the format MM/DD/YYYY...... 56 Figure 2.14 Comparison between the water levels produced by the bimodal retracker and by the original SRAL SAR SAMOSA-3 retracker. The date is in the format MM/DD/YYYY...... 59 Figure 2.15 Scatter plots of lake level estimates versus in situ gauge measurements; (a) from the SAMOSA-3 retracker and (b) from the bimodal retracker and the SAMOSA-3 retracker. The hallow circles represent the lake level estimates when the lake was covered by thick ice ...... 59 Figure 3.1 The transmitted and returned waveforms and the retracking methods. This figure is a derivative from Figure 3 in the ICESat Algorithm Theoretical Basis Document (Brenner et al. 2011)...... 68 Figure 3.2 The spatial contextual information in the neighboring footprints along a satellite track. (a) Definition of the neighborhood, (b) The central contaminated waveform and its neighboring waveforms, (c) The Gaussian peaks and the decomposition of the central contaminated waveform...... 71 Figure 3.3 Locations of the four application sites ...... 79 Figure 3.4 Elevation profiles of the frozen snow surface over Lake Teshekpuk on the Arctic coastal plain along the transect from footprint A to footprint B. (a) The problematic profile collected at November 4, 2005 and the normal profiles collected at other dates; (b) The profiles are retrieved using the standard Centroid method, the Probabilistic Relaxation methods, and the highest peak given in Equation (16), respectively...... 82 Figure 3.5 Illustration of the iteration process. (a) The waveforms within the neighborhood highlighted in Figure 3.4, (b) the contaminated waveform and its decomposed Gaussian peaks, (c) probability of each peak of being the true signal peak at each iteration, (d) average probability change at each iteration ...... 84 Figure 3.6 Comparison of the probabilistic relaxation derived profiles with the original ICESat/GLAS data product and the high-resolution reference data. (a) over tundra surface in the Arctic coastal plain, (b) over ice-sheet surface of Greenland, (c) over sand desert surface of Xinjiang...... 86 Figure 3.7 Scatter plots of the original ICESat/GLAS data products and the measurements derived from the probabilistic relaxation retracking method with the reference elevation data. PR in the graph is the abbreviation of probabilistic relaxation. (a) over tundra surface in the Arctic coastal plain, (b) over ice-sheet surface of Greenland, (c) over sand desert surface of Xinjiang. 87 Figure 3.8 Waveforms of the footprints highlighted in the inset of Figure 6c. (a) waveforms of the three footprints within the neighborhood; (b) the reference points determined by the Centroid and the Probabilistic Relaxation methods for the waveform of footprint 57...... 91 Figure 4.1 ICESat ground tracks during 2003-2009 and the locations of DOI/GTN-P automatic weather stations in the ACP of northern Alaska. The deep blue polygons are the lakes in this region and Lake Teshekpuk is the largest one. Only the tracks in Fall and Spring campaigns are shown in the figure. The measurements collected in early summer are not included in the snow accumulation analysis since the snow usually melts in May or early June...... 105 Figure 4.2 ICESat/GLAS campaigns from 2003 to 2009. The duration of each campaign is denoted roughly by the rectangle width. L1 was the first laser and flied only one campaign

before its failure, L2a was the first campaign for Laser 2, and L3b was the second campaign for Laser 3...... 105 Figure 4.3 Retrieval of snow accumulation through measuring lake surface elevation change during the winter season. The surface elevations ELVt1 and ELVt2 were collected respectively in the Fall- and Spring- campaigns as shown in Figure 4.2...... 107 Figure 4.4 Two types of reference points on transmitted and returned waveform. For centroid retracking scheme, the time reference point for the transmitted and the returned waveforms is indicated by TC on the time axis. For max-amplitude-peak scheme, the time reference point for the transmitted and the returned waveforms is indicated by TM on the time axis. The returned waveform was from the footprint highlighted in Figure 4.5...... 110 Figure 4.5 Surface elevation profiles from the centroid and max-amplitude-peak schemes over the largest lake Teshekpuk on 16 March, 2004. The profile runs north to south for about 14km. The return waveform of the footprint highlighted in black symbol is shown in Figure 4.4...... 113 Figure 4.6 ICESat overpass patterns over the lakes in our study area. The blue and the orange circles are the footprints collected respectively in Fall campaign and in Spring campaign. (a) Ascending pass; (b) Descending pass; (c) Both ascending and descending passes in one campaign...... 116 Figure 4.7 Daily average snow depth and air temperature from 2003 to 2009 at South Meade weather station in northern Alaska. The left vertical axis is air temperature, and the right axis is snow depth. The location of this station is shown in Figure 4.1. The date is in the format of YYYY/M/D. The vertical bars represent the ICESat Campaigns that were used to derive the snow accumulation on lake surfaces...... 120 Figure 4.8 The simulated growth of lake ice thickness based on the measured daily air temperature at the five weather stations between 2005 and 2006 ...... 121 Figure 4.9 Net snow accumulation estimates on Alaskan Arctic Coastal Plain during 2003-2007. The snow accumulation is shown as a vertical bar and the height of the bar is proportional to the net snow accumulation. A negative net accumulation is indicated by a bar point downward from the horizontal line (zero snow accumulation). The black line shows a portion of one ICESat pass, which is used as the transect line for plotting the net snow accumulation and topographical profiles in Figure 4.11...... 125 Figure 4.10 Comparison of ICESat snow accumulation estimates to in situ snow depth observations from automated weather stations. (a) Both the effect of ICB and lake ice growth contribution to surface elevation change were not removed in the derivation. (b) Only the effect for ICB was removed in the derivation. (c) Both the effect of ICB and the contribution of lake ice growth to surface elevation change were removed in the derivation. The stippled dotted line represents the fitted regression line...... 127 Figure 4.11 ICESat derived snow accumulation over lake surface during the winter of 2006- 2007 along the satellite track from the coast to the Brooks Range. The transect line of the satellite ground track is shown in Figure 4.9. Surface elevation profile along the transect is plotted based on the surface DEM (https://lta.cr.usgs.gov/IFSAR_Alaska). The dashed line denotes the general trend of the snow accumulation estimates ...... 128

LIST OF TABLES

Table 2.1 Winter ice cover, gauge stations and Sentinel-3 ground tracks in the case study lakes ...... 24 Table 2.2 The correlation coefficients r of the regressions over the 15 lakes with and without the ice-affected estimates ...... 46 Table 2.3 The Bias and the RMSE between the SRAL SAR lake level estimates and the in situ gauge water levels...... 48 Table 3.1 Geographic coordinates and acquisition dates of the ICESat/GLAS tracks in applications ...... 80 Table 3.2 Evaluation of the PR derived measurements versus original ICESat/GLAS data products with reference to high resolution topographic data ...... 88 Table 4.1 Geographical locations and operation periods of nine automatic weather stations ... 105 Table 4.2 Comparisons of the ICESat/GLAS elevation profiles of Teshekpuk Lake surface (above EGM2008) created by the centroid and max-amplitude-peak schemes ...... 114 Table 4.3 Summary of the snow accumulation estimates on Alaskan ACP ...... 123 Table 4.4 Lake surface rise under different scenarios of coefficient α and ice density ρice...... 130

Chapter1: Introduction

The global average surface temperature has increased by about 0.6 °C over the past century

(Houghton et al. 2001). The Arctic is warming at twice or more the rate of the average global

warming in last decades (Achberger et al. 2011; Karl et al. 2015; Koenigk et al. 2013; Solomon

2007).A large portion of Arctic regions are covered by numerous shallow lakes (Duguay et al.

2003). Those lakes are intimately tied to the regional climate and environmental changes through

the heat and water budgets. They play critical roles in the local hydrological and ecological system

(Hinkel et al. 2012). In some Arctic areas, lakes are important fresh water sources for residential

and industrial applications during the long winter season (Jones et al. 2009).The variation of lake

water levels, particularly on the high-latitude lakes, correlates well with the regional and the global

climate patterns (Ghanbari and Bravo 2008; Gibson et al. 2006) and is therefore a very sensitive

indicator of the global climate change. With the trend of global warming, these lakes are

experiencing dramatic changes in recent decades. Many studies indicated that the Arctic lakes

exhibit longer ice-free season with later freeze-up in the fall and earlier break-up in the spring

(Brown and Duguay 2010; Magnuson et al. 2000; Schindler et al. 1990; Surdu et al. 2014). Snow

accumulation on the frozen lake surface can significantly affect lake ice growth and thickness, and the ice break-up date (Duguay et al. 2003; Hinkel et al. 2012; Maykut 1978; Zhang and Jeffries

2000). Snow itself is also a well-established indicator of global climate change. There is a general decreasing trend of snow cover throughout the Arctic in terms of the Snow Water Equivalent

(SWE), snow-cover onset, snow-free date, snow-cover duration and snow cover extent(Brown and

Robinson 2011; Callaghan et al. 2011a; Liston and Hiemstra 2011; Park et al. 2012). Therefore, the monitoring of the variations in lake water level and lake snow accumulation in the Arctic

regions could provide more insights of the global climate change and facilitate our understanding

of its influences on the local hydrological and ecological systems.

However, we have very limited knowledge of the lake water levels and snow accumulation

in Arctic regions due to inadequate measurements. Traditionally, lake water level is measured at a

gauge station established near the lake shore while snow accumulation is recorded by a weather

station or field survey. Due to the high cost of installation and maintenance, particularly for the

Arctic regions with harsh environmental conditions, the number of gauge and weather stations

tends to be very small. These stations are usually very sparse and only cover very limited areas.

Dedicated field expeditions focused on snow surveys may cross over a large area, but they are

temporally sporadic and conducted only along the expedition routes. Consequently, no long-term

and dense in situ observations of lake water level and lake snow accumulation are available for the

regional hydrologic and the climatic analysis.

Some efforts have been made to derive snow depth information using remote sensing

technology. Snow radar is a microwave frequency-modulated altimeter implemented in the

Operation IceBridge program. It operates over a very wide frequency range 2 – 8 GHz and can

estimate snow depth over ice surfaces by tracking the positions of snow/air and snow/ice interfaces

(Brucker and Markus 2013; Farrell et al. 2012; Galin et al. 2012; Kanagaratnam et al. 2007; Kurtz and Farrell 2011). However, most of these data were collected for selected areas in Greenland and

Antarctica, and no such data are available elsewhere. Passive microwave remote sensing (e.g.

SSM/I, SMMR, ASMR-E), has also been used to retrieve snow depth information on land surface based on the difference in brightness temperatures at two microwave channels (e.g. 19 and 37

GHz) (Chang et al. 1987; Derksen et al. 2005; Foster et al. 2005a; Green et al. 2012; Markus et al.

2006). But the spatial resolution of passive microwave data is too coarse (e.g. 25 km for SSM/I)to

provide accurate snow accumulation measurements for the Arctic coastal regions where seasonally

frozen lakes are abundant.

Satellite radar and laser altimetry measures elevation profiles of Earth’s surface at the

global scale. They offer an alternative way to measure the lake water levels. There have been

thirteen satellite radar altimetry missions since 1985 including Geosat, Geosat Follow-on, ERS-1

and -2, Envisat, Topex/Poseidon, Jason-1, -2 and -3, Cryosat-2, Saral/Altika, HY-2A and Sentinel-

3. Sentinel-3 is the most recent satellite mission launched on 16 February 2016 and is the second satellite mission with a Synthetic Aperture Radar Altimeter (SRAL) onboard. Numerous studies have investigated the application of satellite radar altimetry data in the monitoring of lake water levels (Birkett 1995; Birkett and Beckley 2010; Frappart et al. 2006a; Frappart et al. 2015; Göttl et al. 2016; Kleinherenbrink et al. 2014; Morris and Gill 1994b; Nielsen et al. 2015; Santos da

Silva et al. 2010; Villadsen et al. 2016). However, most of these studies focused on lakes at low or middle latitudes, and few of them explored the applicability of satellite radar altimetry data over high-latitude seasonally frozen lakes.

ICESat/GLAS is the first satellite laser altimetry mission, which operated during the period of 2003 – 2009. With a relatively small footprint and precise vertical elevation measurements,

ICESat/GLAS provides the possibility of measuring snow depth over relatively flat surfaces through tracking the surface elevation changes in the winter season. Bindshadler(2005) estimated the new snow accumulation in one snowfall event on Antarctic ice sheet using the elevation differences at intersections (or crossovers) of ICESat overpasses before and after the event.

Treichler(2017) derived the snow accumulation in a mountainous region in southern Norway using the elevation difference between ICESat and three Digital Elevation Models (DEM). To our best of knowledge, there is no other study that explores the possibility of deriving snow accumulation

for the Arctic regions, particularly the snow accumulation on lake surfaces. This research investigate the capability of different satellite radar and laser altimetry missions in the monitoring of lake water levels and snow accumulations in Arctic coastal regions.

Chapter 2 analyzes the performances of Sentinel-3 SAR altimetry observations over inland lakes, particularly the performances over seasonally frozen Arctic lakes. SRAL is a dual-frequency

SAR Radar ALtimeter onboard the Sentinel-3 satellite. It is a new generation of satellite radar altimeter system that produces densely sampled elevation measurements (along-track ~300m) for different types of Earth’s surfaces since June 2016. The SAR altimetry waveform is quite different from the waveform produced by conventional altimeters. Four retracking algorithms (or retrackers) have been designed specifically for the SAR waveform to retrieve elevations for different types of surfaces. Those include Ice-Sheet retracker for ice sheet surfaces, Ocean retracker for open seas, OCOG retracker for general ice surface or sea ice margins, and Sea-Ice retracker for sea ice surfaces. None of them were specially intended for inland waters. In this chapter, an assessment of the performances of these four different retrackers is conducted for inland lakes, particularly for seasonally ice-covered lakes. We select fifteen lakes with variable sizes and at different latitudes for the assessment. Each retracker is evaluated by comparing the time series of retrieved water levels with the concurrent in situ gauge observations. The results show that Ice-Sheet, OCOG and Ocean exhibit similarly strong capability of monitoring water levels. The average RMS for the three retrackers across the fifteen lakes are 0.11 m, 0.12m and

0.11 m, respectively. Over ice-covered lakes, the water levels produced by the SAR retrackers deviate from the gauged water levels and the errors increases as the lake ice thickens over winter.

We developed a new empirical retracking algorithm which significantly improves the

measurements and is capable of providing more reliable and consistent water level estimates for

the ice-covered lakes.

Chapter 3 presents a new probabilistic relaxation algorithm to improve the ICESat

elevation measurements in Arctic regions. ICESat elevation measurements are derived from the

retracking analysis of the returned waveforms, which are the densely sampled laser energy of

returned pulses over time represented as curves. Two standard retracking schemes have been

designed and applied to the processing of the returned laser signal waveforms for different types

of Earth’s surfaces. The “Centroid” retracking scheme is used for terrestrial land surfaces, while

the “Maximum-Amplitude-Peak” (MAP) scheme is applied to ice sheets, sea ice and ocean

surfaces. Although the two schemes work well for the different types of surfaces in general, they

may generate erroneous measurements when the returned signal waveform is complicated and

deformed by adverse atmospheric condition (thin clouds), bad weather phenomena ( ice fog,

blowing snow, and dust storms), heterogeneous and complex terrain features within the footprint,

or strong data noises. In particular, the “Centroid” scheme is often more severely affected as compared to the MAP scheme. In this chapter, we present a new retracking method that exploits the spatial contextual information from neighboring footprints along the satellite ground track, in addition to the waveform geometric information as used in the standard MAP retracking method.

Our method utilizes a probabilistic relaxation algorithm to integrate the spatial contextual

information with the waveform geometric information to identify the waveform peak that most

likely represents the true surface elevation, rather than simply detecting the peak with the largest

magnitude as is the case with the standard procedure. Our analysis demonstrates that the new

probabilistic relaxation retracking method is able to correct the measurement errors given by the

standard MAP retracking method and produce much more reasonable and accurate elevation

measurements. We also show that our probabilistic relaxation based retracking method provides

better measurements for some specific types of land surface (such as inland lakes, coastal stretches,

desert or sand dunes, etc.) than the standard ICESat products created by the “Centroid” retracking

method.

Chapter 4 introduces a novel method to derive snow accumulations for Arctic regions

through tracking the surface elevation changes of numerous frozen arctic lakes measured by

ICESat repeat altimetry observations. Time-variable biases exist between the repeat elevation measurements acquired in different ICESat campaigns. The correction of these inter-campaign biases in this study significantly improves the quantification of the surface elevation change detected by the corrected repeat ICESat measurements, thus enabling more consistent subsequent snow accumulation estimates. Besides snow fall, the lake surface rises owing to the phase transformation from water to ice also contributes to the surface elevation change. We developed a method to measure and remove this contribution from the total lake surface elevation change, which leads to more accurate estimates of snow accumulation on frozen surfaces of 277 lakes in

Arctic regions. The results were validated using in situ snow depth observations from terrestrial stations on the Arctic coastal plain. The snow accumulation derived from the processed ICESat elevation measurements are highly correlated with in situ snow depth observations. The final R2

and RMSE are 0.77 and 5 cm, respectively, with the corrections of the ICESat inter-campaign biases and also the removal of contribution by lake surface phase transformation. Our method makes it possible to provide much denser snow depth information as compared to the existing in situ observations for Circum-Arctic coastal regions and also the Qinghai-Tibet Plateau where seasonally frozen lakes are abundant.

Chapter 2: Analysis of Sentinel-3 SAR Altimetry Waveform

Retracking Algorithms for Deriving Temporally Consistent Water

Levels over Inland Lakes

2.1 Introduction

About four percent of the Earth’s non-glaciated land surface is covered by about 117

million lakes (Verpoorter et al. 2014). These lakes provide habitats for numerous species

(Schindler and Scheuerell 2002) and the most accessible freshwater resources r for human

domestic, agricultural, and industrial activities (Postel et al. 1996). Monitoring the lake water

dynamics is important for water resource management and ecosystem service assessment. Lake

water levels, particularly those high-latitude lakes, are very sensitive to the regional and the global

climate changes (Ghanbari and Bravo 2008; Gibson et al. 2006). To understand the impact of

climate changes and anthropogenic activities on the fresh water resources, it is necessary to obtain

the information about the seasonal and inter-annual variability of the lake water levels.

Traditionally, lake water levels are measured at gauge stations established near lake shores.

However, most of the lakes remain ungauged and many of the basic hydrologic parameters, e.g.

the magnitude of seasonal cycle and the long-term water level variation, are largely unknown. In particular, there is a widespread decline in the networks of gauge stations in most part of the world due to the cost of installation and maintenance as well as management issues (Center 2008; Fekete and Vörösmarty 2002; Hannah et al. 2011; Shiklomanov et al. 2002).

Satellite radar altimeters measure the Earth surface elevation from space and have been used to monitor water levels for the lakes where no gauge stations are available. A satellite radar

altimeter emits a series of radar pulses towards the Earth’s surface and accurately measure the

range between satellite and the reflecting surface by tracking the time delay between the emission

and reception of the radar pulse. The elevation measurement is then jointly determined by the

range and the satellite position above the reference ellipsoid. The emitted and the returned radar

pulses are recorded as pulse power over time, which is referred to as “waveform”. The time elapsed

between the emission and the reception is precisely calculated by identifying the reference points

on the emitted and the returned altimeter waveforms.

There have been thirteen satellite radar altimetry missions since 1985, including Geosat

(1985 – 1989), Geosat Follow-on (1998 – 2008), ERS-1 (1991 – 2000) and ERS-2 (1995 – 2011),

Envisat (2002 – 2012), Topex/Poseidon (1992 – 2005), Jason-1 (2002 – 2013), Jason-2 (2008 –

present) and Jason-3 (2016 – present), Cryosat-2 (2010 – present), Saral/Altika (2013 – present),

HY-2A (2011 – present) and Sentinel-3 (2016 – present). Most of these satellite missions utilized

the conventional pulse-limited radar altimeter to make elevation measurements of Earth surface.

The effective footprint diameter of satellite pulse-limited radar altimeters ranges from 1.6 km to

13.4 km, depending on the radar pulse duration, the altitude of the satellite orbit, and the roughness

of the reflecting surface (Chelton et al. 1989). A great number of studies have evaluated the performances of these conventional pulse-limited altimeters in the retrieval of lake/river level variations (Asadzadeh Jarihani et al. 2013; Birkett 1995; Birkett and Beckley 2010; Frappart et al.

2006b; Frappart et al. 2015; Morris and Gill 1994a, b; Schwatke et al. 2015). The accuracy of altimetry-derived lake/river levels is largely affected by the target size, the topographic undulation of the reflecting surface, and the environment surrounding the target (Birkett and Beckley 2010;

Maillard et al. 2015). The root mean square error (RMS) of the altimetry-derived lake levels as compared to gauge data can degrade from several centimeters for large lakes to meters for small

lakes (Birkett et al. 2011; Birkett 1995; Birkett and Beckley 2010), owing partly to a reduced number of measurements over the small lakes and partly to the radar pulse contamination by the variable terrain surfaces within the relatively large altimetry footprint.

The advent of ESA’s Cryosat-2 mission has marked a new era of satellite radar altimetry.

The CryoSat-2 satellite measures the Earth surface elevation with a synthetic aperture interferometric radar altimeter. It employs the along-track beam formation to generate a much smaller footprint strip (about 300 m along track and 1 km cross track), compared with the circular footprint (~ 10 km diameter) of the conventional pulse-limited altimeters (Wingham et al. 2006).

The reduced size of the footprint strip enables the water level retrieval for inland water bodies with a relatively small size and increases the accuracy of water level estimates (Nielsen et al. 2017;

Villadsen et al. 2016).

The Sentinel-3 mission is a constellation of two identical satellites: the Sentinel-3A launched on February 16, 2016, and Sentinel-3B launched on April 25, 2018. Each satellite has a repeat cycle of 27 days with a sub-cycle of ~4 days (Donlon et al. 2012). With a high-inclination

(98.65°) polar orbit, Sentinel-3A/B provide global altimetry coverage up to 81.35° latitude

(Donlon et al. 2012). A Synthetic Aperture Radar Altimeter (SRAL) instrument is one of the three primary payloads onboard each satellite. The SRAL is a dual-frequency altimeter that employs a primary Ku-band (13.575 GHz) to measure the distance between the satellite and Earth’s surface, and uses a secondary C-Band (5.41 GHz) to correct the range delays due to the ionosphere. The

SRAL can operate at two modes: the Low Resolution Mode (LRM) and the Synthetic Aperture

Radar (SAR) mode. In the LRM mode, the SRAL works as a conventional pulse-limited radar altimeter. In the SAR mode, it employs SAR technology inherited from Cryosat-2 to increase the along-track sampling resolution (~300 m) and elevation measurement accuracy (Donlon et al.

2012). The shape of the SAR altimetry waveform echoed from a flat surface differs significantly

from the classic shape of conventional pulse-limited radar altimetry waveform (Phalippou and

Enjolras 2007; Raney 1998; Ray et al. 2015). After Doppler processing, the SAR waveform has an impulse-like shape, in contrast to the step-function shape of a conventional pulse-limited radar waveform (Raney 1998).

Seven waveform retracking algorithms (“retrackers”) have been developed to determine accurate elevations for different types of surfaces and for different operating modes of Sentinel-3 altimeter (MSSL/UCL/CLS 2015). The retrackers implemented for the LRM mode include Ocean-

3 for ocean surfaces, OCOG for ice surfaces, ICE for the ice caps, and MLE4 for the ice sheets. In the SAR mode, the retrackers include SAMOSA-3 for ocean surfaces, OCOG for sea-ice margins,

Ice-Sheet for ice sheets, and Sea-Ice for sea ice surfaces. The LRM retrackers were inherited from

conventional pulse-limited satellite radar altimetry missions, i.e., Envisat mission (Frappart et al.

2006a). The SAR retrackers, however, were developed using completely new analytical waveform models (Dinardo et al. 2015; Jain et al. 2014) or by modifying the conventional retrackers to account for the differences between the conventional pulse-limited waveform and the SAR altimetry waveforms.

It should be noted that none of the retrackers above were specially designed for inland waters. The performance of the LRM (or conventional) retrackers over inland waters have been evaluated in previous studies (Frappart et al. 2006a; Santos da Silva et al. 2010). However, until

now no research effort has been reported to assess the performances of SRAL SAR retrackers in

the retrieval of water levels over inland lakes. Particularly, a large quantity of lakes are distributed

between 45°N and 75°N latitudes (Verpoorter et al. 2014). Those high-latitude lakes are covered

by ice in winters and the ice-cover duration and thickness vary depending on the latitudes (Surdu

et al. 2014; Weyhenmeyer et al. 2004). It has been reported that the presence of lake ice could cause biases in the radar altimetry range and lead to unreliable estimates of lake water levels

(Birkett 1995; Birkett and Beckley 2010). The common practice is to identify and exclude the

observations acquired in the water-frozen season, leading to the discontinued lake level measurements. The derivation of temporally consistent and continuous water levels for high- latitude lakes in all seasons entail the development of a new robust retracker that can address the ice cover influences.

In this research, we aim to evaluate the performances of different SRAL SAR retrackers in retrieving inland lake water levels, assess the effect of the lake ice cover on the returned SAR altimetry waveforms and associated measurement error in lake level retrieval, and develop a new empirical bimodal retracker capable of generating the reliable water-equivalent lake level estimates for the ice-covered lakes in winter seasons. The remainder of this paper is organized as follows. Section 2.2 describes the case study lakes and the in situ datasets utilized in this study.

Section 2.3 introduces the SRAL data products, the SRAL SAR retrackers and our new empirical bimodal retracking algorithm. Section 2.4 evaluates the performances of SRAL SAR retrackers by comparing their lake level estimates with the in situ gauge measurements over 15 lakes with different ice cover conditions. The influences of lake ice on the echoed SRAL SAR altimetry waveform and the performance of our new bimodal retracking algorithm over ice-covered lakes are examined in details. In Section 2.5, we summarize the research findings and draw some conclusions.

2.2 Case study lakes and in situ water level measurements

2.2.1 Case study lakes and their winter ice conditions

In this study, we selected 15 inland lakes and reservoirs (Figure 2.1) from four countries to

assess the measurement accuracy of SRAL SAR retrackers. Among these lakes, Reservoir

Porttipahta in Finland is the smallest with a surface area of 205.6 km2, and Lake Superior in North

America is the largest with a surface area of 81935.7 km2. Table 2.1 lists the geographical locations of the 15 case study lakes, and associated information about the gauge stations and the

Sentinel-3 ground tracks. The lake boundary polygons from the Global Lakes and Wetland

Databases (GLWD) (Lehner and Döll 2004) are used as masks to extract SRAL SAR altimetry measurements over these lakes for the subsequent analysis.

Depending on the latitude, these lakes experienced varying ice conditions in the 2016–

2017 winter. Four lakes in Finland and one lake in Sweden are located between 59° N and 69° N latitudes on the Fenno-scandinavia Peninsula. (Table 2.1 and Figure 2.1). The four lakes/reservoir in Finland are fully ice-covered in winter, and the dates of lake freeze-up and breakup correlate nonlinearly with the air temperature gradient from north to south (Weyhenmeyer et al. 2004). At

69°N latitude, the freeze-up and breakup occur usually on early November and late June, respectively (Lei et al. 2012), while at 59°N latitude, the freeze-up and breakup often happen in late November and middle May, respectively (Karetnikov and Naumenko 2011). Lake Vanern in

Sweden remained completely ice-free during the 2016-2017 winter, although it was ice-covered

in nine winters from 1979 to 2002 (Weyhenmeyer et al. 2008).

Due to the relatively high latitude, Great Slave, Athabasca and Cedar lakes in Canada are

fully ice-covered in winters, and the ice cover duration of Great Slave Lake could be longer than

five months (Howell et al. 2009). Ice coverage and duration of the Great Lakes (Superior, Huron,

Ontario, Erie and Michigan) vary depending on the average air temperature in winters (Assel 2003;

Assel et al. 2013; Wang et al. 2012a). In the relatively cold winters (i.e. 2008/2009), Lake Superior

and Lake Erie can be fully covered by ice for 1 – 2 weeks, while Lake Huron, Lake Ontario, and

Lake Michigan are partly covered by ice(Assel and Wang 2017). In relatively warm winters (e.g.,

2016/2017), all of the five Great Lakes are partly covered by the ice(Assel and Wang 2017). Lake

Okeechobee in Florida and the Salton Sea in California are both located at very low latitudes and are completely free from ice cover throughout the year.

Based on the Great Lakes Ice Cover Data (Assel and Wang 2017) and visual interpretation of Landsat-8 remote sensing images acquired between November 1, 2016 and June 1, 2017, we determined the ice cover condition of all the case study lakes in the winter of 2016/2017 (Table

2.1).

Table 2.1 Winter ice cover, gauge stations and Sentinel-3 ground tracks in the case study lakes

Sen-3 Lake Gauge Station Area Winter ice ground Vertical Distance to Name Country Lat(°) Lon(°) Name (km2) cover tracks datum track (km)

1 Inarijarvi 69.02 27.89 1184 Fully 271, 566 Nelim N2000 19.6

2 Porttipahta 68.09 26.54 205 Fully 271 Porttipahta N2000 12.2 Finland 3 Lokan 67.96 27.63 487 Fully 385 Lokan N2000 18.9

4 Oulujarvi 64.35 27.21 889 Fully 71, 652 Vaala N2000 14.5

5 Vanern Sweden 58.91 13.30 5550 None 357, 682 Vanern RH00 7.4

6 Great Slave 61.80 -113.82 27816 Fully 37, 681 YellowKnife CGVD28 18.9

7 Athabasca Canada 59.18 -109.34 7781 Fully 54, 493 CrackingStone CGVD28 10.0

8 Cedar 53.34 -100.16 2817 Fully 109, 765 Oleson Point CGVD28 28.5

9 Superior 47.54 -87.76 81935 Partly 165, 548 Grand Marais IGLD85 29.3

10 Huron US & 44.96 -82.26 59756 Partly 421, 576 Harbor Beach IGLD85 21.4

11 Ontario Canada 43.67 -77.76 19328 Partly 107, 148 Olcott IGLD85 5.8

12 Erie 42.16 -81.24 25691 Partly 576, 649 Fairport IGLD85 12.5

13 Michigan 44.01 -86.76 57399 Partly 662, 735 Calumet Harbor IGLD85 57.7

14 Salton Sea US 33.30 -115.83 929 None 624 Westmorland NGVD1929 10.3

15 Okeechobee 26.95 -80.81 1436 None 225 Okeechobee NGVD1929 11.2 * The area and location coordinates are from the Global Lakes and Wetlands Database (GLWD) (Lehner and Döll 2004). The distance of a gauge station to Sentinel-3 ground tracks is the length of the straight line between the gauge station and the nearest SRAL SAR measurement point.

Figure 2.1 Geographic distribution of the case study lakes

2.2.2 In situ water level and ice thickness measurements from gauge stations

Lake water level measurements from in situ gauge stations are obtained from five online sources. The in situ gauge data are provided by Finish Environment Institute (SYKE)’s environmental information management system – Hertta (http://www.syke.fi/fi-

FI/Avoin_tieto/Ymparistotietojarjestelmat) for four Finnish lakes, by the Swedish Meteorological and Hydrological Institute (SMHI) (http://vattenwebb.smhi.se/station/) for Lake Vanern, by the

Environment and Climate Change Canada Real-time Hydrometric Data Website

(https://wateroffice.ec.gc.ca/mainmenu/real_time_data_index_e.html) for the Canadian lakes, and by NOAA’s Center for Operational Oceanographic Products and Services

(https://tidesandcurrents.noaa.gov/) and the USGS National Water Information System

(https://waterdata.usgs.gov/nwis) for US lakes. As listed in Table 2.1, water levels measurements

collected at gauge stations are referenced to different local vertical datum for different countries.

Due to the lack of critical information of the local vertical datum used by Canada, Finland, and

Sweden, only the in situ water level measurements at US gauge stations have been referenced to

the geoid EGM2008 for the consistency with Sentinel-3 SRAL elevation measurements, using the

vertical datum transformation tool VDatum provided by NOAA (https://vdatum.noaa.gov/).

Two types of instruments are usually used at gauge stations to measure lake water levels:

the Float-Actuated System (FAS) and the Pressure-Actuated System (PAS) (Forrester 1983;

Turgeon 1999). The FAS uses a float actuated sensor to measure the water level of a stilling well

that is connected to the bottom of a lake through an intake pipe. The FAS is usually equipped with

a heater to prevent surface water in the well from freezing in winter. When the installation of a

stilling well is impractical, the PAS is used to measure the water level through a pressure sensor,

which is located below the water surface where surface ice cannot reach. Both FAS and PAS

instruments are able to record the water-equivalent lake level in winter when the lake is covered by ice.

The in situ ice thickness data on Lake Inarijarvi and Great Slave Lake are provided respectively by SYKE Hertta system and the Canadian Ice Service Archive

(https://www.canada.ca/en/environment-climate-change/services/ice-forecasts-

observations.html). The ice thickness records are available for Lake Inarijarvi from 1961 to present

and for Great Slave Lake from 1958 to 2016. The in situ measurements are collected at locations

close to shore where the water depth exceeds the maximum ice thickness and are on an

approximately weekly basis when the ice cover is safe to walk on. The ice thickness is measured

to the nearest centimeter with a special auger kit or a hot wire gauge.

2.3 Derivation of Sentinel-3 SRAL SAR lake water level estimates

2.3.1 SRAL data products

The SRAL instrument works at two modes. The LRM mode is intended for the surfaces with homogeneous and smooth topography, e.g. open-ocean and smooth ice sheet. The Pulse

Repetition Frequency (PRF) of Ku band is 1.92 KHz and the footprint diameter over smooth

surface is about 1.6 km at this mode (Sentinel-3-Team 2017). In the SAR mode, the SRAL

instrument is able to measure the surface elevations at a high along-track resolution (~300m),

which greatly improves the retrieval of elevations over more variable surfaces, e.g. the inland

waters, the terrestrial land surfaces and the coastal areas. The PRF of Ku band at this mode is 18

KHz, much higher as compared to LRM mode. For inland waters, the surface elevations are

collected only in the SAR mode, and no LRM altimetry data are available. The SRAL is also

supported by a dual-frequency passive microwave radiometer (MWR) for the correction of delay

due to the wet tropospheric attenuation of Ku-band signal. The MWR with two channels at 23.8

GHz and 36.5 GHz provides measurements of the surface brightness temperature, which is

sensitive to the growth of lake ice.

Three types of SRAL level-2 data products are provided to meet different delivery time

requirements (ACRI-ST and Telespazio-VEGA 2015). The Near Real-Time (NRT) product,

delivered usually within 3 hours after the acquisition, contains very basic geophysical information

and is intended for marine meteorology and ocean-air gas transfer studies. The Short Time Critical

(STC) product, processed together with more accurate auxiliary information, is disseminated

within 48 hours after the acquisition. The Non-Time Critical (NTC) product, typically delivered

within 1 month after the data acquisition, is created through the most precise geophysical

corrections derived from state-of-the-art models, e.g. the wet and the dry tropospheric corrections,

the tidal corrections, and the ionospheric corrections. In this study, the NTC products acquired between June 15, 2016 and September 30, 2017 are used to retrieve lake water levels for a whole annual hydrologic cycle.

The NTC product contains three data files, including the “reduced”, “standard”, and

“enhanced” data files (Sentinel-3-Team 2017). The “reduced” file contains only a subset of the 1

Hz Ku-band parameters. The “standard” file contains almost all the 1Hz and 20 Hz Ku-band and

C-band parameters. The “enhanced” data file also contains the waveforms and the associated

parameters necessary for the reprocessing of the waveform, besides the “standard” parameters. We

utilized the “enhanced” data in the following analysis.

Satellite radar altimetry measures surface elevation by emitting a radar pulse towards the

Earth’s surface and then receiving the echo. The surface elevation is determined by satellite orbital

position and the range between satellite and the reflecting surface, as shown in Equation (1):

= + + + + (1)

ℎ𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝐻𝐻 − 𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − �∆𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∆𝑅𝑅𝑤𝑤𝑤𝑤𝑤𝑤 ∆𝑅𝑅𝑑𝑑𝑑𝑑𝑑𝑑 ∆𝑅𝑅𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ ∆𝑅𝑅𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝� − 𝐺𝐺2008 = + (2)

𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑅𝑅𝑡𝑡𝑡𝑡𝑡𝑡 𝜏𝜏𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 where is the surface elevation, H is the height of the satellite above the reference ellipsoid

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 WGS1984,ℎ is the tracker range given by the nominal tracking point on the waveform, the

𝑡𝑡𝑡𝑡𝑡𝑡 epoch 𝑅𝑅 is determined by a specific retracking algorithm, , , ,

𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤 𝑑𝑑𝑑𝑑𝑑𝑑 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ and 𝜏𝜏 are the corrections that account for the range biases∆𝑅𝑅 induced∆𝑅𝑅 by ionosphere,∆𝑅𝑅 ∆𝑅𝑅 wet and

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 dry troposphere,∆𝑅𝑅 solid Earth tide and pole tide, respectively, represents the geoidal correction

2008 between the Sentinel-3 reference ellipsoid WGS1984 and the𝐺𝐺 geoid model EGM2008.

The range between satellite and the reflecting surface is calculated by tracking the time

delay between the emission and the reception of the radar pulse. The reception time of the returned

radar pulse is initially computed using a fixed nominal tracking point on the returned waveform,

known as nominal tracker. The range given by the nominal tracker is referred to as the tracker

range (Rtrk). A specific algorithm is developed for a certain type of surface to pin up another point

on the waveform that corresponds to the best representation of the surface response to the incident

radar pulse. The algorithm is referred to as a retracker, and the point pinned up by the retracker is

known as the retracking point. The epoch (τretrk) denotes the relative distance of the retracking point

with respect to the nominal tracking point. The correction of the tracker range Rtrk by adding the

epoch (τretrk) yields the retracked range (Rretrk), which helps produce more accurate elevation

measurement for that type of surfaces.

Since inland lakes are closed water systems as compared to open oceans, the ocean tides

and sea state biases are not considered in the range correction calculation. The SRAL level-2

“enhanced” data file provides and at 20 Hz, while the other geophysical correction terms

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 are given at 1 Hz. The 1 Hz geophysical𝐻𝐻 𝑅𝑅 correction terms are linearly interpolated to match and

measurements at 20 Hz. The “enhanced” data file offers two types of ionospheric𝐻𝐻

𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟𝑟𝑟 corrections:𝑅𝑅 the dual-frequency (Ku/C band) retrieved correction and the model-derived correction.

Since the dual-frequency ionospheric correction might be hampered by land contamination of the

C band signal (Fernandes et al. 2014), this study adopts the correction derived from global ionosphere map (GIM) model. The “enhanced” data file contains two types of dry and wet

corrections derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) model. The first type of correction is computed at the sea level height (0 m altitude), while the second type is computed at lake surface height. It has been demonstrated that the wet and the dry tropospheric corrections have strong dependence on the surface height (Birkett et al. 2011; Crétaux et al. 2009; Fernandes et al. 2014). We use the second type of correction to calculate the lake surface elevations.

2.3.2 SRAL SAR waveform and SAR retrackers

The SRAL instrument records the strength of each radar echo on 128 consecutive gates

(waveform bins) (Donlon et al. 2012). The time interval between two adjacent waveform gates is

decided by the pre-defined radar bandwidth (Chelton et al. 1989). The bandwidth for SRAL Ku

band is 320 MHz (Fletcher 2012) and the effective time interval between two adjacent waveform

gates is 3.125 ns, which can be translated into a one-way range resolution of ~46.84 cm. The

nominal tracking gate (nominal tracker) used by SRAL is gate 43 (counting from 0) (personal

communication with Copernicus EO Support, 2017), instead of the common adoption of the central

gate position, e.g. gate 63 for Envisat (ESA 2007). The shape of the SAR altimetry waveform

differs significantly from the conventional pulse-limited radar altimetry waveform (LRM

waveform). Figure 2.2a shows a typical SRAL SAR altimetry Ku-band waveform and Figure 2.2b

shows a conventional pulse-limited radar altimetry Ku-band waveform returned from open water

surface. The SAR altimetry waveform has an impulse-like shape, in which the returned radar signal has a much faster decay rate after its initial rise to the peak power. This makes a strong contrast to a step-function shape of the conventional pulse-limited altimetry waveform (Raney 1998).

Figure 2.2 Radar altimetry waveforms echoed from the open water surface of Great Slave Lake in Canada. (a) SAR waveform acquired by Sentinel-3 SRAL on August 23, 2016; (b) Conventional pulse-limited altimetry waveform acquired by Envisat on August 11, 2002.

Four retracking algorithms have been developed for retracking Sentinel-3 SRAL SAR waveform, including OCOG retracker for sea-ice margins, Ice-Sheet retracker for ice sheet surfaces, Sea-Ice retacker for sea ice surfaces, and SAMOSA-3 retrcaker for open ocean and coastal zones (MSSL/UCL/CLS 2015).

The OCOG retracker, also known as Ice-1 retracker in previous satellite radar altimetry missions, is a model-free tracker based on the Offset Center of Gravity method developed by

Wingham (1986). It was demonstrated that this retracker gives the best estimates for inland water levels among the four conventional retrackers (Ice-1, Ice-2, Ocean and Sea-Ice) used by previous pulse-limited radar altimetry missions (Frappart et al. 2006a). It first estimates the amplitude of the returned waveform using Equation (3):

( [ ]) = (3) 𝑛𝑛−1( [ ])4 ∑𝑖𝑖=0 𝑤𝑤 𝑖𝑖 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑛𝑛−1 2 where P is the amplitude of the returned𝑃𝑃 waveform,�∑𝑖𝑖=0 𝑤𝑤 𝑖𝑖 n is the number of waveform gates, and

OCOG [ ] is the waveform power above background thermal noise at gate i.

𝑤𝑤 𝑖𝑖 Then, it determines the retracking point through finding the position on the waveform

where the waveform power exceeds a predefined threshold through Equation (4):

[ 1] = ( 1) + (4) [ ] [ 1] 𝑤𝑤𝑡𝑡ℎ𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑜𝑜𝑜𝑜𝑜𝑜−𝑤𝑤 𝑖𝑖𝑒𝑒− 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑒𝑒 where is the retracking point𝑖𝑖 between𝑖𝑖 − gate 𝑤𝑤 𝑖𝑖𝑒𝑒 −1𝑤𝑤 𝑖𝑖and𝑒𝑒− gate , is the first gate that

𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑒𝑒 𝑒𝑒 𝑒𝑒 waveform𝑖𝑖 power exceeds the threshold 𝑖𝑖 .− For Sentinel𝑖𝑖-3 𝑖𝑖SAR OCOG retracker

𝑡𝑡ℎ𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑜𝑜𝑜𝑜𝑜𝑜 equals to 100% of (MSSL/UCL/CLS𝑤𝑤 2015), while for Envisat Ice-1 retracker

𝑡𝑡ℎ𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑜𝑜𝑜𝑜𝑜𝑜 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑤𝑤 is 25% of the amplitude𝑃𝑃 (Frappart et al. 2006a).

𝑤𝑤𝑡𝑡ℎ𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑜𝑜𝑜𝑜𝑜𝑜 𝑃𝑃𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 31

The Ice-Sheet retracker, inherited from the Cryosat-2 mission (MSSL/UCL/CLS 2015), fits a semi-analytical model to the SAR waveform using Levenbert-Marqhart’s method (Press et al. 2007). The semi-analytical model is in the form of a modified Gaussian function given by

Equation (5):

( ) = ( ) (5) −𝑓𝑓 𝑡𝑡 where is a coefficient associated with the𝑤𝑤 𝑡𝑡estimation𝑎𝑎𝑒𝑒 of the waveform amplitude, is the time delay, 𝑎𝑎( ) is a 5-part piecewise function where each part addresses one region of the echoed𝑡𝑡 SAR waveform𝑓𝑓 𝑡𝑡 (MSSL/UCL/CLS 2015). ( ) corresponds to the section before the leading edge,

1 ( ) addresses the first part of the leading𝑓𝑓 𝑡𝑡 edge, ( ) describes the second part of leading edge,

2 3 𝑓𝑓 (𝑡𝑡) represents the linking region between the leading𝑓𝑓 𝑡𝑡 edge and the trailing edge, and ( ) traces

4 5 the𝑓𝑓 𝑡𝑡trailing edge. 𝑓𝑓 𝑡𝑡

The Sea-Ice retracker for Sentinel-3 SAR waveform is quite different from the conventional Sea-Ice retracker that adopts a simple threshold of half the waveform amplitude to determine the epoch (ESA 2007; Laxon 1994).The SAR Sea-Ice retracker, as a simplified version of the Sentinel-3 Ice-Sheet retracker above, divides the SAR waveform into three segments: the leading edge, the linking region, and the trailing edge. The leading edge is modelled with a

Gaussian function. The trailing edge is fitted with an exponentially decreasing function. The linking region is described using Equation (5) with ( ) as a third order polynomial function

(MSSL/UCL/CLS 2015). 𝑓𝑓 𝑡𝑡

The SAMOSA-3 retracker fits the echoed waveform with a fully-physical SAR waveform model developed based on the basic Delay-Doppler processing principles for SAR altimeter

(Raney 1998). This model describes the SAR waveform as a convolution of three terms

(MSSL/UCL/CLS 2015) as shown in Equation (6):

w(t, f ) = P (t, f ) S (t, f ) ( )P ( ) (6) c ct where ( , ) represents the flat surfaced FS impulsed ⊗ response,R d ⊗ (2 , Z )2 is the radar system point

𝐹𝐹𝐹𝐹 𝑑𝑑 𝑅𝑅 𝑑𝑑 target 𝑃𝑃response,𝑡𝑡 𝑓𝑓 ( ) is the surface probability density𝑆𝑆 function𝑡𝑡 𝑓𝑓 (Berry et al. 2012; 𝑐𝑐𝑐𝑐 𝑍𝑍 2 MSSL/UCL/CLS 𝑃𝑃2015), is the time delay, is the speed of light, and is the Doppler

𝑑𝑑 frequency. The outputs of𝑡𝑡 the SAMOSA-3 retracker𝑐𝑐 includes the epoch (𝑓𝑓τ), the waveform amplitude (P), significant wave height (SWH), surface RMS slope, skewness and mis-pointing angles (Dinardo et al. 2015).

All the SAR retrackers above assume that the echoed waveform has one dominant peak.

The leading edge of this dominant peak represents the reflection of radar pulse energy by the surface within SRAL SAR footprint. Except for OCOG retracker, the other three SAR retrackers use the mid-height point of the leading edge given by the fitting process as the retracking point to compute the epoch (τ), then refine the range estimates for different types of surfaces. The mid- height point of the leading edge represents the mean elevation of lake surface within the footprint illuminated by SRAL SAR signal pulse.

2.3.3 A new bimodal retracker for the retrieval of water-equivalent lake surface elevation over ice-covered lakes

For lakes located at high latitudes, the lake surface turns from water to ice and then back

to water again in a full phenological cycle. Our analysis indicates that the shape of SRAL SAR

waveform returned from high-latitude lakes can be significantly influenced by the ice cover on

these lakes. During the winter when lake surface is covered by very thick ice, the returned

waveforms can have two distinct peaks (not the assumed single peak): the first one generated by

the top snow/ice interface and the second one generated by the bottom ice/water interface. These

bimodal waveforms often fail the SRAL SAR retrackers, resulting in lower lake surface elevation

than the real values. In this study, we develop a new empirical bimodal retracker that can overcome

the influence of thick lake ice and provide consistent estimates of true water-equivalent lake surface elevation for the ice-covered lakes in winter season. More details of lake ice influences on

the shape of SRAL SAR waveform and on the estimation of lake surface elevation will be

presented in Section 2.4.

The presence of lake ice is detected using the simultaneous radiometric measurements of

lake surfaces through the onboard microwave radiometer MWR. The MWR radiometer measures

the brightness temperature of lake surfaces at two channels, 23.8 GHz and 36.5 GHz. The

brightness temperature (TB) can be expressed as a product of the emissivity (ε) and the physical

temperature (TS) of the measured surface (Foster et al. 1984; Liu et al. 2005). The emissivity

increases greatly as lake surface transforms from the phase of liquid water to the phase of ice when

lake water temperature drops below 0 °C (Hewison 2001; Hewison and English 1999; Kang et al.

2010), leading to a rapid increase of TB. Therefore, the temporal variation of TB is a sensitive

indicator for the detection of lake ice cover (Kang et al. 2010).

When the lake is covered by thick ice and the returned waveform has two peaks (bimodal

waveform), the water-equivalent lake surface elevation ( ) can be estimated using the following

𝑊𝑊𝑊𝑊 equation: ℎ

= ( ) × (7)

𝑊𝑊𝑊𝑊 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖 where is the elevation of ℎthe ice ℎtop surface− 𝜌𝜌 (ice/snow− 𝜌𝜌 interface),𝑍𝑍 and are the

𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖𝑖𝑖 densityℎ of water and ice respectively, is the ice thickness. 𝜌𝜌 𝜌𝜌

𝑖𝑖𝑖𝑖𝑖𝑖 Assuming that the water density𝑍𝑍 and the ice density are 1000 kg/m3 and 915 kg/m3,

respectively, the water-equivalent lake surface elevation ( ) would be 8.5 cm lower than the ice

ℎ𝑊𝑊𝑊𝑊

top surface ( ) if the ice thickness ( ) is 1 m. In this study, the ice thickness ( ) is

𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖 estimated usingℎ 𝑍𝑍 𝑍𝑍

× . × = (8) ∆𝑃𝑃 3 125 𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖 𝑍𝑍 = 2 (9) 𝑐𝑐 𝑖𝑖𝑖𝑖𝑖𝑖 where P is the gate gap between the two peaks𝑐𝑐 on 𝑛𝑛the𝑖𝑖𝑖𝑖𝑖𝑖 leading edge determined by the local maxima∆ of these two peaks, 3.125 ns is the time interval between two adjacent gates, is the

𝑖𝑖𝑖𝑖𝑖𝑖 propagation velocity of light in ice, is the speed of light in vacuum space, 299792458𝑐𝑐 m/s,

𝑖𝑖𝑖𝑖𝑖𝑖 is the refractive index of ice, 1.7861 𝑐𝑐at Ku band, estimated by Warren and Brandt (2008). 𝑛𝑛

Since the first peak is generated by the ice top surface, the leading edge of the first peak represents the radar pulse energy reflected by the ice top surface over the time elapsed. Then the elevation of ice top surface ( ) can be calculated using the leading edge of the first peak

𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 through Equation (10): ℎ

= + (10)

Where H, , and haveℎ𝑇𝑇 𝑇𝑇𝑇𝑇been𝑇𝑇𝑇𝑇𝑇𝑇 given𝐻𝐻 − �Equation𝑅𝑅𝑡𝑡𝑡𝑡𝑡𝑡 𝜏𝜏𝑇𝑇 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(1), � − ∑ ∆are𝑅𝑅 − the𝐺𝐺2008 same set of geophysical

𝑡𝑡𝑡𝑡𝑡𝑡 2008 corrections𝑅𝑅 in Equation𝐺𝐺 (1), denotes the relative distance∑ ∆𝑅𝑅 in meter of the retracking point

𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 for ice top surface with respect𝜏𝜏 to the nominal tracking point (Gate 43). The retracking point for ice top surface is defined as the maxima of the leading edge of the first peak.

In this study, we adopts the maxima instead of the mid-height point of the leading edge as the retracking point to retrieve the elevation of ice top surface, to avoid the complication of fitting an semi-analytical or fully-physical model to the waveform as done by the SRAL SAR retrackers above. Due to the different choices of retracking points (maxima V.S. mid-height point), systematic differences exist between this bimodal retracker and the other SRAL SAR retrackers in the retrieval of surface elevation. To achieve the consistency with a specific SRAL SAR retracker

above, the systematic difference can be readily estimated using all the footprints collected when

the lake surface is in open water condition. The waveforms of these footprints have only one

dominant peak and are not influenced by lake ice cover. The systematic difference ( ) between the bimodal retracker and a specific SRAL SAR retracker is calculated for each lake∆ℎ through

Equation (11) and is then added to the water-equivalent lake level estimates calculated in the section below.

= ( ) (11) 1 𝐿𝐿 𝑙𝑙 𝑙𝑙 where L is the total number of measurements∆ℎ 𝐿𝐿 ∑collected𝑙𝑙=1 𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 in− 𝜏𝜏ice𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟-free season, l is the index of each

waveform, is the relative distance between the maxima of the leading edge and the nominal 𝑙𝑙 𝑚𝑚𝑚𝑚𝑚𝑚 tracker (Gate𝜏𝜏 43), is the epoch given by the corresponding SRAL SAR retracker. 𝑙𝑙 𝜏𝜏𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 2.3.4 Estimation of lake water level using SRAL SAR elevation measurements

The water level for a lake on the date of a satellite overpass is estimated by averaging the

elevation measurements along the satellite track inside the lake. In general, the lake surface either

in the phase of water or ice and snow is spatially homogeneous and smooth. The surface elevation

measurements collected by SRAL along a transect over the lake, however, could vary significantly

when the satellite ground track is close to the lake shore or when it passes through the islands in

the lake, due to the contamination of land surface within the radar footprint. Figure 2.3 shows the

surface elevation measurements over Lake Inarijarvi in Finland collected by Sentinel-3 on July 4,

2017 when the surface is in open water condition. Lake Inarijarvi has a complex and irregular shoreline and a large number of islands are distributed in the lake (Figure 2.3). The spurious elevation measurements (the orange points) in the lake surface elevation profile were generated, when Sentinel-3 overpassed the islands.

To exclude the spurious measurements, each lake surface elevation profile is pre-screened

using robust statistical analysis. For each elevation measurement of the surface profile, a statistic

score ( ) is calculated based on the median and the median absolute deviation (MAD) of the

𝑀𝑀𝑀𝑀𝑀𝑀 elevation𝑍𝑍 measurements of the profile (Liu et al. 2012). The measurements with greater than

𝑀𝑀𝑀𝑀𝑀𝑀 3.0 are identified as spurious measurements and then excluded from the subsequent𝑍𝑍 estimation of

the lake level. As shown in Figure 2.3, the orange points are excluded and the blue points are

retained for the following calculation. The standard deviation decreased from 0.82 m of the original

profile to 0.18 m of the filtered profile. Then, the lake water level on the date of satellite overpass

is estimated by averaging the filtered elevation profile and compared to the in situ measurement

collected at gauge station on the same day.

Figure 2.3 The removal of spurious measurements from lake surface profile using robust statistical analysis. The orange points are the measurements excluded and the blue points are the retained measurements. The dashed line represents the in situ gauge water level on July 4, 2017. The profile runs from south to north.

The performance of each SRAL SAR retracker in the retrieval of lake water level is

evaluated with three indicators: the Pearson correlation coefficient (r), the bias (Bias) and the root

mean square error (RMSE) between SRAL SAR lake level estimates and in situ gauge

measurements. The Bias and RMSE are calculated using the following two equations, respectively.

= ( , , ) (12) 1 𝑚𝑚 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑚𝑚 ∑𝑖𝑖=0 𝐻𝐻𝑆𝑆𝑆𝑆𝑆𝑆 𝑖𝑖 − 𝐻𝐻𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑖𝑖 37

= ( , , ) (13) 1 𝑚𝑚 2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 �𝑚𝑚 ∑𝑖𝑖=0 𝐻𝐻𝑆𝑆𝑆𝑆𝑆𝑆 𝑖𝑖 − 𝐻𝐻𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑖𝑖 − 𝐵𝐵𝑖𝑖𝑎𝑎𝑎𝑎 where is the total number of Sentinel-3 overpasses on a lake during the study period, , is

𝑆𝑆𝑆𝑆𝑆𝑆 𝑖𝑖 the lake𝑚𝑚 water level estimates given by a SRAL SAR retracker on a Sentinel-3 overpass𝐻𝐻 date,

, is the in situ gauge measurement on the same day.

𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑖𝑖 𝐻𝐻 The Bias is used to assess the closeness of SRAL SAR lake level estimates to the in situ

gauge measurements. The correlation coefficient (r) denotes the capability of each SRAL SAR

retracker in the retrieval of lake water level variations. The RMSE indicates the accuracy of each

retracker in the retrieval of lake water levels. Note that in Equation (13), the Bias is removed for

the calculation of RMSE. The RMSE, therefore, stands for the relative error (precision) of SRAL

SAR lake level estimates to the in situ measurements, instead of absolute error (accuracy).

2.4 Results and Discussions

2.4.1 Lake surface profiles retrieved by different SAR retrackers

The surface elevation profiles produced by SRAL SAR retrackers are compared on Lake

Erie and Great Slave Lake (Figure 2.4). The performances of these retrackers are evaluated in

terms of the number of valid measurements, the consistency of the measurements and the

difference of the measurements from in situ gage observations. The influence of ice cover on the

performances of the different retrackers is also examined.

Figure 2.5a and 2.5b show the surface elevation profiles along Track 576 over Lake Erie

and along Track 681 over Great Slave Lake in open water condition during the summer season,

2016. The elevation measurements generated by the four SAR retrackers along Track 576 over

Lake Erie are generally consistent without outliers. For the profiles along Track 681 over Great

Slave Lake, the measurements north of the 62.33°N are not consistent with the majority of the

measurements in the profile, overestimating the water surface elevation. The overestimation is

most probably due to the contamination of the coastal land surface. Those measurements can be effectively filtered out using the robust statistical analysis described in Section 2.3.4.

Figure 2.4 Sentinel-3 ground tracks (a) over Great Slave Lake and (b) over Lake Erie.

As shown in Figure 2.5a and Figure 2.5b, the elevation measurements produced by OCOG retracker are systematically higher than those by other three retrackers. The mean difference between OCOG and the Ice-Sheet is 23.3 cm for Lake Erie (Figure 2.5a) and 21.0 cm for Great

Slave Lake (Figure 2.5b). The elevation measurements from the Ice-Sheet retracker are slightly higher than those from the SAMOSA-3 retracker. The mean differences between them are 7.1 cm for Lake Erie and 6.3 cm for Great Slave Lake. The Sea-Ice retracker produces the lowest elevation measurements. Compared with the measurements from the OCOG retracker, the mean difference of the Sea-Ice retracker is 62.9 cm for Lake Erie and 55.8 cm for Great Slave Lake. The relative

order of the surface elevation measurements produced by these four retrackers is consistent for all

Sentinel-3 overpasses over all the 15 lakes in our study.

Figure 2.5 Lake surface profile produced by different SRAL SAR retrackers; (a) along Track 576 over Lake Erie on June 22, 2016, (b) along Track 681 over Great Slave Lake on August 18, 2016, (c) along Track 681 over Great Slave Lake on February 23, 2017. The black dashed line in each plot represents the in situ gauge water level for each lake on the corresponding date. The profile runs from south to north.

When the lake is covered by ice in the winter season, the differences of surface elevation measurements between the four retrackers become much larger. As shown in Figure 2.5c, the mean difference of elevation measurements is 73.5 cm between the OCOG retracker and the Ice-Sheet retracker over Lake Erie, and 207.4 cm between the OCOG retracker and the Sea-Ice retracker

over Great Slave Lake. This indicates that the ice cover may lead to systematical biases for the

four retrackers in their determination of the reference retracking points on the waveform.

Among the four retrackers, the Sea-Ice retracker often fails over lake surfaces, leading to

a very high rate of missing data. The percentage of missing data for the Sea-Ice retracker is 83%,

43% and 20% respectively in Figure 2.5a, Figure 2.5b and Figure 2.5c. For Track 681 over Great

Slave Lake, the overall percentage of missing data during our study period is 42%. The percentage

of missing data for Track 576 over Lake Erie is 83%. For some Sentinel-3 overpasses over Lake

Erie, for example, on September 11, October 8, November 4 and December 1, 2016, no measurements were produced by the Sea-Ice retracker. Due to the very high rate of missing data over lake surfaces, the Sea-Ice retracker is not considered as a valid retracker for the lake water level retrieval and hence will not be included in the subsequent analysis.

2.4.2 SAR retracker performances over the lakes with different ice cover conditions

The number of Sentinel-3 ground tracks over the 15 lakes varies depending on the lake size and location. The small lakes, e.g., Lake Okeechobee and Lake Lokan, have only one satellite track. Large lakes, such as Great Slave Lake and Lake Erie, may have multiple satellite tracks

(Figure 2.4). For those lakes with multiple satellite ground tracks, we only select two tracks closest to the gauge station for the validation analysis (Table 2.1). The tracks selected for Lake Erie and

Great Slave Lake are shown in Figure 2.4. During the study period between June 15, 2016 and

September 30, 2017, there are 18 Sentinel-3 overpasses for each track over each lake.

The ice cover conditions over Lake Erie and Great Slave Lake in winter seasons are significantly different. Great Slave Lake is usually fully covered by ice for 6 months in a year

(Howell et al. 2009), while Lake Erie is partly covered for about two weeks in a year (Assel 2003;

Assel et al. 2013; Wang et al. 2012a). Figure 2.6 and Figure 2.8 below compare the time series of

lake level estimates produced by the three SAR retrackers over these two lakes to the in situ gauge

measurements.

Figure 2.6 shows the temporal variations of water level on Lake Erie derived from the three

SAR retrackers during 2016-2017. In the 2016-2017 winter, only a very small fraction of Lake

Erie near the northeast and the southwest coast is covered by ice (Assel and Wang 2017). The time

series of the lake level on Lake Erie were constructed based on Sentinel-3 surface elevation measurements along Track 576 and Track 649 (Figure 2.4), which were not affected by the ice cover in the 2016-2017 winter. The lake levels derived from Ice-Sheet retracker and SAMOSA-3 retracker are systematically lower than the in situ gauge measurements, while the lake water levels derived from OCOG retracker are slightly higher. The mean bias as compared to the in situ gauge data are -0.22 m for Ice-Sheet retracker, 0.03 m for OCOG retracker, and -0.29 for SAMOSA-3

retracker. Nevertheless, all the three time series are highly consistent with the in situ water levels.

As shown in Figure 2.7a, 2.7b and 2.7c, the Pearson’s correlation coefficients r is 0.98, 0.97 and

0.98, and the RMSE is 4.24 cm, 4.66 cm and 4.34 cm for the ICE-Sheet, OCOG and SAMOSA retrackers, respectively.

Figure 2.8 shows the temporal variations of lake level on Great Slave Lake from the three

SAR retrackers during the 2016-2017. Apparently, in the 2016 – 2017 winter, the lake water level

estimates from all the three retrackers deviate greatly from the in situ gauge measurements, due to

the effect of ice cover, which will be discussed in detail in Section 2.4.3 below. The error bars of

these ice-affected estimates from the SAR retrackers are significantly wider than those when the

lake was in open water condition. The deviation magnitude of these ice-affected estimates from the in situ gauge measurements increases rapidly as the winter progresses. The maximum deviation appeared on April 23, 2017, being -1.82 m for the Ice-Sheet retracker, -1.53 m for the OCOG

retracker and -1.58 m for the SAMOSA-3 retracker. The ice-affected estimates are separated from the rest valid estimates by the two red dashed lines in Figure 2.8.

The scatter plots in Figure 2.9a, 2.9b and 2.9c show the relationship between the lake level estimates from SRAL SAR retrackers and the in situ gauge measurements over Great Slave Lake.

After excluding the ice-affected estimates between the two dashed lines, a linear regression line is fitted and the correlation coefficients r and RMSE are calculated. For the water level estimates from the Ice-Sheet, OCOG, and SAMOSA retrackers, the correlation coefficient r is 0.96, 0.90, and 0.96, and the RMSE is 5.22 cm, 7.10 cm, and 5.77 cm, respectively.

Figure 2.6 Comparison of water level estimates from Sentinel-3 retrackers and the in situ gauge measurements over Lake Erie during 2016-2017. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The date is in the format of MM/DD/YYYY.

Figure 2.7 The scatter plots of water level estimates from SRAL SAR retrackers against in situ gauge measurements over Lake Erie. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The dashed line in each plot is the regression line of SRAL SAR water level estimates against concurrent in situ gauge measurements.

Figure 2.8 Comparison of water level estimates from Sentinel-3 retrackers and the in situ gauge measurements over Great Slave Lake during 2016-2017. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The date is in the format of MM/DD/YYYY.

Figure 2.9 The scatter plots of water level estimates from SRAL SAR retrackers against in situ gauge measurements over Great Slave Lake. (a) Ice-Sheet retracker, (b) OCOG retracker, and (c) SAMOSA-3 retracker. The SRAL SAR water level estimates have been excluded from the scatter plots. The dashed line in each plot is the regression line of SRAL SAR water level estimates against concurrent in situ gauge measurements.

The comparison of our lake level estimates against in situ gauge water levels over the 15

lakes are summarized in Table 2.2 and Table 2.3. As shown in Table 2.2, without the consideration

of ice-affected lake level estimates, the correlation coefficient r for the 15 lakes ranges from 0.87

to 0.99 for the Ice-Sheet retracker, from 0.79 to 0.99 for the OCOG retracker, from 0.89 to 0.99

for the SAMOSA-3 retracker. In general, all three retrackers can provide well depiction of the lake

water level variation when the lake surface is in open water condition.

There are seven lakes that are fully covered by ice in the 2016-2017 winter. However, only

four of them have been identified with apparent ice-affected estimates and the r is recalculated for these four lakes as shown in the three columns on the right of Table 2.2. For Great Slave Lake,

Lake Athabasca and Lake Cedar in Canada, the correlation coefficients r improved greatly, after the exclusion of ice-affected estimates. For Great Slave Lake, the r values of the three retrackers increase from 0.17, 0.17 and 0.10 to 0.95, 0.89 and 0.95, respectively. However, the improvement

of r is relatively small for Lake Inarijarvi in Finland. Moreover, no obvious ice-affected estimates were detected for other three lakes in Finland, even though they were also fully ice-covered during the 2016-2017 winter. The lake level estimates on Canadian lakes in winter season were severely affected by ice, while for Finnish lakes the estimates were slightly or barely affected by ice cover.

In the following two sections (Section 2.4.3 and 2.4.4), we will discuss in detail the possible causes of this disparity.

Table 2.2 The correlation coefficients r of the regressions over the 15 lakes with and without the ice-affected estimates

Winter All estimates No ice-affected estimates Lake Lat(°) Ice Cover Ice-Sheet OCOG SAMOSA-3 Ice-Sheet OCOG SAMOSA-3

1 Inarijarvi 69.02 Fully 0.93 0.96 0.93 0.94 0.98 0.96

2 Porttipahta 68.09 Fully 0.96 0.97 0.96 0.96 0.97 0.96

3 Lokan 67.96 Fully 0.93 0.94 0.94 0.93 0.94 0.94

4 Oulujarvi 64.35 Fully 0.87 0.91 0.87 0.87 0.91 0.87

5 Vanern 58.91 None 0.96 0.96 0.95 0.96 0.96 0.95

6 Great Slave 61.80 Fully 0.17 0.17 0.10 0.96 0.90 0.96

7 Athabasca 59.18 Fully 0.58 0.68 0.62 0.98 0.99 0.98

8 Cedar 53.34 Fully 0.69 0.68 0.70 0.94 0.79 0.93

9 Superior 47.54 Partly 0.89 0.88 0.89 0.89 0.88 0.89

10 Huron 44.96 Partly 0.97 0.95 0.97 0.97 0.95 0.97

11 Ontario 43.67 Partly 0.99 0.99 0.99 0.99 0.99 0.99

12 Erie 42.16 Partly 0.98 0.97 0.98 0.98 0.97 0.98

13 Michigan 44.01 Partly 0.95 0.96 0.96 0.95 0.96 0.96

14 Salton Sea 33.30 None 0.98 0.96 0.97 0.98 0.96 0.97

15 Okeechobee 26.95 None 0.96 0.94 0.94 0.96 0.94 0.94

The Bias and the RMSE between the lake level estimates and the in situ gauge

measurements were calculated for all lakes without the consideration of ice-affected estimates.

Due to the lack of critical information of local vertical datum used by Canada, Finland and Sweden,

only the in situ gauge measurements on the Great Lakes, Salton Sea and Lake Okeechobee are

referenced to the same geoid (EGM2008) used in Sentinel-3 SRAL SAR measurements.

Therefore, we only focus on the Bias values of these seven lakes. As shown in Table 2.3, the Bias

values of these seven lakes range from -43.91 cm to 5.66 cm for Ice-Sheet retracker, from -19.21

cm to 15.55 cm for OCOG retracker, and from -44.96 cm to 0.19 cm for SAMOSA-3 retracker.

On average, the Bias is -24.06 cm, -1.76 cm and -28.39 cm for the three retrackers, respectively, which indicates that the lake level estimates produced by OCOG retracker are the closest to the water level measured at gauge stations.

These biases were most likely caused by the systematic over- or under-estimation of the

range by each retracker as shown in Section 2.4.1. The possible uncertainties in the conversion of

local vertical datum to geoid EGM2008 might also be responsible for these differences. In

addition, the biases could also be partly attributed to the short wavelength geoid undulations due

to the mismatching of the locations between gauge stations and Sentinel-3 ground tracks. For Lake

Michigan, the distance between Station Calumet Harbor and Track 735 is about 57.7 km (see Table

2.1). The geoid (EGM2008) undulation between the gauge station and the closet point on Track

735 is 45.9 cm, based on the estimation from online datum transformation tool provided by NOAA

(https://vdatum.noaa.gov/vdatumweb). Further study is needed to determine the true reasons for

these biases. Nevertheless, the Sentinel-3 lake level estimates correlate very well with the in situ

gauge measurements and is capable of reflecting the variations of actual lake water level.

The RMSE represents the accuracy of each SRAL SAR retracker in the retrieval of lake

water level. It is calculated for each lake after removing the bias between SRAL SAR lake level estimates and the in situ gauge measurements using Equation (12). As shown in Table 2.3, the

three retrackers have very close precision in the retrieval of lake water level variations when the

lake surface is in open water condition. The RMSE values for the 15 lakes range from 3.57 cm to

25.63 cm for Ice-Sheet retracker, from 3.53 cm to 29.13 cm for OCOG retracker, and from 3.74

cm to 26.23 cm for SAMOSA-3 retracker. Lake Ontario and Lake Vanern have the lowest RMS

among the 15 lakes for all the three SAR retrackers, which are all below 4 cm. Averaging the

RMSE of the 15 lakes gives a mean value of 11.06 cm, 11.61 cm and 11.21 cm for the Ice-Sheet, the OCOG and the SAMOSA-3 retrackers, respectively. The performance of Ice-Sheet retracker

is slightly better than the other two retrackers. Previous study demonstrated that the OCOG

retracker works the best for conventional pulse-limited radar altimetry missions in the retrieval of

inland water levels (Frappart et al. 2006a). This study shows that the other two Sentinel-3 SRAL

SAR retrackers can provide at least as good retrieval of lake water level variations as the OCOG

retracker.

Table 2.3 The Bias and the RMSE between the SRAL SAR lake level estimates and the in situ gauge water levels.

Area Bias (cm) RMSE (cm) Lake 2 (km ) Ice-Sheet OCOG SAMOSA-3 Ice-Sheet OCOG SAMOSA-3

1 Inarijarvi 1184.6 -49.71 -44.64 -52.64 16.14 9.24 13.67

2 Porttipahta 205.6 -39.10 -35.23 -42.32 25.63 24.38 26.23

3 Lokan 487.6 -47.25 -50.90 -48.16 25.38 20.94 22.95

4 Oulujarvi 889.7 -58.14 -44.47 -62.43 21.6 16.03 22.40

5 Vanern 5550.5 -6.99 16.80 -13.94 3.68 3.53 3.95

6 Great Slave 27816.3 30.36 50.15 23.99 5.22 7.10 5.77

7 Athabasca 7781.6 -3.38 17.37 -9.83 6.24 4.41 7.07

8 Cedar 2817.3 21.74 26.65 14.92 12.92 29.13 15.08

9 Superior 81935.7 -22.94 1.81 -30.38 7.27 7.62 7.43

10 Huron 19328.9 -15.02 10.18 -22.08 4.52 5.63 4.65

11 Ontario 19328.9 -31.67 -6.13 -38.89 3.57 3.55 3.74

12 Erie 25691.0 -21.6 3.38 -28.74 4.24 4.66 4.34

13 Michigan 57399.4 -43.91 -17.87 -33.84 6.04 6.19 4.92

14 Salton Sea 929 -38.92 -19.21 -44.96 3.93 4.98 5.02

15 Okeechobee 1436.8 5.66 15.55 0.19 19.58 26.73 21.00 Average -24.06* -1.76* -28.39* 11.06 11.61 11.21 * The mean bias of each retracker is calculated only over 7 lakes, including the Great Lakes of North America, Salton Sea and Lake Okeechobee in US.

It’s worthy to note that all three retrackers can achieve a very low RMSE of less than 4 cm

for large lakes as shown in Table 2.3. These values are comparable to and often better than the

precision of different pulse-limited radar altimeters over large lakes reported in previous studies

(Asadzadeh Jarihani et al. 2013; Birkett 1995; Birkett and Beckley 2010; Morris and Gill 1994b;

Schwatke et al. 2015). The RMSE values of SRAL SAR altimeter over small lakes, such as,

Porttipahta with an area of 205.6 km2 and Lokan with an area of 487.6 km2, increase to the range

of 20 – 27 cm, indicating a degradation of SRAL SAR performance. Nevertheless, the performance

over small lakes is still comparatively better than that of conventional pulse-limited radar altimeters, as compared to previous assessments of conventional pulse-limited radar altimeters.

For example, the precision of lake level estimates derived from EnviSat altimetry measurements over three small lakes near Curuai in Amazon basin ranges from 25 cm to 324 cm (Frappart et al.

2006a). The area of these three lakes is between 100 km2 and 300 km2. Jarihani et al (2013)

evaluated the performances of multiple satellite radar altimetry missions on two small lakes in

Australia, Lake Eildon with an area of ~138 km2and Lake Argyle with an area 1000 km2. The best

precision is 89 cm for GFO, 42 cm for EnviSat, 150 cm for T/P, 112 cm for Jason-1 and 28 cm for

Jason-2. Even though a more rigorous comparison between Sentinel-3 SAR altimeter and the other

conventional pulse-limited altimeters over the same set of lakes is needed, this empirical analysis

shows the generally improved performance of Sentinel-3 SAR altimeter in the retrieval of lake

level variations.

2.4.3 Detection of lake ice with simultaneous Sentinel-3 MWR measurements

The lake ice is detected using the simultaneous measurements of brightness temperature

over lake surfaces acquired by the onboard microwave radiometer MWR at the two channels, 23.8

GHz (TB-238) and 36.5 GHz (TB-365). Figure 2.10a shows the time series of brightness temperature over Great Slave Lake acquired between June 25, 2016 and September 27, 2017. TB-

238 and TB-365 both increase quickly after November 30, 2016 when air temperature drops below

0 °C as shown in Figure 2.10b, indicating the formation of ice cover on lake surface. After the

initial increase, TB remains relatively stable throughout the winter. Then it gets another rise on

May 20, 2017 as pointed by the red arrow in Figure 2.10a when the air temperature exceeds 0 °C

and as the ice begins to melt. This radical rise is caused by the higher air temperature and the

increasing shortwave flux absorption at the melting lake ice/snow surface (Kang et al. 2012; Kang et al. 2010), indicating the onset of ice break-up. A similar process also occurred on Lake Inarijarvi in Finland during the 2016-2017 winter. As observed in Figure 2.10a and 2.10c, the sudden increase of brightness temperature coincides with the deviation of Sentinel-3 SRAL SAR lake level estimates from the in situ gauge measurements during the winter season.

Figure 2.10 Coincidence between the sudden increase of brightness temperature and the deviation of lake level estimates from in situ observations over Great Slave Lake during 2016- 2017. (a) Brightness temperature from Sentinel-3 MWR channels at 23.8 GHz and 36.5 GHz. (b) Lake level estimates given by Sentinel-3 Ice-Sheet retracker. (c) Daily air temperature at the gauge station Yellowknife.

Besides the coincidence above, there are three interesting observations that are worthy to

note and will be explained in details in Section 2.4.4 below. First, the high value of brightness

temperature On May 20, 2017 in Figure 10a indicates the presence of ice cover. The SRAL SAR

lake level estimate on that day, interestingly, didn’t deviate significantly from the in situ gauge

measurement. Second, as marked by the yellow arrows in Figure 2.10c, the deviation of SRAL

SAR estimates from in situ gauge measurements increased as the winter progressed. The similar

trend was also observed for Lake Athabasca and Lake Cedar in Canada. In addition, the four lakes

in Finland were also fully covered by ice in the 2016-2017 winter. SRAL SAR estimates for these

four lakes, however, were slightly or basically not affected by the ice cover, which was observed

through the analysis of correlation coefficients r in Section 2.4.2.

2.4.4 Influence of lake ice on SAR altimetry waveform

To fully understand the deviation of SRAL SAR lake level estimates from in situ gauge

measurements, we examined the lake ice influences on the SAR waveforms during the whole

winter. Ku-band altimetry radar pulse has a capability to penetrate snow and ice (Hawley et al.

2006; Patel et al. 2015; Scott et al. 2006). It was reported that the penetration could reach to a depth of 15 m over Antarctic land ice, where the snow and ice are dry (Patel et al. 2015). If the snow and ice begin to melt, the penetration would be largely hampered by liquid water and limited to the ice surface (Makynen and Hallikainen 2009). Over the dry, ice-covered lake surfaces, the echoed altimetry pulse energy is composed of three components: the energy from the air/ice interface, the energy from the ice mass, and the energy from the ice/water interface (Atwood et al.

2015; Beckers et al. 2017; Gunn et al. 2015b). Due to the strong dielectric contrast between the ice cover and the water below, the energy from the ice/water interface is the largest (Atwood et al.

2015), which generates a dominant peak in the waveform of echoed radar pulse.

Figure 2.11 presents the time series of waveforms over Great Slave Lake acquired between

November 12, 2016 and June 16, 2017. These waveforms were from Sentinel-3 footprints located at the center of Track 681 (Figure 2.4). During this period, the lake surface experienced a full

phenological cycle, transforming from open water to ice, and then back to open water. Waveforms

in Figure 2.11a and 2.11i are typical for open water. Waveforms in Figure 2.11b and 2.11h have

single narrow sharp peak (hereinafter referred to as specular waveform), generated by specular

scattering of mirror-like surface. The mirror-like surface was most likely formed by a thin-layer

of liquid water on the ice/snow surface, which comes either from the percolation of the water

below the ice at the beginning of winter or from the melting of snow and ice at the end of the

winter. Waveforms in Figure 11c-11g are characterized by two peaks: a small peak and a dominant

peak. As the winter proceeded from January 5, 2017 to April 23, 2017, the temporal distance

between the two peaks gradually increased in Figure 2.11. In the field experiments, Gunn et al.

(2015a) and Atwood et al. (2015) demonstrated that the first small peak of the waveform measured

by a ground-based Ku-band microwave scatterometer corresponds to the pulse energy

backscattered from the top of ice surface, while the second dominant peak represents the pulse

energy from ice/water interface. The increase in temporal distance between the two peaks indicates

the growth of lake ice during the winter time. Gunn et al. (2015b) retrieved the growth of lake ice through tracking the temporal distance between the two peaks of the waveforms measured by ground-based Ku-band and X-band scatterometer.

Figure 2.11 The time series of SRAL SAR waveforms over Great Slave Lake during the 2016- 2017 winter. The epochs (τ) are produced by SAMOSA-3 retracker. The date is in the format MM/DD/YYYY.

As discussed in Section 2.2.2, all SAR retrackers except for OCOG estimate the surface

elevation by fitting an analytical or a semi-analytical waveform model to the observed SAR waveform. All the models assume that the waveform has only one primary peak and the fitting is performed to minimize the differences between the observed waveform and the theoretical model.

As demonstrated, the presence of ice on lake surface leads to two peaks on the returned waveform.

To minimize the difference, the fitted model is often shifted to more closely accommodate the

dominant peak produced by the lower ice surface. Therefore, the reference retracking point (the

epoch τ in Figure 2.11) given by a SAR retracker tends to represent the elevation of the bottom of

lake ice (or the ice/water interface), which is usually lower than the actual water-equivalent lake

level recorded by gauge station. With the growth of lake ice, the derivation of SRAL SAR water

level estimates from the actual gauge water level increases, as demonstrated in Figure 2.10c. On

December 9, 2016 and May 20, 2017, the narrow single-peak waveforms indicates that the Ku-

band pulse did not penetrate the ice cover probably due to the liquid water atop the thin ice. The

lake level estimates derived from SRAL SAR retrackers on these two dates represent the elevation

of the upper ice surface, which did not derivate significantly from the gauge water level as shown

in Figure 2.10c.

Although Lake Inarijarvi in Finland is fully covered by ice in winter, the ice cover is much

thinner than that on Great Slave Lake, due to the heating effect of the warm surface water in Nordic

Seas transported by the North Atlantic Current from subtropical Atlantic ocean regions (Rahmstorf

2006). Since no ice thickness data is available for Great Slave Lake in the 2016-2017 winter, we compared the historical weekly-mean ice thicknesses for these two lakes. The weekly-mean ice thickness was calculated by averaging all the in situ measurements collected in the same week each year from 2010 to 2016. As shown in Figure 2.12, the maximum weekly-mean thickness for

Great Slave lake is 114.6 cm, almost as twice high as the maximum weekly-mean thickness (62.5 cm) for Lake Inarijarvi. In addition, the maximum weekly-mean ice thickness (62.5 cm) for Lake

Inarijarvi is lower than the ice thickness value for Great Slave Lake in the first week of January as indicated by the red dash line in Figure 2.12. This is the time when the first bimodal SAR waveform appears on Great Slave Lake, as shown in Figure 2.11c. Therefore, it is reasonable to infer that in

most time of the winter the ice cover on Lake Inarijarvi is not thick enough to generate the bimodal

waveforms as observed on Great Slave Lake in Figure 2.11.

Figure 2.12 Weekly-mean ice thickness on Great Slave Lake and Lake Inarijarvi from 2010 to 2016. The dates of the first and of the last bimodal waveform in Figure 2.11 are denoted by the red arrows.

For further verification, we plot the time series of waveforms over Lake Inarijarvi during the 2016-2017 winter in Figure 2.13. These waveforms are from the footprints located at the center of Track 272. The two specular waveforms with single narrow sharp peak at the beginning

(December 17, 2016) and the end (June 24, 2017) of the winter in Figure 2.13c and 2.13j are similar to the ones observed on Great Slave Lake in Figure 2.11b and 2.11h, indicating the appearance of mirror-like thin ice surface. During the period between these two dates, even though Lake

Inarijarvi was covered by ice, all the waveforms have only one dominant peak, as shown in Figure

2.13d – 2.13i. No bimodal waveform was generated. In other words, these single-peak waveforms

meet the assumptions of the semi-analytical or the fully-physical waveform models used by SRAL

SAR retrackers. The retracking points determined by these SRAL SAR retrackers are barely

affected by the ice cover on Lake Inarijarvi. The other three lakes in Finland locate at more

southern regions as compared to Lake Inarijarvi. Lokan and Porttipahta are two reservoirs with

much greater water depth. The ice covers on these lakes are thinner than Lake Inarijarvi due to the

greater water depth (Duguay et al. 2003) and the more southern location. Therefore, it explains that the SRAL SAR lake level estimates for the four lakes in Finland were much less affected by ice cover as compared to the lakes in Canada.

Figure 2.13 The time series of SRAL SAR waveforms over Lake Inarijarvi during the 2016- 2017 winter. The epochs (τ) are produced by SAMOSA-3 retracker. The date is in the format MM/DD/YYYY.

2.4.5 Application of bimodal retracker for the retrieval of water-equivalent lake levels

With the understanding of ice cover influences on SRAL SAR waveform, we have

developed an empirical bimodal retracker in Section 2.3.4 to retrieve the water-equivalent level

for lakes covered by thick ice through taking account for the ice thickness and the elevation of ice

top surface. In this section we applied this new bimodal retracker to Great Slave Lake as an

example to assess its effectiveness. We firstly retrieved the water-equivalent lake surface elevation

using Equation (7) for each waveform along Track 37 on Great Slave Lake between January 05,

2017 and April 23, 2017. The mean lake water level for each Sentinel-3 overpass during the period

was estimated based on the water-equivalent surface elevations given by the bimodal retracker and

was then compared with the in situ gauge measurements.

Figure 2.14 shows the time series of lake level estimates produced by our bimodal retracker

(red solid triangles) and by the original SAMOSA-3 retracker (black solid circles). Clearly, the new bimodal retracker can effectively correct the erroneous lake level estimates given by

SAMOSA-3 retracker during the winter when the lake is covered by thick ice. The difference between the estimates given by our bimodal retracker and by SAMOSA-3 retracker can be as high as 1.42 m.

The new bimodal retracker adopts the maxima of the leading edge as the retracking point, instead of the mid-height point used by SAMOSA-3. The elevation value of each SRAL SAR waveform given by the maxima of leading edge is inherently lower than the elevation given by the mid-height point of leading edge, resulting in systematically lower lake level estimate. The green hallow diamonds in Figure 2.14 represent the lake level estimates produced by the maxima of leading edge for all Sentinel-3 overpasses along Track 37 when the lake surface is in open water condition. A systematic difference can be easily observed between the lake level estimates

produced by the two different retracking points. We estimated the mean difference using Equation

(11) based on all the single-peak waveforms returned from open water surface along Track 37 on

Great Slave Lake. There are in total 493 waveforms for the ten Sentinel-3 overpasses. The

difference between the maxima and the mid-height point of the leading edge is estimated for each

of these 493 waveforms. These 493 values follow a Gaussian distribution with a mean of 0.30 m

and a standard derivation of 0.15 m. To achieve the consistency with SAMOSA-3 retracker, we

added this mean difference value (0.30 m) to the lake level estimates between January 05, 2017

and April 23, 2017 produced by our bimodal retracker. The lake level estimates produced by our

bimodal retracker (the red solid triangles in Figure 2.14) are referred to as Bimodal-Maxima

estimates. The lake level estimates with the removal of the mean difference are then referred to as

Bimodal-MidHeight estimates (the blue hallow circles in Figure 2.14).

There were in total seventeen Sentinel-3 overpasses along Track 37 on Great Slave Lake

during our study period. Using the five Bimodal-MidHeight estimates (the blue hallow circles in

Figure 2.14) and the other twelve lake level estimates (the black solid circles) produced by

SAMOSA-3 retracker, we construct a new series of lake level estimates for Great Slave Lake along

Track 37. This new series of lake level estimates is then compared to the in situ gauge

measurements, as shown in Figure 2.15. In comparison with the original SAMOSA-3 retracker,

the correlation coefficient r of the new series of lake level estimates with the in situ gauge measurements increases from 0.13 to 0.93 and the RMSE reduces from 59.62 cm to 4.79 cm as shown in Figure 2.15a and 2.15b. This analysis demonstrates that the new bimodal retracking method is capable of providing consistent estimates of lake levels for ice-covered lakes during the winter season.

Figure 2.14 Comparison between the water levels produced by the bimodal retracker and by the original SRAL SAR SAMOSA-3 retracker. The date is in the format MM/DD/YYYY.

Figure 2.15 Scatter plots of lake level estimates versus in situ gauge measurements; (a) from the SAMOSA-3 retracker and (b) from the bimodal retracker and the SAMOSA-3 retracker. The hallow circles represent the lake level estimates when the lake was covered by thick ice

2.5 Conclusions

Satellite radar altimetry has been widely used for monitoring lake water levels over the past three decades. Sentinel-3 is the most recent satellite mission with a SAR altimeter (SRAL) onboard and provides elevation measurements along the ground track for the global surfaces. The waveforms produced by the SAR altimeter is quite different from the conventional pulse-limited altimetry waveforms. Four SRAL SAR retracking algorithms have been developed, but their

performances on the retrieval of inland lake water levels have not been investigated, particularly, when lakes are covered by the ice.

In this research, we assessed four SAR retrackers. Sea-Ice retracker often fails to generate valid estimation of the range between the satellite and the reflecting surface, leading to a large rate of missing data. Therefore, this retacker is not suitable for the retrieval of inland lake water levels.

By comparing with the in situ gauge measurements of 15 lakes, we found out that the OCOG yields the lowest Bias among the three retrackers. In general, Ice-Sheet, SAMOSA-3 and OCOG retrackers exhibit very close capability in the monitoring of lake water level variations. The mean

RMSE over the 15 lakes are 11.06 cm, 11.21 cm and 11.61 cm, respectively. The RMSE values of

Sentinel-3 lake level estimates over large lakes are often < 4 cm, which are comparable to and often better than the accuracy generated by conventional satellite radar altimetry missions. For small lakes, the accuracy of Sentinel-3 lake level estimates is comparatively better than the accuracy of conventional satellite radar altimetry missions.

For the lakes covered by thick ice in winter season, the lake level estimates produced by

SRAL SAR retrackers are found to deviate from the in situ gauge measurements due to the ice- induced bimodal shape of the returned SAR altimetry waveform. The deviation increases as the lake ice thickens during the winter season. In this study, we developed a new empirical bimodal retracker to retrieve the water-equivalent lake levels for ice-covered lakes. The comparison with in situ gauge measurements demonstrates that this new method is capable of providing temporally consistent estimates of water-equivalent lake levels for high-latitude lakes in winter seasons. This improvement of the lake level estimates makes it possible to analyze the variations of high-latitude lake levels using satellite radar altimetry observations over the entire annual hydrological cycle instead of in the mere open water condition.

Chapter 3: Improving Satellite Waveform Altimetry Measurements

with a Probabilistic Relaxation Algorithm

3.1 Introduction

Satellite altimetry has been widely used for global elevation measurements of various types

of Earth surface on a regular basis since the mid-1980s (Davis 1992; Frappart et al. 2017; Fu and

Cazenave 2000; Troitskaya et al. 2012). The spaceborne altimeter sensors emit a series of electromagnetic pulses in the nadir direction towards the Earth surface and accurately measure the two-way travel time of the signal. Depending on the frequency of the emitted pulses, altimeters can be classified into two types: radar altimeters and laser altimeters. Radar altimeters employ microwave electromagnetic waves at Ku-band (e.g. 13.5 GHz for Envisat/RA-2) or Ka-band (e.g.

35.5 GHz for SARAL/Altika). For most of the missions, a secondary frequency channel at C-band

(e.g.5.3 GHz for Jason-1/Poseidon-2) or S-band (e.g. 3.2 GHz for Envisat /RA-2) is also used for the correction of the range delay caused by the ionosphere over the ocean (Benveniste 2011). Laser altimeters operate at visible and near-infrared wavelengths. ICESat/GLAS was launched by NASA in January 2003 with an orbit of 600 km altitude and an inclination angle of 94°. The Geoscience

Laser Altimeter System (GLAS) was the sole payload for the mission and worked at two wavelengths, 532 nm and 1064 nm (Zwally et al. 2002). It was the first space-borne laser altimetry mission and provided elevation measurements of Earth surface between 86˚S to 86˚N latitudes from 2003 to 2009 (Zwally et al. 2002). GLAS transmitted 40 laser pulses per second toward the

Earth surface. The illuminated footprints of laser pulses on the ground surface have an elliptical shape with a diameter of about 70 m, and these laser footprints were spaced at 170 m intervals along the satellite tracks. The primary objective of ICESat/GLAS mission was to measure the ice

sheet elevation changes in Antarctica and Greenland (Herzfeld and Wallin 2014; Zwally et al.

2002). The data have also been widely used to estimate sea-ice freeboard and sea ice thickness

(Kwok et al. 2004), forest canopy height (Lefsky et al. 2007), snow depth (Bindschadler et al.

2005; Shu et al. 2018; Treichler and Kääb 2017), as well as lake water-level changes (Song et al.

2014; Wang et al. 2013). The accuracy of ICESat/GLAS elevation measurements could reach 2 cm under clear-sky conditions over the Antarctic ice sheet (Fricker et al. 2005). In normal situations, the expected vertical accuracy is about 14 cm (Kurtz et al. 2008; Shuman et al. 2006).

The elevation of each laser footprint is jointly determined by satellite orbital position, laser beam direction and the range between satellite and the reflecting surface. The laser energy intensity of transmitted and returned pulses are densely sampled and recorded as a curve over time, which are referred to as laser waveform. The range is calculated by tracking the elapsed time between the emission and the reception of the laser pulse. The elapsed time between the emission and reception is precisely determined by identifying the reference points on the transmitted and the returned altimeter waveforms. The transmitted waveform is approximately a simple Gaussian shape curve

(Zwally et al. 2002). The waveform returned from a flat and homogeneous surface usually has a single dominant peak with a Gaussian shape. For a rough and heterogeneous surface, the returned waveform may exhibit several peaks with a complex shape (Brenner et al. 2011; Pirotti 2010).In the creation of the ICESat/GLAS data products, the Earth surface was classified into four major land cover types (land, ocean, sea ice, and ice sheet) to accurately determine the reference points.

The surfaces of ocean, sea ice and ice sheet are relatively homogeneous and flat, while the land surfaces are usually heterogeneous and complex. Two standard retracking methods were designed specifically to cope with these two categories of surfaces according to the characteristics of their waveform shapes. The Maximum-Amplitude-Peak (MAP) retracking method is suitable for

relatively smooth and gradually changing surfaces(Brenner et al. 2011), while the Centroid retracking method is designed for all different types of terrestrial land surfaces. The terrestrial land surface is usually a complex mosaic of different geomorphic features. The land surface elevation may vary significantly within the laser footprint, and the elevation measurement corresponding to the centroid reference point represents the average surface height within the illuminated footprint.

In contrast, the surfaces of ice sheets, sea ice and oceans are relatively smooth and homogeneous, and the returned waveforms from such surfaces are mostly characterized by a single dominant peak with a Gaussian curve shape. The MAP retracking method identifies individual peaks on the returned waveform by fitting a series of Gaussian curves, and then selects the Gaussian peak with a maximum amplitude to represent the surface height within the footprint.

Although the Centroid method is a proper choice for land surfaces with drastic elevation variations, the MAP method could be a better choice for some terrestrial geographical features with a relatively small elevation variation, such as, inland lakes, deserts, coastal zones, etc. The current MAP retracking method may fail to produce reliable elevation measurements for relatively flat surfaces due to the atmospheric influence. In fact, bad weather conditions may lead to the low energy intensity and the shape deformation of the returned waveform (Zwally et al. 2002). The presence of low clouds, ice fogs, and blowing snow or dust/sand storms, often causes strong multiple particle scattering on the returned waveform (Duda et al. 2001; Mahesh et al. 2002; Yang et al. 2010). These affected waveforms may significantly deviate from the theoretical waveform model and hence fail the two standard retracking methods, leading to centimeter to meter level of error in elevation retrievals (Fricker et al. 2005; Palm et al. 2011; Urban et al. 2008; Yang et al.

2010). In some extreme situations, the error could be up to 8 m in Antarctica (Palm et al. 2011).

The measurements contaminated by atmospheric scattering usually exhibit high detector

gain value and low surface reflectivity. The detector gain value ranges from 1 to 255. It is set to a

higher level when the returned laser pulse energy becomes weaker. The reflectivity is the ratio of

the returned laser pulse energy to the emitted energy, ranging from 0 to 1. The higher gain value

and the lower reflectivity indicate the stronger level of atmospheric scattering. The Arctic region

is covered by cloud over half the time of the year (Shupe et al. 2011). Blowing snow is also a

common phenomenon in the winter season in this region (Liston and Sturm 2002). ICESat/GLAS

measurements in the polar regions are more likely subject to the scattering than in other regions.

In the Arctic coastal plain of northern Alaska, about a half million elevation measurements had

been collected by ICESat/GLAS during 2003 and 2009. The footprints with detector gain value

higher than 250 and the footprints with reflectivity less than 0.1 accounted for about 19% and 13%

respectively of the total observations, suggesting the widespread influences of atmospheric

scattering and the importance of correcting the influences for ICESat measurements in these

regions.

Some heuristic approaches have been used to identify and then exclude the laser

observations that were heavily affected by atmospheric scattering. Yi et al. (Yi et al. 2005) used

the gain threshold value of 30, Kwok et al. (Kwok et al. 2006) used 50, and Felikson et al. (Felikson et al. 2017) used 150 to filter potentially contaminated footprints over Greenland ice sheet and arctic sea ice, respectively. Later, Yi et al. (Yi et al. 2011) recommended to use different thresholds of gain values for the measurements collected in different campaigns. Siegfried et al. (Siegfried et al. 2011) suggested that the measurements with surface reflectivity less than 0.24 most likely do not meet the data quality requirement of ICESat mission. Yi et al. (Yi et al. 2011) and Zwally et al. (Zwally et al. 2008) used 0.05 as the surface reflectivity to identify the affected measurements.

However, no robust numerical algorithms have been reported to treat the waveforms contaminated by the atmospheric forward scattering for the purpose of reliable elevation retrieval.

In this study, we present a new robust retracking method that exploits the spatial contextual information from neighboring footprints along the satellite ground track, in addition to the waveform shape information of an individual footprint as in the standard Centroid and MAP retracking methods. Our method utilizes a probabilistic relaxation algorithm to integrate the spatial contextual information with the individual waveform shape information to identify the reference peak that most likely corresponds to the true surface elevation.

In the following sections, we will first introduce the standard NASA ICESat/GLAS data products and two associated standard waveform retracking methods. Then, the conditions that would fail these two retracking methods will be discussed. Next, we will present the mathematical formulation of the probabilistic relaxation retracking (PR) algorithm. It is followed by a number of application examples to demonstrate its effectiveness. Finally, we summarize key research findings and draw conclusions.

3.2 Datasets

ICESat/GLAS altimetry system conducted a total of 18 measurement campaigns during

2003-2009. Each campaign lasted 34 – 38 days, as a sub-cycle of the more densely spaced 91-day exact repeat orbit (Yi et al. 2011). There are 15 different types of ICESat/GLAS data products available at National Snow and Ice Data Center (NSIDC) (http://nsidc.org/data/icesat). GLA01 provides the original transmitted and returned waveform data. GLA12, GLA13, GLA14 and

GLA15 provide surface elevations for ice sheets, sea ice, land, and oceans, respectively. In this study, GLA01, GLA12 and GLA14 data products are used.

Three independent high resolution topographical datasets are used to validate and evaluate the surface elevation estimates produced by our probabilistic relaxation retracking method in comparison with the standard ICESat/GLAS data products. Those datasets include IceBridge LVIS elevation data over the Greenland ice sheet (Blair and Hofton 2010), the Arctic DEM over the tundra in the Arctic Coastal Plain, and the Shuttle Radar Topography Mission (SRTM) 1 arc- second elevation data over the Taklimakan desert in China. IceBridge LVIS elevation data were acquired by an airborne laser altimeter with a footprint diameter of 20 m and a spacing between footprints of 10 m. The vertical accuracy of LVIS data is better than 0.12 m (Brunt et al. 2017).

The LVIS data set used in this study was acquired on 2 May 2012, following ICESat/GLAS track

0174. The Arctic DEM data set provided by the Polar Geospatial Center

(http://pgc.umn.edu/arcticdem) at University of Minnesota has a high spatial resolution of 5 m, which was created from high resolution satellite stereo images acquired by DigitalGlobe Inc. The

SRTM DEM, provided by U.S. Geological Survey (USGS) Earth Explorer

(https://earthexplorer.usgs.gov/), was created using the interferometry radar data acquired by the

Shuttle Radar Topographic Mission in 2000. It has a spatial resolution of 30 m. Its vertical accuracy is variable depending on the topography and the presence of vegetation. The best accuracy is estimated to be 4.07 ± 0.47 m (Gorokhovich and Voustianiouk 2006). To ensure fair and valid comparison, all elevation data sets have been vertically referenced to the same geoid – EGM2008.

3.3 ICESat/GLAS standard retracking methods

The transmitted and returned laser pulse waveforms represent the pulse energy over the elapsed time in nanosecond (ns), as shown in Figure 3.1. The elevation of the reflecting surface is given by Equation (14) below:

h = H – (R + ΣΔRc) – hgeoid (14) where h is the elevation of the laser footprint, H is the height of the mass center of the satellite above the Topex/Poseidon reference ellipsoid, R is the nadir range between the mass center of the satellite and the laser footprint, ΣΔRc represents the sum of the instrumental and geophysical corrections applied to the range R to account for instrumental biases, propagation delays of the electromagnetic waves in the atmosphere and geophysical effects, and hgeoid is the difference between the reference ellipsoid and a specific geoid model (EGM2008 in this study).

The range R is given in Equation (15):

R = (Treturn – Ttrans) × c / 2 (15)

where c is the speed of light; Ttrans and Treturn represent the times of the transmission and the reception of the laser pulse, which are precisely determined by the two reference points on the transmitted and the returned waveforms, as shown in Figure 3.1. The standard Centroid retracking method defines the geometric centroid of the waveform above the background noise level as the reference point to calculate the range and surface elevation (Gardner 1992). The standard MAP retracking method identifies individual peaks on the returned waveform by fitting multiple

Gaussian curves to the peaks. The mid-point of the highest Gaussian peak is then identified as the time reference point to calculate the range and surface elevation (Brenner et al. 2011). The transmitted waveform is fitted by a single Gaussian peak. For the returned waveform, the adjacent peaks with an interval of less than 30 ns are merged during the fitting process. Then, one or two

Gaussian peaks are fitted and the maximum amplitude peak is identified (Brenner et al. 2011).

This merging procedure often results in a wide Gaussian peak for the returned waveform, as shown by the green curve (WFR) in Figure 3.1. Both the standard Centroid and the MAP method try to

capture the main shape of returned waveform to represent the surface elevation within the illuminated area.

Figure 3.1 The transmitted and returned waveforms and the retracking methods. This figure is a derivative from Figure 3 in the ICESat Algorithm Theoretical Basis Document (Brenner et al. 2011).

In general, the Centroid retracking method is a good choice for terrestrial land surfaces due to its relatively high relief and heterogeneous vegetation cover. However, many terrestrial geographical features, such as inland lakes, large rivers, deserts, tundra and coastal zones, are relatively homogeneous with a small elevation variation. For these types of terrestrial surfaces, the

MAP retracking method may be more suitable and reliable than the Centroid retracking method

(Brenner et al. 2011; Duda et al. 2001). Also, it should be pointed out that some terrestrial landscapes exhibit strong seasonal variations. In the wet season, wetlands are likely to be filled with water during the flood period and effectively become flat surfaces. During the long winter season, the tundra regions are more homogeneous and smooth with a full cover of snow and ice, compared with the brief summer season when mosses, herbaceous sedges and grasses prevail

(Hinkel et al. 2012). For those seasonally changing terrestrial surfaces, the MAP retracking method

may be a better choice to retrieve their surface elevations for some specific seasons. However,

ICESat/GLAS GLA14 products for all types of terrestrial land surfaces were produced by only the

Centroid retracking method, without distinguishing permanent or seasonal homogeneous

terrestrial land surfaces for the MAP retracking method.

No matter which retracking method is adopted, producing a reliable measurement would be a challenge when the returned waveforms are affected by bad weather conditions. The suspended particles of clouds, ice fog, blowing snow and dust could cause forward scattering on laser pulse photons and increase the photon travel path, referred to as “atmospheric path delay”

(Duda et al. 2001). The lower the cloud is, the greater the scattering effect would be (Mahesh et al. 2002). The near-surface blowing snow and ice fog can have a much stronger scattering effects than clouds. Even a thin layer of blowing snow can result in a large path delay (Yang et al. 2010).

The forward scattering deforms the returned waveform and could introduce many spurious peak- features as shown in Figure 3.1. Another typical manifestation of the weather contamination is the long tail on the right side of the returned waveform. Both the MAP and the Centroid retracking methods try to capture the main shape of the returned waveform to represent the surface elevation, but are often misled by spurious features and the long tail. Under the influences of the long tail and the spurious peaks, the time reference points defined by them are often shifted to the right on the time axis, resulting in a longer range and hence biased, lower elevation measurements. We recognize that the shape information of a single waveform alone is not adequate to address the problem associated with the spurious peaks and the long tail. In this research, we attempt to introduce the spatial contextual information to tackle this problem.

3.4 New probabilistic relaxation retracking method

3.4.1 Spatial contextual information along the satellite track

On a flat or gradually changing terrain surface, the adjacent footprints along the satellite

track would generate waveforms with similar shape characteristics due to the geographical

proximity and spatial autocorrelation. The spatial contextual information among the adjacent

footprints may offer additional clues to help retrieve the true surface elevation.

Figure 3.2a shows a 5-footprint neighborhood of the satellite track on a horizontal

continuous smooth surface. These footprints should produce gradually varying elevation

measurements lacking a dramatic change. Without signal contamination, the returned waveforms

of these footprints should be dominated by a single Gaussian peak, and the dominant peaks of

these waveforms could align on the time axis with close time proximity. Assuming that the

highlighted red footprint in Figure 3.2a is a footprint contaminated by thin cloud cover and that no

dominant peak can be clearly identified for its waveform, this contaminated waveform probably

fails by the MAP retracking method. However, when this waveform is examined together with its

neighboring waveforms in Figure 3.2b, a small peak feature on this contaminated waveform (as

shown in Figure 3.2c stands out, which is close to the dominant peaks of the neighboring

waveforms. With reference to these neighboring waveforms, we can infer that this small peak on

the contaminated waveform of the central red footprint most likely corresponds to the true surface

elevation. This small but true signal-peak is often missed by the two standard retracking methods

that rely solely on the major shape information of the single waveform returned from the red

footprint as shown in Figure 3.1.

In this study, we present a new retracking method that is capable of identifying the true signal-peak for elevation measurement by integrating the waveform shape information of the

central contaminated footprint with the spatial contextual information from the neighboring footprints. Our new retracking method consists of several computational steps as described below.

Figure 3.2 The spatial contextual information in the neighboring footprints along a satellite track. (a) Definition of the neighborhood, (b) The central contaminated waveform and its neighboring waveforms, (c) The Gaussian peaks and the decomposition of the central contaminated waveform.

3.4.2 Decomposition of the returned waveform

The returned waveform can be modeled by a combination of multiple Gaussian-shaped curves (Zwally et al. 2002), as defined in Equations (16) and (17):

( ) = + ( ) (16) 𝑀𝑀 𝑊𝑊 𝑡𝑡 𝜀𝜀 ∑𝑗𝑗=1 𝑊𝑊𝑗𝑗 𝑡𝑡 ( ) 2 ( ) = − 𝑡𝑡−𝑡𝑡𝑗𝑗 (17) 2 2𝜎𝜎𝑗𝑗 𝑊𝑊𝑗𝑗 𝑡𝑡 𝐴𝐴𝑗𝑗𝑒𝑒

where W(t) is the energy intensity of returned waveform at time t, Wj(t) is the intensity of Gaussian peak j (j=1,..,M) at time t, M is the total number of Gaussian peaks on the waveform, Aj is the amplitude of Gaussian peak j, tj and σj are the center location on the time axis and the standard deviation (band width) of Gaussian peak j, respectively, and ε is the background noise level of the waveform. Following the method in Brenner (2011), a nonlinear least square fit is implemented to estimate the parameters for each Gaussian peak. The fitting minimizes the difference between the modeled waveform and the observed waveform. As shown in Figure 3.2c, the central contaminated waveform is decomposed into four Gaussian peaks. Each of the four neighboring waveforms in

Figure 3.2b is also decomposed into individual Gaussian peaks using the same procedure.

Our new retracking method tries to identify the peak with the largest probability of being the true signal-peak for the surface elevation retrieval. Each Gaussian peak of the central contaminated waveform is assigned an initial probability of being the true signal-peak according to its amplitude, which is calculated using Equation (18) in the following section. Then, the initial probability of each peak is iteratively modified through its compatibility with the peaks of the neighboring waveforms. Once the process has converged or reached the predefined number of iterations, the peak with the maximum posterior probability is selected as the true signal-peak for the elevation retrieval. As shown in Figure 3.2b and Figure 3.2c, the first peak (the red dotted curve) is not the one with the largest amplitude, but its probability of being the true signal-peak should be very high when the neighboring waveforms are taken into consideration. We adopt the probabilistic relaxation method to incorporate the spatial contextual information from the neighboring waveforms.

3.4.3 Identification of the true signal-peak using the probabilistic relaxation method

The probabilistic relaxation method was first introduced by Rosenfeld (1976). It is an iterative technique that allows the incorporation of contextual information in the labelling

(classification) problem. The basic idea is to make a tentative, rather than firm, initial classification of an object based on the attributes of the object, and then repeatedly refine the classification decision based on the local contextual information at each iteration (Rosenfeld and Kak 1982).

The initial classification decision will be positively or negatively reinforced by the contextual

information, depending on the compatibility between the object being processed and its

neighboring objects. The mathematical formulation of the probabilistic relaxation method is in line

with Bayes’ theorem, which updates the prior probability of an event to a posterior probability by

incorporating the conditions related to the event. In this study, we implemented the probabilistic

relaxation algorithm to compute the posterior probability of a Gaussian peak to be the true signal- peak by introducing the spatial contextual information. The initial prior probability of a peak is determined according to its amplitude, then the prior probability will be positively or negatively updated at each iteration by evaluating its compatibility with the neighboring waveforms.

After the returned waveforms, including the central waveform and the neighboring waveforms, are decomposed into several Gaussian peaks (Figure 3.2c), an initial prior probability of being the true signal-peak is assigned for each peak according to its peak amplitude (the shape information). The higher the peak, the larger the initial prior probability will be. Numerically, the initial prior probability of a peak is defined by Equation (18):

= (18) 𝑖𝑖𝑖𝑖 0 𝐴𝐴 𝑖𝑖𝑖𝑖 𝑀𝑀𝑖𝑖 𝑃𝑃 ∑𝑗𝑗=1 𝐴𝐴𝑖𝑖𝑖𝑖

= 1 (19) 𝑀𝑀𝑖𝑖 0 ∑𝑗𝑗=1 𝑃𝑃𝑖𝑖𝑖𝑖

where is the initial prior probability of peak j on waveform i, is the amplitude of the peak j 0 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 on waveform𝑃𝑃 i, is the number of peaks on the waveform i𝐴𝐴, which varies among different

𝑖𝑖 waveforms. is𝑀𝑀 in the range [0, 1], and the sum of the probabilities of all peaks on the waveform 0 𝑖𝑖𝑖𝑖 i is equal to unity𝑃𝑃 as shown in Equation (19).

The spatial contextual information (conditional information) is quantified by the

compatibility between each candidate peak of the central waveform and the peaks of the

neighboring waveforms. The total number of footprints along the satellite track is S. Each footprint

along the satellite track will be treated as a central footprint and is denoted by s (s = 1, 2, …, S).

The candidate peak of the central waveform (s) under examination is denoted by index k (k = 1, 2,

..., L). The compatibility ( ) of candidate peak k with all the peaks on the neighboring waveforms 𝑟𝑟 𝑘𝑘 at iteration r (r = 1, 2,…, 𝑄𝑄R) is given by Equation (20) and Equation (21):

= , (20) 𝑟𝑟 𝑁𝑁 𝑀𝑀𝑖𝑖 𝑟𝑟−1 𝑄𝑄𝑘𝑘 ∑𝑖𝑖=1 ∑𝑗𝑗=1 𝑤𝑤𝑖𝑖𝐶𝐶𝑘𝑘 𝑖𝑖𝑖𝑖𝑃𝑃𝑖𝑖𝑖𝑖

1 , = (21) �𝑡𝑡𝑘𝑘−𝑡𝑡𝑖𝑖𝑖𝑖� 𝑘𝑘 𝑖𝑖𝑖𝑖 𝑀𝑀𝑖𝑖 1 𝐶𝐶 ∑𝑗𝑗=1 �𝑡𝑡𝑘𝑘−𝑡𝑡𝑖𝑖𝑖𝑖� where N is the number of neighboring footprints, is the weight of the neighboring waveform i,

𝑖𝑖 is the number of peaks on the neighboring waveform𝑤𝑤 i, is the mid-point location of the

𝑖𝑖 𝑘𝑘 candidate𝑀𝑀 peak k on the central waveform under examination,𝑡𝑡 is the mid-point location of the

𝑡𝑡𝑖𝑖𝑖𝑖 peak j of the neighboring waveform i on the time axis, , is the normalized temporal proximity

𝑘𝑘 𝑖𝑖𝑖𝑖 between the candidate peak k on the central waveform𝐶𝐶 under examination and the peak j on the

neighboring waveform i. The closer the two peaks, the higher , is. is the probability of 𝑟𝑟−1 𝑘𝑘 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 the peak j to be true-signal peak for the neighboring waveform i𝐶𝐶 at (r – 1𝑃𝑃)th iteration.

At each iteration r, the probability of peak k on the waveform under examination will 𝑟𝑟 𝑘𝑘 be updated using the prior probability 𝑃𝑃 in the preceding iteration (r – 1) and the compatibility 𝑟𝑟−1 𝑘𝑘 at current iteration r as in Equation𝑃𝑃 (22): 𝑟𝑟 𝑄𝑄𝑘𝑘

= 𝑟𝑟−1 𝑟𝑟 (22) 𝑃𝑃𝑘𝑘 𝑄𝑄𝑘𝑘 𝑟𝑟 𝐿𝐿 𝑟𝑟−1 𝑟𝑟 𝑃𝑃𝑘𝑘 ∑𝑘𝑘=1 𝑃𝑃𝑘𝑘 𝑄𝑄𝑘𝑘 where the compatibility at iteration r is calculated based on the prior probability of the peaks 𝑟𝑟 𝑘𝑘 on all neighboring footprints𝑄𝑄 in the preceding iteration (r – 1) according to Equation (20). The posterior probability of each peak on the central waveform under examination (k = 1, 2,.., L) is updated using the computational steps given in Equations (20) – (22).

For each iteration r, every footprint along the satellite track will be processed as a central footprint using the procedure described above. We will then obtain the posterior probability 𝑟𝑟 𝑖𝑖𝑖𝑖 for all waveform peaks of all footprints along the satellite track, which will be used as the prior𝑃𝑃

probabilities for the computation at the next iteration (r + 1).

The whole iteration process will cease when the convergence criteria are satisfied for all

footprints along the satellite track or when the predefined number of iteration (100 in this study)

is reached. The calculated probabilities of the peaks on every waveform along the satellite track at

current iteration (r) are compared with their probabilities at the preceding iteration (r – 1). We

consider that the convergence state of the waveform under examination is achieved if the

magnitude of the probability changes is smaller than a predefined threshold α as in Equation (23):

< (23) 1 𝑀𝑀𝑖𝑖 𝑟𝑟 𝑟𝑟−1 𝑀𝑀𝑖𝑖 ∑𝑗𝑗=1�𝑃𝑃𝑗𝑗 − 𝑃𝑃𝑗𝑗 � 𝛼𝛼

where and are the probabilities of peak j on the waveform i at the current and preceding 𝑟𝑟 𝑟𝑟−1 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 iterations.𝑃𝑃 The𝑃𝑃 threshold α is set to 0.005 in our case studies. In most cases, the iteration process

converges after a few iterations.

In current iteration, if the convergence state of the footprint under examination is achieved, then this footprint will be skipped in all the following iterations and the probabilities of the peaks on this waveform will retain the same. Therefore, the whole iteration process can be generalized as the follows.

For iteration r = 1, … R

For the central footprint s = 1, … S

Check the convergence state of footprint s

If not satisfied

Update the probabilities of each peak on this waveform s

Else

Move to the next footprint s + 1

End

After the iteration process ceases, the peak with the highest probability on each waveform will be used as the true signal-peak to determine the reference point (tnew) and hence to calculate the corresponding surface elevation using Equation (24):

= + × + (24) 𝑐𝑐 ℎ𝑛𝑛𝑛𝑛𝑛𝑛 ℎ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 �𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 − 𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛� 2 ∆ℎ𝐺𝐺𝐺𝐺 where is the elevation value using the reference point determined by our probabilistic

𝑛𝑛𝑛𝑛𝑛𝑛 relaxationℎ method, is the surface elevation given in ICESat/GLAS products, is

ℎ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 76

the time reference point given by either Centroid or MAP retracking method, is the reference

𝑛𝑛𝑛𝑛𝑛𝑛 point derived from our new probabilistic relaxation method, c is the speed 𝑡𝑡of light, is the

𝐺𝐺𝐺𝐺 Gaussian-Centroid (G-C) offset (i_GmC in GLA12/14 product) on the transmitted waveform.∆ℎ The

inclusion of this term aims to maintain the consistency of the types of reference points on both

transmitted and returned waveforms and can correct a bias up to 6 cm in the elevation measurement

(Borsa et al. 2014).

In our probabilistic relaxation retracking method, a one-dimensional neighborhood needs to be defined for the utilization of the spatial contextual information. For our case studies, we adopted a 3-footprints or 5-footprints neighborhood. For a 5-footprints neighborhood, when a footprint is processed, the two adjacent footprints before it and the two adjacent footprints after it along the satellite track are used to define the size of the neighborhood. The immediate neighbor footprint received a weight twice as large as that of the distal neighbor footprint in the iterative posterior probability computation. For the same type of terrain surface, the smoothness and continuity condition may be easily satisfied for a geographically small neighborhood but may not be fulfilled for a large neighborhood. Therefore, an appropriate choice of the neighborhood size based on the surface smoothness is important for applying our retracking method. The footprint size of ICESat/GLAS lase pulse is about 70 m in diameter, and the spacing between adjacent footprints is about 170 m. In our case studies, we adopted a 5-footprints neighborhood (~680 m) for relatively smooth lake surface and the Greenland ice sheet and a 3-footprints neighborhood (~

340 m) for relatively bumpy tundra and desert surfaces.

The incorporation of the spatial contextual information from footprints within the neighborhood is only applicable to the types of terrain surfaces that are relatively smooth and have gradually changing elevation. If the majority of the neighboring footprints were extremely

contaminated by atmospheric factors or there is abrupt and dramatic elevation change (e.g. cliffs,

trees) within the neighborhood, the spatial contextual information given by the neighboring

footprints would not be useful and hence our probabilistic relaxation method would not be

applicable.

To ensure the applicability of our probabilistic relaxation method, we first identify the

extremely contaminated footprints along the satellite track and then check the surface continuity

and smoothness condition before applying our probabilistic relaxation method. We utilize the

reflectivity (i_reflctUC) and the gain value (i_gval_rcv) in GLA12/14 data product

(https://nsidc.org/data/glas/data-dictionary-glah014) and the signal-to-noise ratio (SNR) as

indicator variables to detect extremely contaminated footprints. The SNR value for each footprint

is calculated based on the maximum intensity of the waveform and the mean background noise

following the method in (Shu et al. 2018). The contaminated footprint tends to have low reflectivity,

high gain value and low SNR value. The footprints with (i_reflctUC <0.05 && i_gval_rcv >=250

&& SNR < 12) are considered extremely contaminated. They are not used as neighboring footprints for the central footprint under processing. The surface smoothness condition is examined through checking the topographic slope on the two sides of the central footprint. The slope on each side is calculated based on the elevation value of each footprint determined by the highest peak in

Equation (16). A line is fitted on each side for the neighboring footprints and the central footprint to compute the slope. The neighboring footprints will be incorporated in our probabilistic relaxation method only if the slope on that side is less than 0.25°. If the slope on both sides are larger than 0.25°, the terrain surface is considered to not satisfy the smoothness and continuity condition, and our probabilistic relaxation method will not be applied. In the case that a central

footprint under processing has no neighboring footprint, the elevation measurement determined by the highest peak in Equations (16) and (17) will be adopted.

3.5 Application examples

We applied our probabilistic relaxation retracking method to four different types of terrestrial surfaces including frozen lake, tundra, ice sheet, and desert. The locations of

ICESat/GLAS ground tracks used in our application examples are shown in Figure 3.3. The ground track number, geographic coordinates, and the acquisition dates of these data are shown in Table

3.1. For each application site, we compare the topographic profile derived from our probabilistic relaxation retracking method with the profiles from original ICESat/GLAS data product and from the high resolution reference elevation data to demonstrate the effectiveness of our method.

Figure 3.3 Locations of the four application sites

Table 3.1 Geographic coordinates and acquisition dates of the ICESat/GLAS tracks in applications

Sites ICESat Profile Lon (°) Lat (°) Track Acquisition date Greenland ice sheet -45.01 64.79 0174 2005/11/07 Alaska lake -153.84 70.72 0134 2005/11/04 Alaska tundra -153.35 70.89 0334 2004/03/16 Xinjiang desert 86.14 40.13 1128 2003/10/06

3.5.1 The snow surface of Lake Teshekpuk in Arctic Coastal Plain

First, we evaluated the applicability of our probabilistic relaxation method to the frozen

lake surface. A lake normally contains liquid water when the temperature is higher than the

freezing point. It is covered by solid ice when the temperature is below the freezing point, and may

also be covered by snow when snow falls on the frozen ice surface. The water level of a lake may

vary at seasonal and inter-annual time-scales in response to hydrological processes (e.g. rainfall,

evaporation, runoff and exchanges with groundwater). No matter what the phase of a lake surface is (water, ice or snow), it is usually relatively flat and has no drastic surface elevation variations.

Therefore, the prospect of applying our method to lake surfaces is good for all seasons.

Our case study site is Lake Teshekpuk, located on the Arctic Coastal Plain of northern

Alaska (Figure 3.3). It is the largest lake in this region with an area over 800 km2. We examined

ICESat/GLAS elevation measurements along the satellite track A-B (Figure 3.3) at different dates

from the ICESat/GLAS repeat campaigns during 2003-2009. Because this site was classified as

part of terrestrial land, in the creation of ICESat/GLAS data products the elevations measurements on the lake surface were retrieved using the standard Centroid retracking method. We plotted several elevation profiles acquired at different dates, including March 2 and October 18 in 2004,

November 4, 2005, and March 2 and November 18 in 2008. We observed that the elevation profiles

acquired on March 2 and October 18 in 2004 and March 2 and November 18 in 2008 are very similar and consistent, and meet our expectation for a flat lake surface. However, the profile (the blue curve) acquired on November 4, 2005 is very different from other repeat profiles (Figure

3.4a). On that date, Lake Teshekpuk was covered by snow. The drastic elevation variation up to 4 m along the track was counter to our expectation of a relatively smooth surface of the lake. This raised our suspicion that the ICESat/GLAS observations on that date were contaminated and the contaminated waveforms failed the default Centroid retracking method, leading to the spurious elevation measurements.

Figure 3.4 Elevation profiles of the frozen snow surface over Lake Teshekpuk on the Arctic coastal plain along the transect from footprint A to footprint B. (a) The problematic profile collected at November 4, 2005 and the normal profiles collected at other dates; (b) The profiles are retrieved using the standard Centroid method, the Probabilistic Relaxation methods, and the highest peak given in Equation (16), respectively.

We plotted and examined the waveforms of the footprints along the track AB (Figure 3.3) acquired on November 4, 2005. We found out that these waveforms are characterized with multiple spurious peaks and a long tail. The shapes of the waveforms for five footprints in a neighborhood are plotted in Figure 5a. These five footprints were highlighted in different colors in Figure 4b, and the elevation measurements given by the standard ICESat/GLAS data product are apparently spurious and highly likely to be erroneous by visually inspecting the topographic profile. As the first step to tackle the spurious measurements produced by the Centroid retracking method, we retrieved the elevation measurements using the highest peak given by Equation (16) and (17). After this retrieval, the topographic profile becomes much more reasonable than that of the original

ICESat/GLAS data product, as shown by the purple triangles in Figure 3.4b.

Further, we applied our probabilistic relaxation retracking method to enhance the computational results using a 5-footprint neighborhood. Our new retracking method and its iteration process is shown in Figure 3.5. The waveform of the central footprint (red diamond in

Figure 3.4b) was under examination, with reference to the four footprints (grey diamond in Figure

3.4b) in its neighborhood. Figure 3.5a shows the waveforms of the footprints within this neighborhood. The waveform of the central footprint was decomposed into eight separate Gaussian peaks. As shown in Figure 3.5b, Peak 2 is not consistent with the dominant waveform peaks of the four neighboring footprints.

To start our iterative process, we first assigned the initial probabilities for 8 separate peaks

according to Equation (18). Since Peak 1 has a lower amplitude than Peak 2, its initial prior

probability of being the true signal-peak is lower than Peak 2. According to Equation (20), we

computed the compatibilities between the eight peaks of the central footprint and all the peaks of

its four neighboring footprints. Since Peak 1 is closer to the true dominant signal-peaks of four

neighboring waveforms than Peak 2 and other six peaks, the compatibility of Peak 1 with four

neighboring footprints is the highest among the 8 peaks of the central waveform. Therefore, the

posterior probability of Peak 1 calculated according to Equation (22) will increase. As shown in

Figure 3.5c, after 4 iterations, the posterior probability of Peak 1 exceeds that of Peak 2 as well as other 6 peaks. As shown in Figure 5d, the process converges quickly. The average change in the posterior probabilities of these peaks calculated at 10th iteration compared with those at the 9th

iteration, defined in Equation (23), is less than the pre-defined threshold value (0.005). Peak 1 has

the largest posterior probability when the convergence criteria for the iteration process are satisfied,

therefore it was used as the reference point to calculate the elevation for this central footprint in

our probabilistic relaxation retracking method. Apparently, our new retracking method has

effectively identified the true signal-peak, Peak 1, by incorporating the contextual information

from neighboring footprints and hence increased the elevation measurement for central footprint

by 2.35 m.

After applying our new probabilistic relaxation retracking method to all footprints along the satellite track, some of the erroneous measurements that are not consistent with neighboring footprints are corrected using the spatial contextual information. The new elevation profile (the green curve in Figure 3.4b) derived from our probabilistic relaxation method is more consistent with the profiles acquired on other dates in normal condition. As shown in Figure 3.4, the

elevations measurements from original ICESat/GLAS data products on November 18, 2008 with the default Centroid retracking method are all underestimated, as compared to the new profile with our probabilistic retracking method.

Figure 3.5 Illustration of the iteration process. (a) The waveforms within the neighborhood highlighted in Figure 3.4, (b) the contaminated waveform and its decomposed Gaussian peaks, (c) probability of each peak of being the true signal peak at each iteration, (d) average probability change at each iteration

Since there is no high resolution reference data available, we use the original ICESat/GLAS data acquired on October 18, 2004 as the reference data for our assessment of our results in comparison with original ICESat/GLAS data product on November 4, 2005. This is because the profile acquired on October 18, 2004 is consistent with that acquired on other three dates (March

2 in 2004, March 2 and November 18 in 2008) and plausibly correct for the lake surface. Using

the ICESat/GLAS data acquired on October 18, 2004 as the reference, the Root Mean Squares

Error (RMSE) of the elevation measurements derived from our probabilistic relaxation retracking

method is 0.17 m, much smaller than that (0.85 m) of original ICESat/GLAS elevation

measurements acquired on November 4, 2005 (Table 3.2). The standard deviation of the elevation

measurements along the satellite track AB has been reduced from 0.81 m for original

ICESat/GLAS data products to 0.18 m for new elevation retrievals from our probabilistic

relaxation method, indicating a significant improvement in the consistency and reliability of the

elevation measurements over the frozen lake snow surface.

3.5.2 Tundra surface in the Arctic coastal plain

The application site for tundra surface is also located on the Arctic Coastal Plain of northern

Alaska (Figure 3.3), near Lake Teshekpuk. The Arctic tundra is underlain by thick permafrost, and there are two main seasons, a long winter and a brief summer. During the summer, the top layer of seasonally-frozen soil melts, and the tundra is covered by marshes, lakes, bogs streams, and low growing tundra plants, such as, sedges, grasses, dwarf willows, moss, crowberry, black bearberry, and lichen (Markon and Derksen 1994). During the winter, it is very cold and dark, and covered by snow. The ICESat/GLAS track segment CD (Figure 3.3) traverses several creeks and vegetated tundra. The ICESat/GLAS data under examination were acquired on March 16, 2004, and at that time the site was covered by snow. Although the tundra surface here is expected to be more bumpy and rougher than the snow-covered lake surface, it still represents a relatively low-relief terrain with homogeneous surface, particularly when it is covered by snow in winter.

Figure 3.6 Comparison of the probabilistic relaxation derived profiles with the original ICESat/GLAS data product and the high-resolution reference data. (a) over tundra surface in the Arctic coastal plain, (b) over ice-sheet surface of Greenland, (c) over sand desert surface of Xinjiang

For the ICESat/GLAS track segment CD, the elevation measurements, which were retrieved by the standard Centroid retracking method as this site was classified as land in the original ICESat/GLAS data product, were plotted as a topographic profile (in blue) in Figure 6a.

This original ICESat/GLAS profile was compared with the reference profile from the 5 m spatial resolution Arctic DEM (http://pgc.umn.edu/arcticdem), which was created using high resolution satellite stereo images acquired during 2013 – 2015. A time difference exists between the

acquisition of the ICESat/GLAS data and the Arctic DEM data. Since this remote tundra site is situated far away from human activities, the general topographic undulation should be very similar and without significant change during the time period. Seasonal surface elevation change could occur due to the vegetation growth and the snow accumulation. The vegetation height in summer and the snow accumulation in winter in this region are averaged 17.3 ± 8.1 cm (Von Fischer et al.

2010) and 32.5 ± 8.8 cm (Sturm and Liston 2003), respectively. The rate of surface uplift due to glacial isostatic adjustment is about 0.01 m per year (Sella et al. 2007).

Figure 3.7 Scatter plots of the original ICESat/GLAS data products and the measurements derived from the probabilistic relaxation retracking method with the reference elevation data. PR in the graph is the abbreviation of probabilistic relaxation. (a) over tundra surface in the Arctic coastal plain, (b) over ice-sheet surface of Greenland, (c) over sand desert surface of Xinjiang.

The difference between the original ICESat/GLAS data product and the Arctic DEM along the satellite track segment CD ranges from 0.5 m to 4.02 m, with a RMSE of 0.81 m (Table 3.2).

It appears that the original ICESat/GLAS measurements from the Centroid retracking method significantly underestimated the surface elevation, in comparison with the high-resolution Arctic

DEM as the reference. We applied our probabilistic relaxation retracking method to this portion of ICESat/GLAS track, namely, decomposing each waveform into separate peaks and then incorporating the spatial contextual information through an iterative process to find the peak with

the maximum posterior probability for elevation retrieval. The elevation profile derived from our

probabilistic relaxation retracking method is in much better agreement with the reference Arctic

DEM than the original ICESat/GLAS data product. The Pearson’s correlation coefficient r

between our elevation retrievals and the measurements of the Arctic DEM is as high as 0.98, much

larger than that (0.88) of the original ICESat/GLAS data product (Figure 3.7a). The RMSE of our

elevation retrievals with the reference to the Arctic DEM is reduced to 0.22 m, a significant

improvement over the original NASA ICESat/GLAS data product with RMSE of 0.81 m (Table

3.2).

Table 3.2 Evaluation of the PR derived measurements versus original ICESat/GLAS data products with reference to high resolution topographic data

Number of Original ICESat/GLAS products (m) Probabilistic relaxation Results (m) Surface Footprints Max Diff Mean Diff RMSE r* Max Diff Mean Diff RMSE r*

Arctic Lake 88 3.79 1.49 0.85 0.63 0.18 0.17

Tundra 69 4.02 2.03 0.81 0.94 0.95 0.25 0.22 0.99

Ice sheet 73 5.34 1.04 1.24 0.98 0.73 0.19 0.30 0.99 Desert 94 8.55 3.11 2.48 0.99 8.05 2.45 2.35 0.99 *r is the Pearson’s correlation coefficient between the ICESat/GLAS data and the reference DEM data. Max Diff and Mean Diff are calculated by subtracting original ICESat/GLAS measurement or our probabilistic relaxation results from the reference topographic data. For Arctic Lake case, the ICESat/GLAS data acquired on October 18, 2004 (similar season) was used as the reference for the comparison.

3.5.3 Ice sheet surface of Greenland

The application site for the ice sheet surface is in southern Greenland (Figure 3.3).

Greenland is the second largest mass of glacial ice in the world after the Antarctic ice sheet. The

thickness of Greenland Ice Sheet is generally more than 2 km and over 3 km at its thickest point

(Bamber et al. 2001). Our application site is located near the central region of southern Greenland.

The ice sheet surface at our application site is generally smooth with a relatively small surface

slope.

The elevation measurements from the original ICESat/GLAS data product were plotted as a topographic profile along the satellite track segment EF (blue), which was acquired on November

7, 2005. The ICESat/GLAS data product for this site was created using the standard MAP retracking method. Although the profile is smooth in general, there are some spurious undulations

(Figure 3.6b). Both MAP-derived profile and our probabilistic relaxation derived profile are compared with the high resolution reference topographic data (green curve), which was acquired by an airborne wide-swath laser altimeter system LVIS through the IceBridge program on May 2,

2012. There is a 6.5 year span between the acquisition dates of the ICESat/GLAS data and

IceBridge LVIS data. However, the surface elevation change in this region is very small. As reported in a previous study, the ice sheet in the southern central Greenland thickens by 0.05 ±

0.02 m each year (Jezek 2012). The surface uplift due to glacial isostatic adjustment is 0.012 m every year (Khan et al. 2016).

As shown in Table 3.2, the RMSE of the original ICESat/GLAS data product is 1.24 m, with a maximum difference up to 5.34 m. After applying our new retracking method, the derived elevation measurements (red) are almost the same as the reference IceBridge LVIS measurements.

The RMSE of the elevation measurements from our new retracking method is reduced to 0.3 m from 1.24 m, and the Pearson correlation coefficient r is as high as 0.99 as compared to the 0.98 of the original ICESat/GLAS product. This application example indicates that our new probabilistic relaxation method is capable of producing more accurate and reliable elevation measurements than the standard MAP retracking method.

3.5.4 Sand dune surface in an arid desert

The application site is located in the northeast Taklimakan Desert (Figure 3.3), the largest desert in China. It is made up of continuous sand dunes, which are usually over 100 m high and

some even higher than 300 m. In this arid region, a thin layer of blowing particles near the surface

due to winds often occurs, which may lead to the forward scattering effect on the ICESat/GLAS waveforms. The ICESat/GLAS satellite track segment GH extends across four major sand dunes

from north to south, as shown in Figure 3.6c. The original ICESat/GLAS data along this track

segment under examination were acquired on October 6, 2003. We use the 30 m SRTM DEM data

collected on February 11, 2000 as the reference. The northeast Taklimakan desert is an area of low

wind energy (Wang et al. 2002). Even though there might be changes for the small sand dunes, comparison of the LANDSAT images acquired on February 6, 2000 and October 4, 2003 indicates that there was no clear horizontal shift in the major dunes in our application site.

The original elevation measurements from ICESat/GLAS data products for this site were retrieved by the standard Centroid retracking method. Although the original ICESat/GLAS elevation measurements correlate well with the SRTM data in general, the elevation measurements at some points are clearly underestimated (e.g. footprint 57) as shown by the enlarged inset in

Figure 3.6c. Figure 3.8a shows the waveforms of the three adjacent footprints 55, 56 and 57 in the

Figure 3.6c inset. These waveforms line up with each other as indicated by the vertical dashed line in Figure 3.8a. In Figure 8b, the waveform of footprint 57 is decomposed into 6 peaks. The first red peak is identified by our Probabilistic Relaxation (PR) method as the true signal-peak for elevation retrieval. This elevation value is more consistent than the original elevation measurement with the SRTM data. It improves the elevation measurement of footprint 57 by 3.63 m as shown by the inset in Figure 3.6c. Applying our new probabilistic relaxation retracking method, we derived the elevation measurements for all footprints along the satellite track segment GH. As shown in Figure 3.6c, the elevation measurements from our method are in a good agreement with the reference SRTM data with Pearson’s correlation coefficient of 0.99. The RMSE of our new

elevation measurements is reduced to 2.35 m, in comparison with that (2.48 m) of the original

ICESat/GLAS data product.

Figure 3.8 Waveforms of the footprints highlighted in the inset of Figure 6c. (a) waveforms of the three footprints within the neighborhood; (b) the reference points determined by the Centroid and the Probabilistic Relaxation methods for the waveform of footprint 57.

3.6 Discussion

Previously, in the creation of ICESat/GLAS data products, two standard retracking

methods were used to process the laser waveforms returned from the Earth surface for the elevation

retrievals. The Centroid retracking method is designed for the complex terrestrial surfaces, while

the MAP retracking method for smooth and homogeneous surfaces. Both methods are based on

the geometric shape of the returned waveform to locate the reference point for the elevation

computation. Although the majority of terrestrial lands are complex and heterogeneous with

varying elevation and vegetation cover, a considerable portion of terrestrial lands has relatively

smooth and gradually changing terrain surfaces all year-around or seasonally, such as, inland waters (lakes, reservoirs, and rivers), tundra, deserts, coastal beaches, etc., which should have been processed using the MAP retracking method in the creation of ICESat/GLAS data products. The

use of the default Centroid retracking method for these types of terrestrial surfaces has produced a

large quantity of erroneous or spurious elevation measurements as revealed in our application

examples. Our analysis suggests that a more detailed terrestrial land cover classification should be

adopted to distinguish relatively smooth and gradually changing land surfaces from complex land

surfaces for the selection of an appropriate waveform retracking method for elevation retrievals.

In particular, when the returned waveform is contaminated by bad weather conditions

through multiple particle scattering, the waveform may be distorted with multiple spurious peaks

with a long tail. These spurious peaks and the long tail on the waveform adversely affect the

determination of the true reference point for elevation retrieval in both the Centroid and MAP

retracking methods, leading to serious underestimates of the surface elevation. For regions with

more frequent clouds, fog, blowing snow or sand dust, the laser waveforms are more prone to

atmospheric contamination. Clouds prevail in the Arctic over half of the year (Shupe et al. 2011;

Wang and Key 2005). Snow is the primary feature of the Arctic, covering land surfaces for about

8 – 10 months of a year. The frequent and strong winds in this region can disturb the loose and recent snow and carry it long distances across the low-relief tundra or ice sheet surfaces (Liston and Sturm 2002), forming a blowing snow layer. As reported, over half the wind events in the

Arctic region have speed greater than 5 m/s, and the highest speed could reach to 25 m/s (Small et al. 2011). Blowing snow has been demonstrated to have a more significant influence than cloud cover on the estimation of surface elevation (Mahesh et al. 2002; Yang et al. 2010). In our application examples, the measurement error of the original ICESat/GLAS data products can be as large as about 4 m for the Arctic frozen lake, about 5 m for the Greenland Ice Sheet, and about

4 m in the Arctic tundra. In the desert areas, blowing sand and dusts often occur due to lack of vegetation cover. The dust particles may cause the forward scattering effect on the laser

waveforms, leading to the failure of the standard Centroid retracking method. In our desert

application example, the error of the original ICESat/GLAS data product can be as large as 8.55 m. Therefore, the regions prone to clouds, ice fog, and blowing snow and dust may require a more robust retracking method that is resistant to atmospheric contamination.

Our probabilistic relaxation retracking method combines spatial contextual information

from adjacent footprints along the satellite track with the waveform shape information in the

determination of the reference point for the elevation retrieval. This is in contrast to the standard

Centroid and MAP retracking methods that solely rely on the waveform shape information.

Therefore, our method is more resistant to the atmospheric forward scattering effect and can more

reliably identify the true signal peak on the waveform for elevation determination.

Our probabilistic relaxation retracking method is an iterative computational process. Its first step is to assign the initial prior probabilities to the decomposed peaks in terms of their peak amplitudes. The highest peak has the largest prior probability to be the true signal peak. Clearly, the first step of our probabilistic relaxation method is virtually the same as the standard MAP retracking method. The difference of our retracking method from MAP retracking method is that we select the peak with the maximum posterior probability as the true-signal peak after the spatial contextual information is iteratively incorporated through evaluating the neighborhood compatibility, instead of simply selecting the peak with the maximum amplitude in the MAP retracking method. From this perspective, our probabilistic relaxation retracking method extends the MAP retracking method and is less susceptible to the waveform deformation caused by the atmospheric forward scattering. As demonstrated in the four application examples, our new retracking method is applicable to different types of terrain surfaces, including the ice sheets, inland lake surfaces, tundra, and sand deserts. It can effectively correct erroneous or spurious

elevation measurements in the original NASA ICESat/GLAS data products either produced by the

Centroid or MAP retracking method, resulting in much higher reliability and accuracy for the

elevation measurements.

Although our probabilistic relaxation retracking method is more robust than the standard

MAP retracking method for some landscapes, it is still not suitable for complex terrain surface

with strong topographic relief within the laser footprint or for satellite tracks where all the

neighboring footprints are extremely contaminated. The spatial contextual information utilized in

our retracking method stems from the smooth and gradually varying neighborhood, in which the

footprints have similar surface roughness and elevation. The relative smoothness and topographic

continuity of the terrain surface is the basic condition for applying our probabilistic relaxation

retracking method. As demonstrated by application examples, the inland lake surfaces, tundra, ice

sheets and deserts with large sand dunes satisfy the smoothness and continuity condition, making

our probabilistic relaxation retracking method applicable to such Earth surfaces. Also, it should be

noted that if the majority of the neighboring waveforms have been extremely contaminated by the

atmospheric forward scattering effect, the spatial contextual information becomes invalid and unhelpful for identifying the true signal peak and hence our retracking method would not work. In our case studies, we used the gain and reflectivity thresholds to identify footprints that were extremely contaminated in the evaluation of the neighborhood compatibility for the iterative calculation of posterior probability.

Our probabilistic relaxation retracking method is specially designed to process

ICESat/GLAS laser altimetry data. We believe that the basic idea and algorithm can be applied to process the airborne waveform laser and radar altimetry data. Since the footprint of airborne laser is much smaller than ICESat/GLAS laser altimetry system, and the density of footprints is much

higher, a much geographically smaller neighborhood can be used to incorporate the spatial

contextual information for the improved elevation retrieval. Within a smaller neighborhood, the

requirement of surface smoothness and continuity conditions can be easily satisfied. We anticipate

that our probabilistic relaxation retracking method can be applied to wider, even more complicated

terrestrial land surfaces with airborne waveform altimeters. The probabilistic relaxation retracking

algorithm is likely to provide realistic estimates for the multi-peaked echoes sometimes observed

over inland water bodies using radar altimetry when classical retrackers such as Offset Center of

Gravity (OCOG) (Wingham et al. 1986), commonly used over rivers, lakes, floodplains and

wetlands (Frappart et al. 2006a), fails to provide accurate height estimates.

3.7 Conclusion

The ICESat/GLAS laser altimetry system provided elevation measurements of the Earth surface during 2003-2009, which have been widely used in various scientific and practical applications. In the creation of ICESat/GLAS data products, two standard retracking methods have been employed to process the laser waveforms for elevation retrieval. The MAP retracking method was used for ice sheets, oceans, and sea ice, while the Centroid retracking method was used for the remaining terrestrial lands of the Earth surface. Both the MAP and Centroid retracking methods rely on the shape information of the returned laser waveform. Although these two standard methods work well in general, they may generate erroneous measurements when the returned waveform was deformed with multiple spurious peaks and a long tail by adverse atmospheric condition (clouds), bad weather (ice fog, blowing snow, and dust storms), and complex terrain features within the footprint. Some types of terrestrial land cover, such as, inland waters, tundra, desert, wetlands and coastal zones, have relatively smooth and gradually changing surfaces all year-around or seasonally. Our study suggests that these types of land covers should have been

identified and that ICESat/GLAS data acquired over these areas for all seasons or for a specific season should have been processed with the MAP retracking method, rather than using the

Centroid retracking method for all terrestrial lands. The magnitude and frequency of the atmospheric forward scattering effect on the ICESat/GLAS waveforms may vary from place to place. Our case studies show that the original ICESat/GLAS data products over the frozen Arctic lake, the Arctic tundra, arid sand desert, and the ice sheets may contain erroneous elevation measurements due to the use of standard retracking methods and the forward scattering effect by frequent clouds, ice fog, blowing snow and dust.

We have incorporated spatial contextual information in waveform analysis for the first time as part of a novel probabilistic relaxation retracking method. This new method initially assigns a prior probability value for each candidate peak on a returned waveform to be the true signal peak in terms of its amplitude, and then iteratively computes the posterior probability by incorporating the spatial contextual information through evaluating each peak’s compatibility with the footprints in a predefined neighborhood. After the iterative process is converged, the peak with the maximum posterior probability is selected as the true signal peak for the elevation retrieval.

Our application examples demonstrate that our probabilistic relaxation retracking method is more resistant to atmospheric contaminations of the laser waveforms and is able to create more reliable and accurate elevation measurements than the original NASA ICESat/GLAS data products for different types of land surfaces, including inland lakes, tundra, desert and ice sheets. We believe that the basic idea and algorithm of our probabilistic relaxation retracking method can find even wider application in processing the waveform data from airborne laser and radar altimetry systems.

Chapter 4: Estimation of snow accumulation over frozen Arctic

lakes using repeat ICESat laser altimetry observations – A case

study in northern Alaska

4.1 Introduction

Most of the winter precipitation in Arctic regions falls as snow and accumulates on the

ground, which is often redistributed by the wind across the landscape throughout the winter. It has

a direct impact on the regional environment and ecosystem because of its high reflectivity and low

thermal conductivity (Foster et al. 2005b; Green et al. 2012; Hall et al. 1991; Liston and Sturm

2002; Stieglitz et al. 2003). Snow accumulated on lake ice surface acts as an insulating layer effectively reducing the heat transfer between the atmosphere and the underlying ice (Maykut

1978), and thus influences the magnitude and timing of lake ice growth and decay (Duguay et al.

2003). Snow cover and thickness are also important variables determining the fresh water budget

of the lakes. During snowmelt in spring, the release of this freshwater pulse comprises a major contribution to the water supply of rivers and lakes in the Arctic (Arp et al. 2015; Dyer 2008; Kane et al. 2004; Kane et al. 1991; Yang et al. 2003). A general decreasing trend of spring snow depth in Pan-Arctic regions during the past several decades has been reported in several previous studies

(Biancamaria et al. 2011; Brown and Robinson 2011; Callaghan et al. 2011a; Liston and Hiemstra

2011; Park et al. 2012). The change in snow depth has multiple impacts on the environment, ecosystem, and human activities, i.e., the demise or growth of patchy wetlands (Callaghan et al.

2011b), the reproductivity and forage of various animals (Madsen et al. 2007; Turunen et al. 2009), and the recession of boreal forestry (Callaghan et al. 2011b).

However, we have very limited knowledge of snow in Arctic regions due to inadequate measurements. Traditionally, snow depth measurements are collected through in situ observations, such as automated weather stations and field surveys. Weather stations are very sparse and only cover very limited areas, owing to the cost and logistical difficulty in setting up and maintaining them in the remote and harsh Arctic environment. In this study, we focus on the Arctic Coastal

Plain (ACP) of northern Alaska. In this region, the National Water and Climate Center (NWCC),

NOAA National Centers for Environmental Information (NCEI), and Geophysical Institute

Permafrost Laboratory (GIPL) operate a number of weather stations which are still providing snow depth observations. The Snow Telemetry (SNOTEL) program of NWCC has three stations at

Prudhoe Bay, Sagwon and Imnaviat Creek along the Alaskan oil pipeline corridor, which provides snow depth records starting from 2011 (https://www.wcc.nrcs.usda.gov/snow/index.html). NCEI provides daily snow depth data at four stations, including Utqiagvik (known as Barrow previously)

(1901 – present), Colville Village (1996 – present), Kuparuk (1983 – present), and Alpine (2011

– present) (https://www.ncdc.noaa.gov/data-access/land-based-station-data). GIPL offers real- time snow depth data at five stations: Utqiagvik, Deadhorse, Imnaviat, Ivotuk, and West Dock

(http://permafrost.gi.alaska.edu/content/data-and-maps). Except for Utqiagvik and Ivotuk, most of these weather stations are distributed in the east part of Alaskan ACP or along the oil pipeline corridor. The U.S. Department of the Interior (DOI) established 16 automatic climate monitoring stations through Global Terrestrial Network for Permafrost (DOI/GTN-P) program for the ACP of northern Alaska (https://pubs.usgs.gov/ds/812/introduction.html). Twelve of them located in the west part of Alaskan ACP. Snow depth measurements were collected by those stations between

1998 and 2011. Overall, in situ observations from ground stations are very sparse and mostly distributed along coastal regions.

Dedicated field expeditions focused on snow surveys may cross over a large area, but they

are temporally sporadic and conducted only along the expedition routes. In the middle March of

1988, Hall et al. (1991) conducted a three-day in situ survey along the route of the Trans-Alaska

pipeline between Fairbanks and the Arctic Coast, and snow depths were measured at 16 sites.

Nelson and Hinkel (1997) measured snow depths in 1995 for seven locations within the Kuparuk

Basin, including Atqasuk, Utqiagvik, Betty Pingo, Happy Valley, Imnavait Creek, Toolik Lake,

and West Dock. Walker et al. (1999) collected drift snow depths in winter seasons between 1995

and 2002 in the Toolik snowfence experiment site. Liston and Sturm (2002) made snow depth and

density measurements from the headwaters of the Kuparuk basin to the Arctic coast in April of

1994, 1996 and 1997. Sturm and Liston (2003) conducted snow depth surveys at 13 paired lake/tundra locations from Oumalik to Utqiagvik in April 2000 and April 2002. Raynolds et al.

(2008) and Walker et al. (2008) collected snow depth information during trips to the Alaskan ACP from 2001 to 2006, and measurements were made at 1 m spacing with 10 × 10 m grids at Happy

Valley, Sagwon, Franklin Bluffs, Deadhorse, West Dock, and Howe Island. Apparently, historical snow observations from field surveys are spatially and temporally very limited.

Some efforts have been made to derive the snow depth information using remote sensing technology. For example, a snow radar is a microwave frequency-modulated altimeter implemented in the Operation IceBridge program (https://icebridge.gsfc.nasa.gov/). It operates

over a very wide frequency range (2 – 18 GHz) and can estimate snow depth over ice surfaces by

tracking the positions of snow/air and snow/ice interfaces (Brucker and Markus 2013; Farrell et al. 2012; Galin et al. 2012; Kanagaratnam et al. 2007; Kurtz and Farrell 2011). The mean difference between the snow depth measurements collected by the snow radar and by a concurrent in situ survey along a 2 km transect was 0.8 cm (Farrell et al. 2012; Kurtz et al. 2013). However, most of

these data were collected over sea ice or for selected areas in Greenland and Antarctica, and no

such data are available for elsewhere. Passive microwave remote sensing systems, such as Special

Sensor Microwave/Imager (SSM/I), Scanning Multichannel Microwave Radiometer (SMMR),

Advanced Microwave Scanning Radiometer for Earth Observing System (ASMR-E), have also

been used to retrieve snow depth and further to estimate Snow Water Equivalent information on

land surface based on the difference in brightness temperatures at two channels (e.g. 19 and 37

GHz for SMMR, SSM/I and AMSR-E) (Chang et al. 1987; Derksen et al. 2005; Foster et al. 2005a;

Green et al. 2012; Markus et al. 2006) . However, the spatial resolution of passive microwave data

is very coarse (e.g., 25 km for SSM/I), and the accuracy of snow depth estimates from passive

microwave data is largely affected by the sub-pixel spatial variations of vegetation cover (Derksen

et al. 2005; Foster et al. 2005a), snow conditions (e.g. density and stratigraphy) (Derksen et al.

2012; Markus et al. 2006), surface roughness (Stroeve et al. 2006), and particularly the coverage

of thermokarst lakes (Green et al. 2012) that are prevalent features in the circumpolar regions

(Duguay et al. 2003).

The Geoscience Laser Altimeter System (GLAS) on board of ICESat became operational in January 2003 (Zwally et al. 2002). It provided surface profile elevation measurements at global scale from 2003 to 2009. With footprint diameter of ~70 m and centimeter-scale precise vertical elevation measurements, ICESat/GLAS provides the possibility of measuring snow depth over relatively flat surfaces through tracking the surface elevation changes in the winter season.

Bindschadler (2005) estimated the new snow accumulation in one snowfall event on Antarctic ice sheet using the elevation differences at crossovers of ICESat overpasses before and after the event.

Treichler (2017) estimated the snow accumulation in a mountainous region at southern Norway using the elevation difference between ICESat and three Digital Elevation Models (DEMs), and

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the accuracy of the snow depth estimation was subjected to the quality of the reference DEMs and

the bias level between ICESat measurements and the reference DEMs.

In this paper, we present a novel method to retrieve snow depth over frozen lake surfaces

by tracking surface elevation changes with repeat ICESat/GLAS observations. A repeat satellite

track usually does not exactly follow the previous track, and there might be several hundred meters

of cross-track shift (e.g. 100 ~ 500 m for ICESat in northern Alaska). For land surface, the elevation

may change significantly over such a short spatial distance, and the direct use of the repeat-track

elevation measurements for surface elevation change detection is difficult as the effect of small-

scale surface topographic variation between repeat tracks cannot be accurately quantified. In

contrast, the frozen lake surfaces in general are spatially homogeneous and virtually invariant

within a relatively short distance. Due to the homogeneity of lake surfaces, the repeat track

measurements with a certain level of cross-track shift or even measurements from different tracks can be utilized to detect and compute the temporal change in surface elevation as long as the measurement points fall completely within a small- or medium-sized lake or within a certain

distance in a large lake. The frequency and density of repeat surface measurements depend on the

lake size. More satellite tracks and more measurement points along tracks would be generated over

a large lake for a more frequent change detection.

In the following sections, we will first introduce the study area and data sources used in

this study. We will then describe the rationale for deriving snow accumulation measurements using

repeat GLAS laser altimetry observations over relatively flat surfaces of frozen lakes. The main

factors that contribute to the surface elevation changes computed from GLAS altimetry

measurements are identified and quantified. By removing non-snow factors’ contributions to the

computed surface elevation change the snow accumulation is estimated. This method is then

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applied to the Arctic Coastal Plain of northern Alaska, and snow accumulation measurements on

frozen lake surfaces between 2003 and 2009 are derived across this Arctic region. The result is validated and evaluated with reference to the nearby in situ snow depth observations from automated terrestrial weather stations, and the spatial pattern of snow accumulation over this period is briefly examined and discussed. In the final section, we present some concluding remarks.

4.2 Study area and data sources

Our study area is located on the Arctic Coastal Plain (ACP) of northern Alaska

approximately between the Chukchi Sea to the west, the Beaufort Sea to the north, and the Colville

River to the east (Figure 4.1). Roughly 20% of the area in this region is covered by shallow

thermokarst lakes (Frohn et al. 2005; Hinkel et al. 2005). Monthly mean air temperatures are below

0 ˚C throughout the year except for June, July and August (Arp et al. 2013; Duguay et al. 2003;

Hinkel et al. 2012) . The onset of lake freeze-up ranges from mid- to late September (Morris et al.

1995; Surdu et al. 2014) and the ice-out usually begins in early June (Arp et al. 2013; Wang et al.

2012b). The first snowfall begins usually in late August or early September (Sturm and Liston

2003), depending on the air temperature and the relative humidity (Liston and Sturm 2002). The

snow cover lasts until May or early June, depending on the latitude (Macander et al. 2015).

The ICESat mission was Earth’s first polar orbiting satellite to carry a laser altimeter, the

GLAS (Zwally et al. 2002). By combining precise laser ranging capabilities with state-of-the-art

orbit and attitude control and knowledge, ICESat/GLAS provided very accurate measurements of

ice sheet topography. It operated at an altitude of approximately 600 km with a 94˚ orbit

inclination, covering the Earth’s surface between 86˚ S to 86˚ N latitudes. GLAS had three

identical laser transmitters, Laser 1, 2 and 3 (referred to as L1, L2 and L3). Each laser had a 1064

nm channel for surface altimetry and a 532 nm channel for the vertical distribution of clouds and

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aerosols (Zwally et al. 2002). GLAS emitted 40 laser pulses per second towards the Earth surface.

These pulses illuminated a series of footprints along the satellite ground track approximately 70 m

in diameter, spaced at 170 m intervals (Zwally et al. 2002). As compared to GPS-derived DEM,

the elevation retrieval accuracy (bias) and precision (standard deviation) under the clear sky

condition over Antarctic ice sheet were less than 2 cm and 3 cm, respectively (Fricker et al. 2005).

From February 2003 to October 2009, the ICESat operated in a campaign mode, in which surface

elevation measurements were made in up to three periods per year along repeat ground tracks,

corresponding to northern hemisphere fall, spring, and early summer seasons. Each campaign,

except for four special periods, lasted 34 – 38 days and was a sub-cycle of the more densely spaced

91-day exact repeat orbit (Yi et al. 2011). ICESat laser altimetry system conducted a total of 18 measurement campaigns over a period of about 6 years as shown in Figure 4.2. In this study, the campaigns occurred between October and November is referred to as Fall campaign, between

February and April as Spring campaign, and between May and early June as Early-Summer campaign.

ICESat/GLAS dataset consists of 15 types of data products available for scientific use. The

“GLA14” is the Level-2 binary data product specifically for continental land surfaces, and contains the laser footprint geolocation and reflectance, as well as geodetic, instrument, and atmospheric correction information for range measurements. We use the GLA14 in this study as the primary data source for snow accumulation estimation. The data product “GLA09” contains the information about cloud heights and cloud vertical distribution, which is used in this research as ancillary data to identify invalid footprints that may be contaminated by atmospheric forward scattering due to low thin cloud, blowing snow, and/or ice fog (Duda et al. 2001; Mahesh et al.

2002; Palm et al. 2011; Yang et al. 2010). We used the final Release 34 of GLA14 and GLA09

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data products collected through 18 ICESat campaigns during 2003-2009 over the ACP of northern

Alaska.

The in situ snow depth datasets used in this study were obtained by the automatic weather

stations of the Global Terrestrial Network for Permafrost (DOI/GTN-P). The snow depth was

measured with a CSI model SR50 ultrasonic distance sensor mounted approximately 2.5 m above

the ground at the automatic weather station. Nine stations of DOI/GTN-P were located in our study

area (denoted by the red stars in Figure 4.1), which provided the point-based continuous measurements of in situ snow depth and air temperature from 1998 to 2011. Table 4.1 summarizes the locations, the start and the end of records for these nine stations. The in situ datasets recorded by other observation stations and the research expeditions mentioned in the introduction section either fall outside study area or do not match the ICESat campaigns in time, and therefore are not utilized in this study for direct comparison and validation.

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Figure 4.1 ICESat ground tracks during 2003-2009 and the locations of DOI/GTN-P automatic weather stations in the ACP of northern Alaska. The deep blue polygons are the lakes in this region and Lake Teshekpuk is the largest one. Only the tracks in Fall and Spring campaigns are shown in the figure. The measurements collected in early summer are not included in the snow accumulation analysis since the snow usually melts in May or early June.

Figure 4.2 ICESat/GLAS campaigns from 2003 to 2009. The duration of each campaign is denoted roughly by the rectangle width. L1 was the first laser and flied only one campaign before its failure, L2a was the first campaign for Laser 2, and L3b was the second campaign for Laser 3.

Table 4.1 Geographical locations and operation periods of nine automatic weather stations

Latitude Elevation Snow Depth Records Station Longitude(°) (°) (m) Start End Inigok 69.99 -153.09 53 1998/08/17 2011/07/31 Drew Point 70.86 -153.91 5 1998/08/18 2011/07/31 Fish Creek 70.34 -152.05 31 1998/08/18 2011/07/31 Koluktak 69.75 -154.62 60 1999/08/27 2011/07/31 South Meade 70.63 -156.84 15 2003/08/08 2011/07/31 Piksiksak 70.04 -157.08 33 2004/08/08 2011/07/31 East Teshekpuk 70.57 -152.96 7 2004/08/10 2011/07/31 Ikpikpuk 70.44 -154.37 5 2005/08/21 2011/07/31 Lake 145 70.69 -152.63 6 2007/08/13 2011/07/31

4.3 Methods

The rationale for deriving snow accumulation information in this study is to measure elevation changes over a relatively flat frozen lake surface during the winter season using repeat

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GLAS laser altimetry observations (Figure 4.3). The frozen surfaces of thermokarst lakes virtually

serve as ideal snow pillows as in an automated weather station. Although the flat tundra surfaces

may serve the same purpose, we only use the frozen lake surfaces in our study, in order to avoid

the complication associated with the identification of flat tundra surfaces. The surface elevation

measurements collected respectively in Fall and Spring campaigns were used to calculate the lake

surface elevation change due to snow accumulation as shown in Figure 4.2. The elevation

measurements collected in Early-Summer campaigns are not included since snow melt may occur

in May or early June (Macander et al. 2015).

On the Arctic Coastal Plain of northern Alaska, there are 7409 lakes with area larger than

1 km2 (Frohn et al. 2005). The lake polygons were delineated from Landsat-7 images (Frohn et al.

2005) and are used as masks to extract ICESat laser altimetry data. GLAS’s footprint is small enough to provide a large quantity of elevation measurements for those flat frozen lake surfaces in the Fall and the Spring campaigns. In consideration of the 70 m footprint size and possible seasonal and annual fluctuation in lake surface area, only elevation measurements that fall inside a lake over

100 m away from the lake polygon boundary are selected for our analysis.

Our snow accumulation derivation method consists of four computation steps. First, the

GLAS altimetry data are preprocessed to identify and filter spurious observations. Second, reliable elevation measurements are derived for the remaining valid ICESat observations by using the max- amplitude-peak retracking scheme. Third, the true temporal elevation changes of the frozen lake surfaces are derived by taking into account the inter-campaign biases. Finally, the net surface elevation change solely due to snow accumulation is computed by removing surface elevation change contributed by lake ice growth.

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Figure 4.3 Retrieval of snow accumulation through measuring lake surface elevation change

during the winter season. The surface elevations ELVt1 and ELVt2 were collected respectively in the Fall- and Spring- campaigns as shown in Figure 4.2.

4.3.1 Data preprocessing through filtering of the contaminated measurements

ICESat/GLAS measures surface elevation by tracking the two-way travel time of the laser pulse and the exact position of the satellite above the Earth’s reference ellipsoid. Many factors may introduce errors in ICESat measurements of surface elevation. The existence of thin cloud, ice fog and blowing snow increases the laser photon-path length through particle multiple scattering and makes the surface appear farther from the satellite, leading to lower elevation measurements than actual elevation values under clear sky condition (Duda et al. 2001; Mahesh et al. 2002; Palm et al. 2011; Yang et al. 2010; Yi et al. 2005). In some extreme situations, the atmospheric path delay by forward scattering could generate unreliable elevation measurements

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with an error of up to 8 m in Antarctica and Greenland (Palm et al. 2011). Those contaminated

observations usually exhibit high detector gain value and low surface reflectivity. The gain value

for a laser shot was automatically adjusted according to the strength of returned pulse energy. A

lower gain value is set when the returned energy becomes stronger. The reflectivity is defined as

the ratio of the returned energy to the incident pulse energy. To filter out the possibly contaminated

observations, various threshold values were adopted for the gain and reflectivity in previous

studies. Yi et al. (2005) used a gain threshold of 30, while Kwok et al. (2006) used 50. Later, Yi

et al. (2011) recommended to use different thresholds of gain threshold values for the campaigns

with different laser energy levels. Siegfried et al. (2011) indicated that the observations with a reflectivity less than 0.24 most likely do not satisfy the data quality requirements of ICESat/GLAS mission. Yi et al. (2011) and Zwally et al. (2008) used 0.05 as the reflectivity threshold along with other criteria to identify the unreliable measurements. In this study, we utilized the gain value

(i_gval_rcv) and reflectivity (i_reflctUC) variables provided in GLA14 product for data filtering operation. Those observations with i_reflctUC <0.05 && i_gval_rcv >200 are considered to be heavily-contaminated footprints and discarded.

The impact of blowing snow is indicated by blowing-snow variable (i_blow_snow_conf) in the GLA09 product. Its value ranges from 0 to 15 (https://nsidc.org/data/glas/data-dictionary-

glah09). The blowing snow confidence level given by the 1064 nm laser channel is coded as a

value between 0 and 6, while that given by the 532 nm laser channel is coded as a value between

7 and 13. The value of 14 indicates the blowing snow could not be surely determined, while the

value of 15 means the laser signal was not examined at the two channels. For each channel, a

higher value suggests a greater degree of confidence that the observation is indeed influenced by

blowing snow. In this study, the observations with a blowing-snow value (i_blow_snow_conf)

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from 1064 nm laser ranging 4 – 6 or from 532 nm laser ranging 10 – 13 are considered to be heavily influenced by blowing snow and thus removed. These thresholds are determined by visually inspecting the elevation profiles over lake surfaces.

In addition, we identified highly saturated and low signal-to-noise ratio (SNR) observations. The highly saturated observations with the saturation flag variable (i_satCorrFlg) in

GLA14 larger than 2 are excluded. The saturation correction value (i_satElevCorr) in GLA14 is then applied to the remaining observations to reduce saturation influence. As suggested in (Nie et al. 2014), we calculated SNR values based on the maximum intensity of the laser waveform and the mean background noise, and observations with a SNR less than 12 are also filtered out.

After filtering operations described above, the remaining observations are considered valid and subject to subsequent further processing as described in the following section.

4.3.2 Derivation of reliable surface elevation measurements with max-amplitude-peak retracking method

ICESat/GLAS sensor is a full-waveform laser altimetry system, which digitizes and records the echoed signal of each transmitted laser pulse over the time. The histogram of the transmitted and the echoed laser energy over the time is referred to as waveform. For each laser pulse, the surface elevation is determined by using the information about the satellite position relative to the Earth’s reference ellipsoid, and the direction and the range of laser beam between the satellite and the Earth surface. The range is a function of the pulse-travel time between the transmitted laser shot and the received echo. As shown in Figure 4.4, WT and WR are the transmitted and the returned waveforms, respectively. The waveforms are used to identify the reference point on the time axis for the range and hence surface elevation determination, and are also used to retrieve the information about within-footprint topographic relief and vegetation vertical structure

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(Harding and Carabajal 2005). There are two types of re-tracking schemes to identify the reference

points on the ICESat waveforms: the centroid re-tracking scheme and max-amplitude-peak retracking scheme (Brenner et al. 2011). The centroid scheme uses the geometric centroid point of the waveform above the background noise level as the reference point on the time axis (Gardner

1992). The max-amplitude-peak scheme fits up to two Gaussian curves to the waveform and then uses the max-amplitude-peak that has the highest magnitude on the waveform to determine the

reference point on the time axis (Figure 4.4). The max-amplitude-peak scheme is designed for relatively flat and homogeneous surfaces, such as ocean, sea ice and ice sheet, since the returned waveform from these surfaces are mostly dominated by a single peak of Gaussian shape. The centroid scheme is developed specifically for land surface, which is often a complex mosaic of different terrain features with a large topographic variation within the laser footprint. The waveforms returned from land surface tend to have multiple peaks, and the centroid point represents the mean surface within the illuminated footprint.

Figure 4.4 Two types of reference points on transmitted and returned waveform. For centroid retracking scheme, the time reference point for the transmitted and the returned waveforms is

indicated by TC on the time axis. For max-amplitude-peak scheme, the time reference point for

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the transmitted and the returned waveforms is indicated by TM on the time axis. The returned waveform was from the footprint highlighted in Figure 4.5.

The elevation measurements in the ICESat GLA14 product were created by using the

centroid re-tracking scheme, since this product was intended for continental surfaces. Inland lakes

were treated as part of the continental surface, and their surface elevation measurements were also

determined in ICESat GLA14 product using the centroid scheme. Although the centroid re-

tracking scheme works better than the max-amplitude-peak scheme for vegetated or rugged land surfaces in general, our analysis shows that the centroid scheme tends to generate biased (usually lower) elevation measurements over the frozen Arctic lake surfaces. The primary reason is that the atmospheric forward scattering by thin clouds and blowing snow often generate a long tail and multiple small peaks besides the max-amplitude peak on the returned waveform as shown in Figure

4.4 (Duda et al. 2001; Mahesh et al. 2002; Palm et al. 2011; Yang et al. 2010). Although the

waveform of those observations mildly affected by forward scattering have a long tail and multiple

small peaks, the dominant peak of the waveform is clearly discernable, in contrast to the heavily- contaminated observations excluded in Section 3.1, whose waveform does not have a distinguishable dominant peak. The long tail and small peaks shift the centroid point to the right of the max-amplitude peak as shown in Figure 4.4, leading to a larger range and hence a lower surface elevation than the real lake surface level indicated by the dominant peak. As compared to the centroid scheme, the max-amplitude-peak scheme is proven to be significantly less susceptible to forward scattering effects (Brenner et al. 2011; Duda et al. 2001). The water or snow surfaces of the Arctic lakes are flat and homogeneous, so the max-amplitude-peak scheme can generate much more reliable elevation measurements over the lake surfaces than the centroid scheme.

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In this study, we converted the surface elevation measurements from the centroid retracking scheme in ICESat GLA14 products to the more reliable elevation measurements by the max-amplitude-peak scheme based on the relevant ancillary information contained in GLA14 product. In the conversion, the elevation measurement for a laser pulse by the max-amplitude-peak

scheme is calculated using the following equation:

= /2 + /2 (25) 𝑇𝑇 𝑅𝑅 𝐸𝐸𝐸𝐸𝐸𝐸𝑀𝑀 𝑍𝑍𝐶𝐶 − ∆𝑍𝑍𝑀𝑀𝑀𝑀 ∆𝑍𝑍𝑀𝑀𝑀𝑀 − 𝐺𝐺2008 Where ELVM is the resulting elevation with the reference to the geoid EGM2008

determined from the max-amplitude-peak scheme, ZC (i_elev) is the ellipsoid height from the

centroid scheme given in the ICESat GLA14 product, /2 is the range difference between the 𝑇𝑇 𝑀𝑀𝑀𝑀 max-amplitude-peak and centroid reference points on∆𝑍𝑍 the transmitted waveform (G-C offset),

/2 is the range difference between max-amplitude-peak and centroid reference points on the 𝑅𝑅 𝑀𝑀𝑀𝑀 returned∆𝑍𝑍 waveform, and is the geoid undulation between the Topex/Poseidon ellipsoid and

2008 the geoid EGM2008 at the𝐺𝐺 location of each footprint.

The magnitude of /2 on the transmitted waveform could be over 6 cm (Borsa et al. 𝑇𝑇 𝑀𝑀𝑀𝑀 2014). For each laser pulse,∆𝑍𝑍 this value is provided in GLA14 product (G-C offset i_GmC). In

GLA14 product, each returned waveform is fitted with up to six Gaussian curves and the locations of these peaks on time axis are provided by the variable i_gpCntRngOff. /2 is computed 𝑅𝑅 𝑀𝑀𝑀𝑀 based on the relative locations of the max Gaussian peak (contained in i_gpCntRngOff∆𝑍𝑍 ) and the

geometric centroid (i_ldRngOff) reference points. The geoid undulation values are given in GLA14 product (i_gdHt) for the first and the last of the 40 laser pulses in each second, and the geoid undulation values ( ) for the intermediate laser pulses are calculated through the linearly

2008 interpolation from the𝐺𝐺 two given values along the satellite ground track.

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Figure 4.5 Surface elevation profiles from the centroid and max-amplitude-peak schemes over the largest lake Teshekpuk on 16 March, 2004. The profile runs north to south for about 14km. The return waveform of the footprint highlighted in black symbol is shown in Figure 4.4.

The effect of the max-amplitude-peak scheme on producing more consistent elevation measurements over the lake surface is shown in Figure 4.5. The blue curve is the height profile over the snow surface of Lake Teshekpuk given in original ICESat GLA14 product using the centroid scheme. Although the snow surface of Lake Teshekpuk was supposed to be quite flat and smooth, the profile given by the original GLA14 (in blue) shows unrealistic surface elevation variation, and the magnitude of apparent elevation change over the lake snow surface is as much as 1.4 meters. After applying Equation 25, we re-calculated the lake snow surface elevations using the max-amplitude-peak scheme. The resulting surface height profile is shown as the red trace, which is much smoother and close to a lake snow surface in the real world. The standard deviation of this elevation profile is reduced to 0.03 m from 0.37 m for the centroid scheme. The elevation range decreases from 1.46 m to 0.16 m. As shown in Figure 4.5, the centroid scheme tends to give a lower elevation measurement than the max-amplitude-peak scheme. Particularly, the elevation differences between the centroid scheme and the max-amplitude-peak scheme is significantly larger in the flanks of the lake than in the middle of the lake (between 7 and 12 km from the start

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point of the transect). We examined these footprints along the transect and found out that the

waveforms in the flank of the lake were seriously deformed with a long tail, while those in the

middle were not. The long tail of the waveform shifts the centroid to the right of the maximum-

amplitude-peak, thus leading to the significantly lower elevation measurements for the footprints

in the flank. As an example, the waveform from the footprint pointed by the black arrow in Figure

4.5 has been plotted in Figure 4.4.

We analyzed 10 additional surface height profiles over Lake Teshekpuk by comparing the

max-amplitude-peak and centroid re-tracking schemes. As shown in Table 4.2, all the topographic profiles created by the centroid scheme have a lower mean elevation than those by the max- amplitude-peak scheme, again showing the tendency to underestimate surface elevations. The surface height profiles by the max-amplitude-peak scheme have a higher mean elevation value and smaller standard deviation, indicating that the max-amplitude-peak scheme effectively corrects the underestimation problem of the centroid scheme and gives a higher precision of elevation measurements over frozen lake surfaces covered by snow.

Table 4.2 Comparisons of the ICESat/GLAS elevation profiles of Teshekpuk Lake surface (above EGM2008) created by the centroid and max-amplitude-peak schemes

max-amplitude-peak Scheme Initial Centroid Scheme (m) Date of the Number of (m) profile Footprints Max Min Mean STD Max Min Mean STD 2004/03/16 83 1.06 -0.40 0.65 0.37 1.11 0.95 1.02 0.03 2004/06/01 53 1.24 -0.39 0.85 0.33 1.29 0.65 1.10 0.13 2004/06/09 62 1.39 -1.08 0.87 0.40 1.32 -0.96 1.06 0.30 2004/10/26 73 0.89 -0.24 0.34 0.20 0.93 0.26 0.70 0.13 2005/03/10 62 1.04 0.12 0.84 0.20 1.23 1.00 1.07 0.04 2005/06/03 40 1.00 -0.61 0.46 0.43 1.10 0.28 0.79 0.17 2005/11/04 88 0.71 -2.91 -0.64 0.80 0.83 0.17 0.54 0.15 2005/11/18 60 0.60 -0.69 -0.09 0.27 0.77 -0.67 0.23 0.36 2007/04/08 83 1.03 -0.34 0.57 0.36 1.06 0.35 0.87 0.14

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2007/10/16 31 0.83 -0.19 0.40 0.18 0.63 0.14 0.47 0.10

4.3.3 Derivation of true surface elevation changes by correcting inter-campaign biases

The lake surface elevation change is calculated using ICESat repeat observations collected in the Fall and Spring campaigns. Most of the lakes were visited only once by ICESat in a campaign, either on an ascending orbit or a descending orbit, as shown in Figure 4.6a and Figure

4.6b. A small number of lakes near the crossover locations of ICESat ascending and descending orbits were overpassed twice by ICESat in one campaign, as shown in Figure 4.6c. For some huge lakes like Lake Teshekpuk (Figure 4.1), ICESat could overpass them multiple times in a campaign period.

Each ICESat pass over a lake in a campaign consists of a series of the laser footprints along the orbit. By applying the max-amplitude-peak retracking scheme to the series of laser footprints, an elevation profile is formed for the lake along the orbit on a specific date. Each surface elevation profile derived from max-amplitude-peak scheme was examined to filter out possible outliers using the Median-Absolute-Deviation (MAD) method (Liu et al. 2012). For the lakes with one

ICESat overpass in a campaign (Figure 4.6a and Figure 4.6b), the mean elevation was calculated for the remaining footprints of the surface elevation profile as the representative elevation for the corresponding campaign. For the lakes with multiple ICESat overpasses in one campaign, the representative elevation for the corresponding campaign was calculated by averaging all the remaining footprints from the multiple surface elevation profiles after the outliers are filtered out.

As shown in Figure 4.6c, the mean elevation of Fall-profile 1 from the ascending pass and Fall- profile 2 from the descending pass is calculated as the representative surface elevation of this lake for the Fall campaign. Such derived representative elevation stands for an average state of the lake

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surface during the time span between the ascending and the descending passes in the campaign,

which is usually 5 – 7 days in our study area. The magnitude of the apparent surface elevation

change is then calculated as the difference between the representative elevations in the Fall

campaign and Spring campaign.

Figure 4.6 ICESat overpass patterns over the lakes in our study area. The blue and the orange circles are the footprints collected respectively in Fall campaign and in Spring campaign. (a) Ascending pass; (b) Descending pass; (c) Both ascending and descending passes in one campaign.

It has been discovered that there were time-variable biases between different campaigns of

ICESat data acquisition (Gunter et al. 2009; Hofton et al. 2013). The reasons for ICESat inter- campaign biases (ICB) are still not well understood (Gunter et al. 2010). There are two possible

sources: pointing errors (Fricker et al. 2005) and sensor degradation. As Borsa (2014)

demonstrated, the transmitted laser energy of ICESat/GLAS Laser 2 and Laser 3 kept decreasing

during its operative campaigns. These factors might introduce biases to the measurements in

different campaigns. To derive the true surface elevation change, the effect of ICB should be

corrected as follows:

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= (26)

∆𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡2 − 𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡1 − 𝐼𝐼𝐼𝐼𝐼𝐼 Where ∆ELV is the true surface elevation change from the date t1 (ICESat pass in Fall

campaign) to date t2 (ICESat pass in Spring campaign), ELVt2 and ELVt1 are the representative surface elevation at date t2 and date t1, respectively, and ICB is the inter-campaign bias between the Spring campaign (date t2) and Fall campaign (date t1). For the lakes with multiple passes in one campaign, we use the date in the middle of the first and the last passes to time-stamp the computed representative surface elevation.

In this study, we used the ICB values estimated by Hofton et al. (2013). Using a calibration site on Antarctic Ice Sheet at latitude 86ºS, Hofton et al. compared measurements of each ICESat campaign to the IceBridge airborne Land, Vegetation, and Ice Sensor (LVIS) elevation data collected in a 50 km long and 2 km wide swath to estimate ICB values. With the reference to the campaign L3I, the campaign-mean biases were computed for all campaigns. Their results show a consistent increasing trend of ICB value through the 18 ICESat campaigns. The campaign L2B has the lowest bias value of (-1.03 ± 4.27 cm), and the campaign L2E has the highest bias value of

(14.72 ± 3.30 cm). Our adoption of their estimates is based mainly on two considerations. First, the reference elevation data from Airborne LVIS laser system are very accurate, and the large rectangular calibration site at the latitude 86º S encompasses a larger number of the ICESat passes in each campaign for the estimation of ICBs as compared to other studies. Second, the snow and ice surface at this calibration site is more similar to the snow-covered lake surfaces in our study, which produces more saturated returns than the relatively dark surfaces of calibration sites used in other studies, e.g. open ocean surface (Shepherd et al. 2012; Urban et al. 2013; Zwally et al. 2017).

4.3.4 Derivation of snow depth by excluding surface elevation change contributed by lake ice growth

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Snow accumulation information is retrieved through the tracking of lake surface elevation change with the repeat ICESat measurements during the Fall and the Spring campaigns. During the frozen season, the ice/snow surface elevation change inside a lake can be mainly attributed to two factors: snow accumulation, and lake ice formation and growth. Snow compaction or wind- driven erosion may also affect the lake surface elevation change, but this effect can hardly be accurately quantified and is not considered in this study. To derive the snow accumulation, we need to separate the contribution of water-to-ice phase transformation from the measured lake surface elevation change. In winter, as water is converted to ice, the thickness of lake ice grows and the lake surface elevation gradually rises due to the lower density of ice. The magnitude of the lake surface elevation increase (ΔHice) due to the lake ice growth can be estimated from the ice thickness using the following equation:

= ( ) = 0.085 (27)

∆𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 − 𝜌𝜌𝑖𝑖𝑖𝑖𝑒𝑒 ∆𝑍𝑍𝑖𝑖𝑖𝑖𝑖𝑖 ∆𝑍𝑍𝑖𝑖𝑖𝑖𝑖𝑖 = _ _ (28)

∆𝑍𝑍𝑖𝑖𝑖𝑖𝑖𝑖 𝑍𝑍𝑖𝑖𝑖𝑖𝑖𝑖 𝑡𝑡2 − 𝑍𝑍𝑖𝑖𝑖𝑖𝑖𝑖 𝑡𝑡1 where ρwater and ρice are the water and ice density, and ΔZice is the difference of ice thickness between the two ICESat passes at date t1 and date t2. Zice_t1 and Zice_t2 are the lake ice thickness at the date t1 and date t2, respectively.

In this study, lake ice growth is computed using a simple linear thermodynamic model based on Stefan’s ice growth law (Stefan 1890) as follows:

(29)

𝑍𝑍𝑖𝑖𝑖𝑖𝑖𝑖=α√𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 where α is the ice growth coefficient, AFDD is Accumulated Freezing Degree Days that is calculated by summing the daily mean air temperatures which are below freezing point (0 °C).

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This thermodynamic model was intended specifically for inland lakes and rivers where the water

flow velocity is less than 0.3m/s and plays no role in the process of ice formation (Engineers 2006).

The freshwater density is 1 g/cm3. The determination of coefficient α needs empirical

experiences and also a prior knowledge of the snow conditions on the lake surface (Michel 1971).

Jones (2009) showed that for snow-covered lakes in northern Alaska, the ice growth simulated

with α = 2.4 agreed well with in situ observations collected on a lake near Utqiagvik. Following

3 Jones (2009), we adopted α = 2.4 and ρice = 0.915 g/cm to compute the surface upward

displacement for all lakes.

We modeled lake ice thickness based on the records of daily average air temperature from

five automated weather stations (Figure 4.1), including South Meade, Inigok, Fish Creek, Drew

Point and East Teshekpuk. Figure 4.7 shows the daily air temperature and snow depth records at

South Meade station from 2003 to 2009. The modeled lake ice growth during the winter of

2005/2006 near the five stations are shown in Figure 4.8 as examples. There is no significant

regional difference in the simulated lake ice thickness among the five stations. The maximum ice

thickness difference between these stations at the end of winter is less than 10 cm, as shown in

Figure 4.8. The maximum ice thickness at the end of winter is about 160 cm, which could induce

a surface rise by 13.6 cm as compared to the surface level at the beginning of ice formation. The

annual variation in the simulated ice thickness is very small. At South Meade station, the maximum

ice thickness is 167.25 cm for the winter 2003/2004 and 159.39 cm for winter 2004/2005.

The surface elevation change estimate due to lake ice growth in Equation (27) is based on the assumption that lake ice is freely floating and in isostatic balance. Previous studies showed that a considerable number of lakes froze to their bed during winter (Jeffries et al. 1996; Mellor 1982;

Surdu et al. 2014). These lakes attained a maximum ice growth rate in November (Jones et al.

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2009) and then maintained a relatively slower rate until mid-March or later (Jeffries et al. 1996),

when the lakes froze to the bottom. Since the ICESat passes in Spring campaign occurred in mid-

March (Table 4.3), the assumption of the isostatic balance of lake ice is reasonably valid for

estimating surface upward displacement due to water-to-ice phase transformation.

It should be noted that the weight of snow cover could suppress to certain degree the upward displacement of lake surface. A prior knowledge of the snow depth and also the snow density is required to estimate this effect. In this study, this suppressing effect of the snow cover is not considered partly due to the relatively low snow accumulation in this region and partly due to the lack of the data necessary to quantify this effect.

Figure 4.7 Daily average snow depth and air temperature from 2003 to 2009 at South Meade weather station in northern Alaska. The left vertical axis is air temperature, and the right axis is snow depth. The location of this station is shown in Figure 4.1. The date is in the format of YYYY/M/D. The vertical bars represent the ICESat Campaigns that were used to derive the snow accumulation on lake surfaces.

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Figure 4.8 The simulated growth of lake ice thickness based on the measured daily air temperature at the five weather stations between 2005 and 2006

Using the modeled ice thickness from Equation (29), we can estimate ice thickness change

from time t1 to time t2 during the winter using Equation (28) and further estimate the ice surface

elevation change due to the ice thickness change using Equation (27). Then, we derive snow

accumulation estimate (Dsnow) by removing the contribution of lake ice growth (∆Hice) from the lake surface elevation change (∆ELV) given by Equation (26) as follows:

= (30)

𝐷𝐷𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∆𝐸𝐸𝐸𝐸𝐸𝐸 − ∆𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖

4.4 Results and Discussion

4.4.1 ICESat-derived snow accumulation over Alaskan ACP

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The ICESat/GLAS data selected by lake polygons are preprocessed to filter out the

contaminated data using the procedures described in 3.1. After the preprocessing, 633 lakes

contain valid GLAS elevation measurements acquired during the 18 campaigns from 2003 to 2009.

There are 18852 elevation measurements over these 633 lakes. Among them, 283 lakes have 10 or

more elevation measurements collected in all the campaigns from 2003 to 2009. The elevation

measurements over Lake Teshekpuk, the largest lake with an area of 836.34 km2, account for

19.94% of the total measurements.

To estimate the snow accumulation during the winter season, we need to identify a pair of

representative elevation measurements (ELVt1 and ELVt2 in Equation (26)) of the same lake

measured in the Fall campaign and in the repeat Spring campaign, as shown in Figure 4.3. In our

study area, 277 lakes have at least one such pair of representative elevations for the snow

accumulation estimates.

Since ICESat campaigns lasted for 34-38 days, a campaign may cross two months, e.g., start in October and end in November for a Fall campaign. The lakes in our study area may be overpassed by ICESat in different months for each Fall / Spring campaign. We grouped the lakes as one pair set if these lakes were overpassed by ICESat in the same month (e.g. October) in Fall campaign and also in the same month (e.g. March) in Spring campaign. For one winter season, it is possible to have two or more pair sets. Assuming that ICESat overpassed Lake A in October

2003 and Lake B in November 2003 in the Fall campaign, and later overpassed both Lake A and

Lake B in March 2004 in the Spring campaign, then two possible pair sets can be formed up to represent the winter season during 2003 – 2004: Pair-1 (Oct. 2003 / Mar. 2004) and Pair-2 (Nov.

2003 / Mar. 2004). Table 4.3 lists 17 possible pair sets in 2003-2009 based on the ICESat campaigns, and each pair set is labeled as Pair-i (i = 1, 2,…, 17). The number of ICESat

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observations, the number of lakes and the snow accumulation estimates for each pair set are

summarized in Table 4.3.

Table 4.3 Summary of the snow accumulation estimates on Alaskan ACP

Num Fall-Campaign Spring-Campaign Snow accumulation (m) ID of ICESat Obs. ICESat Obs. Campaign Month/Year Campaign Month/Year Max Min Mean STD Lakes total per lake total per lake Pair-1 8 L2a Oct. 2003 53 6.6 L2b Mar. 2004 33 4.1 0.42 0.06 0.22 0.10 Pair-2 69 L2a Nov. 2003 644 9.3 L2b Mar. 2004 840 12.2 0.64 -0.17 0.05 0.14 Pair-3 7 L3a Oct. 2004 26 3.7 L3b Feb. 2005 65 9.3 0.62 0.07 0.29 0.21 Pair-4 57 L3a Oct. 2004 550 9.6 L3b Mar. 2005 655 11.5 0.66 -0.15 0.17 0.16 Pair-5 9 L3a Nov. 2004 49 5.4 L3b Mar. 2005 59 6.6 0.66 0.03 0.25 0.19 Pair-6 12 L3d Oct. 2005 33 2.8 L3e Feb. 2006 48 4.0 0.51 0.16 0.32 0.11 Pair-7 96 L3d Nov. 2005 745 7.8 L3e Mar. 2006 955 9.9 0.70 0.04 0.30 0.17 Pair-8 9 L3g Oct. 2006 37 4.1 L3h Mar. 2007 76 8.4 0.53 0.03 0.29 0.20 Pair-9 12 L3g Nov. 2006 43 3.6 L3h Mar. 2007 50 4.2 0.30 0.04 0.14 0.09 Pair-10 58 L3g Nov. 2006 504 8.7 L3h Apr. 2007 636 11.0 0.66 -0.18 0.08 0.20 Pair-11 18 L3i Oct. 2007 85 4.7 L3j Feb. 2008 95 5.3 0.39 0.02 0.16 0.10 Pair-12 27 L3i Oct. 2007 167 6.2 L3j Mar. 2008 433 16.0 0.63 -0.05 0.22 0.16 Pair-13 23 L3i Nov. 2007 149 6.5 L3j Mar. 2008 187 8.1 0.47 -0.01 0.25 0.14 Pair-14 26 L3k Oct. 2008 168 6.5 L2e Mar. 2009 208 8.0 0.70 0.29 0.47 0.11 Pair-15 19 L3k Nov. 2008 379 19.9 L2e Mar. 2009 453 23.8 0.35 -0.06 0.16 0.09 Pair-16 12 L2d Dec. 2008 77 6.4 L2e Mar. 2009 79 6.6 0.46 0.13 0.28 0.08 Pair-17 27 L2d Dec. 2008 153 5.7 L2e Apr. 2009 158 5.9 0.37 0.18 0.28 0.05

For each lake in the 17 pair sets, we firstly calculate the representative elevations of frozen

lake surface in the Fall campaign and the Spring campaign. Then we calculated the true surface

elevation change by subtracting the ICB value corresponding to the campaigns of the pair as in

Equation (26). Using air temperature records (i.e., Figure 4.7) from the nearest weather station, we

estimated lake ice thickness and the corresponding lake surface elevation rise due to lake ice

growth using Equations (29) and (27). An example is shown in Figure 4.8. Finally, the net snow

accumulation for each pair is calculated by removing the contribution of lake ice growth from the

surface elevation change according to Equation (30). The computational results of four pair sets

during 2003-2007 are presented as a bar chart map in Figure 4.9. Those four pair sets include those

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formed by November 2003 - March 2004 (Pair-2), October 2004 - March 2005 (Pair-4), November

2005 - March 2006 (Pair-7), and November 2006 - April 2007 (Pair-10). These pair sets contain the largest number of lakes whose snow accumulation has been estimated, and other pair sets contain a relatively small number of lakes. The bar chart map in Figure 4.9 represents the spatio- temporal variation of the net snow accumulation during 2003-2007 on the Arctic Coastal Plain of northern Alaska. Pair-7 has the largest number (96) of lakes and the derived net snow accumulation over these lakes ranges from 4 cm to 70 cm. The first quartile, the median and the third quartile of the snow accumulation estimates are -3.7 cm, 0.7 cm and 8.7 cm for the winter between November

2003 – March 2004 (Pair-2), 7.1 cm, 14.7 cm, and 43.4 cm for the winter between October 2004

– March 2005 (Pair-4), 16.5 cm, 25.3 cm and 43.4 cm for the winter between November 2005 –

March 2006 (Pair-7), -6.0 cm, 4.8 cm and 13.5 cm for the winter between November 2006 – April

2007 (Pair-10). A small number of negative net snow accumulation estimates were produced in

Pair-2, Pair-4 and Pair-10. This might be due to snow compaction (Ligtenberg et al. 2011) or the

wind-driven snow erosion (Liston and Sturm 2002).

On the Arctic Coastal Plain of northern Alaska, snow accumulation mainly occurs in the first half of the winter season (September to December), and the snow fall in the second half

(January to May) is usually smaller than the first half. As shown in Figure 4.7, at South Meade weather station, the snow accumulated to a depth of 20 – 30 cm from September to December during 2003 – 2009. The snow depletion up to 10 cm occurred in the second half of the winter between January and early March of 2003 – 2004, 2006 – 2007 and 2008 – 2009. Snow fall could occur in the late March or early April, for example in 2004 and 2006, which may account for a large portion of the total winter snow accumulation. At South Meade station, snow started to melt in May or early June and then disappeared rapidly.

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Figure 4.9 Net snow accumulation estimates on Alaskan Arctic Coastal Plain during 2003-2007. The snow accumulation is shown as a vertical bar and the height of the bar is proportional to the net snow accumulation. A negative net accumulation is indicated by a bar point downward from the horizontal line (zero snow accumulation). The black line shows a portion of one ICESat pass, which is used as the transect line for plotting the net snow accumulation and topographical profiles in Figure 4.11.

4.4.2 Validation of the ICESat-derived snow accumulation

The validation and accuracy evaluation of the net snow accumulation derived by our method is challenging, since no direct in situ observations of snow depths over lake surfaces are available for this period of time. In this study, we utilized in situ snow depth observations from automated weather stations on the tundra to evaluate the estimates of snow accumulation on nearby frozen lake surfaces, with the assumption that the magnitude and pattern of snow fall on frozen lake surfaces were the same or very similar to those on the nearby tundra. .

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We examined 9 weather stations (Figure 4.1) and their surrounding lakes within 15 km

distance to the stations. Within this distance, we assume that the climate conditions, particularly

the snow fall, are similar. A match-up point pair is formed for comparison, if a lake with a valid

snow accumulation estimate is located within 15 km of an automated weather station where snow

depth has been recorded at the same two dates (t1 and t2 in Equation (26)). With the assumption

that the lake and the nearby tundra had the same depth of snow at the date t1, we add the in situ

snow depth recorded at the weather station on date t1 to the net snow accumulation estimated from

ICESat observations between date t1 and date t2 to obtain the total snow accumulation on date t2,

which is compared to the in situ snow depth recorded at the weather station on the same date t2.

We have identified 32 match-up point pairs, which involve 15 lakes and 5 automated weather

stations, including Drew Point, East Teshekpuk, Fish Creek, Inigok and South Meade. Their

locations are shown in Figure 4.1.

The comparison of the ICESat-derived snow accumulation with in situ snow depth records from nearby automated weather stations is shown as scatterplot graphs in Figure 4.10. The three scatterplots from Figure 4.10a to Figure 4.10c demonstrate the improvement of the snow accumulation estimates by removing the impact of ICB and the contribution of lake ice growth.

As shown in Figure 4.10a, the Pearson’s correlation coefficient r is only 0.83 and RMSE is 10.9 cm if both the effect of ICB and the contribution of lake ice growth were not corrected. If only the effect of ICB was corrected as shown in Figure 4.10b, the Pearson’s correlation coefficient r

increases to 0.88, and RMSE is reduced to 9.9 cm. Figure 4.10c shows the further improvements

on the snow accumulation in terms of RMSE (5 cm) when the lake ice growth contribution to the

surface elevation change was accounted for. There is a good agreement between ICESat-derived

snow depth and in situ observations. This indicates that our method is capable and effective in

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deriving usable snow accumulation estimates over lake surfaces based on the ICESat observations.

As shown in the scatterplots, the correction for the ICB effect is important to improve the consistency indicated by a significant increase in in the relative accuracy denoted by the Pearson’s correlation coefficient r, and the account for the lake ice growth contribution to the surface elevation rise is valuable to improve the absolute accuracy by correcting the overestimation bias.

Figure 4.10 Comparison of ICESat snow accumulation estimates to in situ snow depth observations from automated weather stations. (a) Both the effect of ICB and lake ice growth contribution to surface elevation change were not removed in the derivation. (b) Only the effect for ICB was removed in the derivation. (c) Both the effect of ICB and the contribution of lake ice growth to surface elevation change were removed in the derivation. The stippled dotted line represents the fitted regression line.

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Figure 4.11 ICESat derived snow accumulation over lake surface during the winter of 2006- 2007 along the satellite track from the coast to the Brooks Range. The transect line of the satellite ground track is shown in Figure 4.9. Surface elevation profile along the transect is plotted based on the surface DEM (https://lta.cr.usgs.gov/IFSAR_Alaska). The dashed line denotes the general trend of the snow accumulation estimates

4.4.3 Spatio-temporal variation of snow accumulation over Alaskan ACP

The ICESat-derived snow accumulation estimates from this study provide a better coverage

than the in situ observations available for this region. These snow accumulation estimates enable

us to examine the inter-annual variability in snow distribution on the Arctic Coastal Plain of

northern Alaska from 2003 to 2009. Snow distribution could be affected by various factors,

including snow fall, wind speed and direction, and topographic effects (Essery and Pomeroy 2004;

Hirashima et al. 2004; Rees et al. 2014). From Figure 4.9, we can observe inter-annual variabilities

in snow accumulation on the Alaskan Arctic Coastal Plain during 2003-2007. The winter season

of 2005-2006 had a higher snow accumulation than other years by 10 – 20 cm on average.

There is a considerable spatial variability in snow accumulation in this area. Snow

accumulation estimates have been derived for the largest number of lakes in the winter of 2005 –

2006 from the pair set of Pair-7, which are distributed across the whole northern Alaska. In the

winter season between 2005 and 2006, the snow accumulation in the eastern part of the Alaskan

Arctic Coastal Plain, e.g. the areas around Kalikpik River and Fish Creek, was clearly lower than

in the middle and western parts of the Alaskan Arctic Coastal Plain. The region between the

Ikpikpuk River and the Topagoruk River in the middle of the Alaskan Arctic Coastal Plain had

relatively higher snow accumulation than the areas along the Meade River and also along the

Kugrua River in the western part of the Alaskan Arctic Coastal Plain. Namely, in the east-west direction, snow accumulation in the east is lower than in the west part and significantly lower than

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in the middle part. This east-to-west variability pattern is clear for the winter of 2005-2006 due to the large number of snow accumulation estimates. However, no sufficient snow accumulation estimates are available for other winters to discern this pattern.

In general, the snow accumulation in the coastal area was lower than in the southern inland region. The snow accumulation increasing trend from the coast to the inland is most apparent in the east part of the Alaskan Arctic Coastal Plain. Figure 4.11 shows the ICESat-derived snow accumulation during the winter of 2006-2007 along the ICESat ground track (Figure 4.9) from the

Arctic coast to the inland region near the foothills of the Brooks Range. Within 40 km coastal zone, it appears that the snow accumulation is small, without much spatial variation. Further away from the coastline to the inland, snow accumulation shows a significantly increasing trend. The increase in snow accumulation appears closely correlated with the surface topography. The inland area with a higher elevation tends to have a higher snow accumulation. This spatial variation pattern of snow accumulation from the coast to the inland has been observed and reported as “V- shape” pattern (as indicated by the dash lines in Figure 4.11) in previous studies based on the field observations along some survey transects, such as, a transect along Kuparuk basin (Liston and

Sturm 2002) and a transect from Utqiagvik to Oumalik (Sturm and Liston 2003).

4.4.4 Discussion

In this study, we used a one-dimensional thermodynamic model to estimate the contribution of lake ice growth to the lake surface upward displacement, in which we adopted the lake ice growth coefficient α = 2.4 and the ice density ρice =0.915. The ice density for an inland fresh lake may vary from 0.9 to 0.92 g/cm3 (Ager 1962). The thicker the snow cover, the lower α value should be used. The ice growth coefficient (α) is often set to 2.7 for lakes with no snow cover, while for lakes with different depths of snow cover the α value varies from 1.7 to 2.4

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(Engineers 2006). Using the daily mean air temperature from South Meade during 2005 – 2006,

we evaluated the sensitivity of surface upward displacement ΔHice to the varying ice density ρice

and ice growth coefficient α. Since most ICESat passes in Fall and Spring campaigns occurred

respectively in October and March, we simulated the different ice thicknesses on 15 October 2005

and on 15 March 2006 by varying the ice growth coefficients α and the ice density ρice. As shown

in Table 4.4, the maximum difference of the calculated surface upward displacement ΔHice is 3.94

3 cm between the parameter setting α = 2.4 and ρice = 0.9 g/cm and the parameter setting α = 1.7

3 and ρice = 0.92 g/cm . For the estimate of the surface upward displacement, the effect of the ice

density variation in the range from 0.9 to 0.92 g/cm3 is only about 1 cm, while the effect of the ice

growth coefficient variation is about 3 cm. Our study indicates that the lake snow accumulation in

the southern inland area tends to be higher than the northern coastal area. Therefore, the use of the

lake ice growth coefficient α = 2.4 might have underestimated the snow accumulation in the

southern regions. If a lower α value was used (e.g. 1.7) for the lakes with thicker snow cover in

southern regions, the estimates of snow accumulation would increase by about 3 cm (see Table

4.4), which would further highlight the general increasing trend of the snow accumulation from

the northern coast to the southern inland as shown in Figure 4.11.

Table 4.4 Lake surface rise under different scenarios of coefficient α and ice density ρice. 3 Zice (cm) ΔHice (cm) by different ρice (g/cm ) Difference (cm) α ΔZice(cm) 15 Oct. 2005 15 Mar. 2006 ρice=0.9 ρice=0.915 ρice=0.92 due to ρice 2.4 10.00 142.08 118.33 10.65 10.06 9.47 1.18* 2.0 8.34 118.40 98.61 8.87 8.38 7.89 0.98* 1.7 7.09 100.64 83.81 7.54 7.12 6.71 0.83* Difference (cm) due to α 3.14** 2.94** 2.76** * denotes the maximum difference between the ΔHice estimated in each row using the three different ρice values ** denotes the maximum difference between the ΔHice estimated in each column using the three different α values

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It should be noted that the snow accumulation over lake surfaces is different from that over

the tundra on the Arctic Coastal Plain. Previous field-based studies (Sturm and Liston 2003; Zhang

and Jeffries 2000) show that the snow pack over lake surfaces is usually harder, denser and thinner

than that over the tundra surface. Therefore, the snow accumulation derived from ICESat laser

altimetry observations over thermokarst lakes may be systematically lower than the snow

accumulation over surrounding tundra. In our validation and accuracy assessment, the in situ snow depths were recorded over tundra surfaces, which are expected to be greater than the snow depth over surrounding lake surfaces. However, with only the ICESat-derived snow accumulations over lake surface in this study, we are not able to assess the differences between lake snow and tundra snow reported in previous field-based studies. In the future study, a comprehensive analysis of the

ICESat-derived snow accumulations on both lake surface and nearby flat tundra surfaces could possibly provide some insights of the differences.

The snow accumulation estimate derived by differencing two separate repeat ICESat elevation measurements on date t1 and date t2 in our case study represents the net effect of snow fall, snow compaction and the wind-driven snow erosion during the time span between date t1 and date t2. If the snow fall occurred before date t1 and little or no snow fall happened between date t1 and date t2, the snow compaction and/or the wind-driven erosion may lead to very low or even

negative net snow accumulation estimates in our calculation. As shown in Figure 4.9, a small

number of very low or even negative net snow accumulation estimates were observed in the low-

lying coastal areas near Smith Bay and in the downstream areas of Kalikplk River and Fish Creek,

where the snow fall was minimal. These very low and negative net snow accumulation estimates

may be partly resulted from the snow compaction and densification that lowers the surface

elevation (Helsen et al. 2008; Ligtenberg et al. 2011). But, they are more likely caused by the

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scouring of lake snow due to the frequent and strong winds observed at the automated weather stations. The snow depletions were observed at South Meade station (e.g. between February and

March of 2006 in Figure 4.7), where the strong northeast wind (~ 25 m/s) (Stegall and Zhang 2012;

Wendler et al. 2010) often occurred during the cold months of December – February (Small et al.

2011). The strong winds can fetch up the loose surface snow and carry it a long distance through the low-relief surfaces (e.g. coastal areas) before its deposition (Liston and Sturm 2002). The wind- driven erosion is stronger for the flat frozen lake snow surface than on the nearby tundra, since tundra vegetation can trap and immobilize the blowing snow (Sturm and Liston 2003).

The frequency and timing of the repeat ICESat passes are important for our snow accumulation estimates and interpretation. If one ICESat pass (on date t1) occurred at the very beginning of the winter before the first snow fall, and the other pass (on date t2) happened at the end of the winter immediately after the last snow fall, we would be able to derive the total snow accumulation depth for the entire snow year. In our case study, the passes of the Fall campaign occurred in October or November (Table 4.3) and no passes are available in September. Most passes of the Spring campaign occurred in March, with a small number of passes in February and in April. The net snow accumulation derived from ICESat observations between October and

March or between November and April in this study may underestimate the real snow accumulation for the entire snow year for the Arctic Coastal Plain as the snow falls before October and after April were not accounted for. As indicated by the snow records at South Meade station

(Figure 4.7), about 8-10 cm snow accumulation before the beginning of the ICESat Fall campaign and about 10-12 cm snow accumulation after the Spring campaign were not accounted for the winter of 2003 – 2004. For the winter of 2006 – 2007, about the similar amount of snow

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accumulation (5-6 cm) before the ICESat Fall campaign and after the Spring campaign were

missed in the calculation.

To monitor and track the complete snow accumulation process, multiple and frequent

observations during the winter season are required. The timing and frequency of ICESat/GLAS

laser footprints along the track were not optimized for snow depth measurements. ICESat-2

(Markus et al. 2017) with three pairs of laser beams in one overpass (6 parallel ground tracks) and

a 91-day exact repeat orbit with monthly sub-cycle (monthly-repeat instead of campaign-repeat

observations) may provide spatially and temporally dense observations to derive snow depth

measurements and also better capture the temporal variations of snow accumulation over the entire

winter season for the Circum-Arctic regions. The validation and accuracy assessment of our snow

depth derivation method are based on the in situ measurements from automated weather stations

on the tundra. In the future, simultaneous field snow depth measurements on frozen lake surfaces

should be acquired during the operation of ICESat-2 to conduct a more rigorous assessment of our

method. The method developed in this study is applicable to the other regions where seasonally

frozen lakes are abundant, for example, the regions of northern Canada, the arctic coastal plains of

Siberia and also the Qinghai-Tibet Plateau.

4.5 Conclusions

The information about the spatial distribution and temporal dynamics of snow cover is

important for studying the energy balance, hydrologic cycle and the ecosystem in lake-rich Arctic regions. However, only meager snow measurements have been collected through sparse automated weather stations or sporadic field surveys in the past. In this research, we developed a novel method to derive snow accumulation information for Arctic regions using repeat ICESat altimetry observations. By utilizing numerous frozen lakes, it has been demonstrated that densely distributed

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snow accumulation measurements (as compared to the point-based in situ records) can be derived using repeat ICESat observations acquired between 2003 and 2009. Our assessment shows that the snow accumulation estimates from the repeat ICESat observations are consistent with in situ measurements from automated weather stations located on the tundra. The Pearson’s correlation coefficient r between our ICESat-derived snow accumulation estimates and the ground-based in situ measurements is as high as 0.88, and the RMSE of our snow accumulation estimates is approximately 5 cm, after the effect of ICB and the contribution of the lake ice growth are eliminated from the measured surface elevation change. The information derived from our method allows for, as compared to point-based in situ observations, a more detailed investigation of the

spatio-temporal variability of snow accumulation on the Arctic Coastal Plain of northern Alaska.

Our snow accumulation derivation method consists of several key technical elements. The

use of the max-amplitude-peak re-tracking scheme is critical to derive reliable and precise surface

elevation measurements over frozen Arctic lake surfaces. Original ICESat GLA14 product created

by the centroid re-tracking scheme contains a large number of erroneous measurements over lake

surfaces. We developed a computational approach to derive reliable lake surface elevation

measurements by correcting the difference between the max-amplitude-peak scheme and the centroid scheme based on the ancillary information contained in ICESat GLA14 products. There existed inter-campaign biases that have an increasing trend over time. The correction for inter-

campaign biases (ICB) significantly improves the quantification of the true surface elevation

change, and hence enhances the consistency and accuracy of the derived snow accumulation. The

lake surface rise due to the lake ice growth during the winter also contributes to the lake surface

elevation change. A simple thermodynamic model is adequate to model the contribution by the

phase transformation. The removal of the contribution due to lake ice growth from the detected

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total lake surface elevation change leads to more accurate snow accumulation estimates, avoiding the systematic overestimation bias. We believe that our method is applicable to other Circum-

Arctic coastal regions as well as to the Qinghai-Tibet Plateau where seasonally frozen lakes are abundant. With the expected launch of new ICESat-2 laser altimetry system in 2018, our method could be used to derive spatially and temporally dense snow depth measurements in these areas for scientific and practical applications.

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