Satellite Altimetry Applications on Lake Ice Thickness and Land Subsidence

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Ting-Yi Yang

Graduate Program in Geodetic Science

The Ohio State University

2020

Dissertation Committee:

Prof. C. K. Shum, Advisor

Prof. Michael Bevis

Dr. Philip Y. Chu

Prof. Demián Gómez

Prof. Michael Durand

Copyrighted by

Ting-Yi Yang

2020

Abstract

Satellite nadir altimetry uses a space-based sensor to repeatedly measure the height, allowing geodesists and other Earth scientists to monitor temporal changes in surface height on a global or regional basis. Satellite altimetry was originally designed for observing and monitoring global ocean surface topography, but innovative methodologies have been developed and demonstrated for sensing non-ocean surfaces. In this study, two non-ocean altimetry applications have been explored and examined: lake ice thickness retrieval in the Laurentian Great Lakes, and land subsidence rate derivation at

San Joaquin Valley. For lake ice thickness study, because there is not yet an operational satellite-based observing system in the Great Lakes, we explore the feasibility of lake ice thickness retrieval using satellite radar and laser altimetry. Cryosat-2 Low Resolution

Mode and one-year long ICESat-2 Inland Water Surface Height data product are used to estimate lake ice thickness during the winter 2011 through winter 2019 using the ice freeboard method, which has been extensively used for polar sea ice thickness retrieval but has not yet been applied for lake ice thickness change studies. The Cryosat-2 radar altimeter estimated ice thickness is compared with in-situ data, the difference is 0.2 m., indicating excellent agreements. The Cryosat-2 solution is further compared with ice cover and air temperature data, the correlation coefficients are larger than 70% in Lake

Superior, Erie and Ontario, implying the validity of the altimeter-derived interannual variability of lake ice changes. We also discover that Cryosat-2 ice thickness and ice ii cover data have strong linear relationship. The one-year long ICESat-2 dataset is used, for the first time, to quantify the ice thickness in Great Lakes region in the winter 2019.

Comparison between Cryosat-2 and ICESat-2 derived ice thickness, the Cryosat-2 observable shows higher estimates due to problem of penetration in snow layer for both missions. We compare both altimetry derived ice thickness with United States Coast

Guard (USCG) estimated values, and found that both altimetry derived ice thickness values are higher than the USCG estimates. The reason might be USCG estimated ice thickness do not account for ridging, causing theses estimates to be lower than the actual values. One winter in-situ ice thickness data is not enough to confirm, more in-situ data are needed for further validations. For land subsidence rate derivation study, we develop a new method to generate 0.3° x 0.3° two-dimensional deformation map using Cryosat-2

Low Resolution Mode data and spatial interpolation method. The results show that the

Cryosat-2 derived deformation map agrees well with the GPS, Jason-2 altimeter, NASA

JPL InSAR estimated velocities, and in-situ data from cumulative groundwater well. The largest subsidence bowl is identified near the city of Corcoran, California, USA, with the maximum subsidence rate -30 ~ -35 cm/yr due to excessive anthropogenic groundwater pumping. In addition, we implement Kuo et al. (2015) method to process conventional pulse-limited radar altimetry missions, including Envisat, Jason-2 and Jason-3, over land for subsidence. The results show good agreement with the GPS data, and seasonal and flood signals are sensed in altimetry derived time series. It is anticipated that the altimetry observations from this study can be used to validate and complement other spaceborne and in-situ sensors, such as GNSS, InSAR and leveling data.

iii

Acknowledgments

First of all, I would like to express my sincere gratitude to 2019 Graduate Fellowship and summer internship, funded by NOAA Cooperative Institute for Great Lakes Research.

Further, I am deeply indebted to my advisor Dr. C. K. Shum for his professional guideline, funding support, and thoughtful comments and recommendations during my graduate studies. I would like to express my deepest appreciation to the following people for helping with my research projects: my dissertation committee members, Dr. Michael

Bevis, Dr. Philip Y. Chu, Dr. Demián Gómez, Dr. Rattan Lal, and Dr. Michael Durand for their helpful comments during the reviews of dissertation; Dr. Ayumi Fujisaki-

Manome for giving useful advices on lake ice thickness research; Dr. Chung-Yen Kuo and Dr. Yuchan Yi for help and suggestions on land subsidence research; Dr. Geoff

Blewitt for answering GPS questions. I am also thankful to the staff in the School of

Earth Science for all their considerate guidance, and my colleagues, friends, and family for all the unconditional support during this intense academic year. Finally, my biggest thanks go to my mom Yun-hui Wu for her endless love, support, and encouragement.

Vita

2012...... B.S. Department of Geomatics, National

Chung Kung University, Taiwan

2014...... M.S. Department of Geomatics, National

Chung Kung University, Taiwan

2018...... M.S. Geodetic Science, The Ohio State

University

2017 to present ...... Graduate Research Associate, School of

Earth Science, The Ohio State University

Publications

Yang, T. Y., Kessler, J., Mason, L., Chu, P.Y., & Wang, J. (2020). A Consistent Great

Lakes Ice Cover Digital Data Set for Winters 1973-2019. Manuscript submitted

for publication.

Kuo, C. Y., Yang, T. Y., Kao, H. C., Wang, C. K., Lan, W. H., & Tseng, H. Z. (2018).

Improvement of Envisat Altimetric Measurements in Taiwan Coastal Oceans by a

Developed Waveform Retracking System. Journal of Environmental Informatics,

31(1). https://doi.org/10.3808/jei.201500324.

Wang, J., Yang, T. Y., Kessler, J., Hu, H., & Chu, P. (2020). Great Lakes ice duration,

winter severity index, cumulative freezing degree days, and atmospheric

teleconnection patterns, 1973–2018. NOAA Technical Memorandum GLERL, 174.

https://doi.org/10.25923/88c9-hm22.

Iz, H. B., Yang, T. Y., & Shum, C. K. (2020). The rigorous adjustment of the global

mean sea level budget during 2005–2015. Geodesy and Geodynamics.

https://doi.org/10.1016/j.geog.2020.03.001.

Iz, H. B., Yang, T. Y., Shum, C. K., & Kuo, C. Y. (2019). Optimal mathematical and

statistical models to estimate vertical crustal movements using satellite altimetry

and tide gauge data. Journal of Geodetic Science, 9(1), 144-153.

https://doi.org/10.1515/jogs-2019-0014.

Fields of Study

Major Field: Geodetic Science

Table of Contents

Abstract ...... ii

Acknowledgments...... iv

Vita ...... v

Table of Contents ...... vii

List of Tables ...... xi

List of Figures ...... xiii

Chapter 1: Introduction ...... 1

1.1 Satellite Altimetry and its Applications over Non-Ocean Surface ...... 1

1.2 Motivation of This Study and Literature Review...... 2

1.2.1 Lake Ice Thickness Retrieval in Great Lakes ...... 2

1.2.2 Land Subsidence Detection in San Joaquin Valley, California, US ...... 3

1.3 Summary of Chapters ...... 6

Chapter 2: The Principle and Waveform Retracking of Satellite Altimetry ...... 7

2.1 Principle of Satellite Altimetry ...... 7

2.2 Waveform Retracking ...... 10

vii

2.2.1 Waveform ...... 10

2.2.2 Waveform Retracking ...... 12

2.2.3 Retracking Correction ...... 16

2.3 Overview of Satellite Altimetry ...... 17

2.4 Brief Introduction of Utilized Satellite Altimetry Missions...... 18

2.4.1 Envisat ...... 19

2.4.2 Jason-2 and Jason-3 ...... 19

2.4.3 Cryosat-2 ...... 20

2.4.4 ICESat-2 ...... 21

Chapter 3: Lake Ice Thickness Retrieval in the Great Lakes ...... 24

3.1 Introduction ...... 24

3.2 Data ...... 26

3.2.1 Cryosat-2 Radar Altimetry LRM Data ...... 26

3.2.2 ICESat-2 Laser Altimetry ATL13 Data Product ...... 28

3.2.3 In-Situ Ice Thickness Data (in winter 2014) ...... 29

3.2.4 SNODAS Snow Depth and Snow Density Data ...... 30

3.2.5 CO-OPS and CHS Water Level Gauge ...... 33

3.2.6 NOAA GLERL Ice Cover: AMIC and Ice Duration ...... 35

3.2.7 GHCN-D Air Temperature: AFDD ...... 37

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3.3 Methodology ...... 40

3.3.1 Procedure for Cryosat-2 Altimetry Data ...... 40

3.3.2 Procedure for ICESat-2 Data Processing...... 50

3.4 Results and Validations ...... 52

3.4.1 Validation using In-Situ Ice Thickness Data in Lake Superior, Winter 2014 .. 52

3.4.2 Compare Derived Ice Thickness with Ice Duration, AMIC, AFDD, and snow

depth ...... 54

3.4.3 Compare Cryosat-2 Estimated Ice Thickness with ICESat-2 results ...... 63

3.4.4 Compare Cryosat-2 and ICESat-2 Results with USCG 9th District Estimated

Data ...... 66

3.4.5 Validate Altimetry Derived Water Level Height Using Water Level Gauge

Records ...... 70

3.4.6 Corroborate Snow Density ...... 76

3.4.7 Validate Surface Type Classification by PlanetScope Satellite Images ...... 77

3.5 Error Sources of Ice Thickness Estimation ...... 81

3.6 Conclusion ...... 85

Chapter 4: Land Subsidence Monitoring in San Joaquin Valley ...... 87

4.1 Introduction ...... 87

4.2 Data ...... 91

4.2.1 Satellite Radar Altimetry - Envisat, Jason-2, Jason-3 and Cryosat-2 LRM data

...... 91

4.2.2 USGS 3DEP DEM...... 92

4.2.3 CORS and Nevada Geodetic Lab GPS ...... 93

4.2.4 NASA JPL InSAR Measured Subsidence Rate ...... 94

4.3 Methodology ...... 95

4.3.1 Data processing procedure for Envisat, Jason-2 and Jason-3 ...... 95

4.3.2 Data processing procedure for Cryosat-2 ...... 98

4.4 Results and Validations ...... 100

4.4.1 Performance of Cryosat-2: validated by GPS, JPL InSAR, and Jason-2 data 100

4.4.2 Performance of Envisat, Jason-2, and Jason-3: validated by GPS observed

trends ...... 108

4.4.3 Combination of Envisat, Jason-2, and Jason-3 (May 2002 ~ Oct 2019) ...... 115

4.5 Error Sources of Land Subsidence Rate Derivation ...... 117

4.6 Conclusion ...... 118

Chapter 5: Conclusions and Future Work ...... 120

References ...... 125

Appendix A: Time Series of Waveform Characteristic w.r.t Ice Cover ...... 134

List of Tables

Table 2-1. The range of Cryosat-2 corrections (Bouzinac, 2012) ...... 8

Table 2-2. Operating characteristics of satellite altimeters used in the study ...... 23

Table 3-1. Main characteristics of GHCN-D, SNODAS and HRRR ...... 31

Table 3-2. List of selected water level gauges ...... 34

Table 3-3. AMIC and ice duration of each lake from winter 2011 to winter 2019 ...... 36

Table 3-4. List of selected GHCN-D air temperature stations ...... 38

Table 3-5. AFDD (unit: days) of each lake from winter 2011 to winter 2019 ...... 39

Table 3-6. Threshold used to identify between surface types ‘ice’ or ‘water’ ...... 43

Table 3-7. The differences and its STD between IGLD85 and EGM08 height (Cryosat-2)

...... 47

Table 3-8. Bias and its STD (unit: m) between Threshold and OCOG retracker ...... 48

Table 3-9. The differences and its STD between IGLD85 and EGM08 height (ICESat-2)

...... 51

Table 3-10. Differences between mean of altimetry-derived and in-situ ice thickness .... 53

Table 3-11. Correlation coefficient between altimetry-derived ice thickness and ice duration (ID), AMIC, AFDD, and snow depth (SD*). Table that correlation larger than

70% is filled in gray color...... 55

Table 3-12. The coefficients of linear regression: y = ax + b, where x is the Threshold

40% ice thickness, y is the ice duration, AMIC, AFDD, and snow depth ...... 62

Table 3-13. The correlation and RMSE of Cryosat-2 derived water surface height and water level gauge records in each lake from July 2010 to April 2019 ...... 70

Table 3-14. The correlation and RMSE of Cryosat-2 derived water surface height and water level gauge records in each lake from October 2018 to September 2019 ...... 70

Table 4-1. The list of GPS stations in the study region ...... 93

Table 4-2. The subsidence rate comparison between GPS, Crsyoat-2 (left), and JPL

InSAR (right) estimates at GPS sites locations...... 107

Table 4-3. Land subsidence rate comparison between GPS and the closest altimetry points (within 25 km). Thre10/ModThre10/Unret represent Threshold 10%/Modified

Threshold 10%/ unretracked results. Gray filled table is the most accurate method compared with GPS...... 110

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List of Figures

Figure 2-1. Diagram of satellite altimetry theory (Credit: ESA)...... 9

Figure 2-2. The required corrections for altimetry over inland area (Credit: ESA)...... 9

Figure 2-3. Waveform generation process over ocean surface (Credit: AVISO)...... 10

Figure 2-4. Characteristics of an ocean waveform (Credit: Passaro et al., 2014)...... 11

Figure 2-5. Waveform examples of Cryosat-2 for different types of surface...... 12

Figure 2-6. A schematic of Threshold (A) and Modified Threshold Retracker (B, Credit:

Lee, 2008). In Figure 2-6(B), (a) Red solid line is the original gate of Threshold 10%, and red dashed line is the retracked gate from Modified Threshold 10%, (b) An example of Difference I., (c) An example of Difference II...... 14

Figure 2-7. Schematic of OCOG (Credit: Lee, 2008)...... 16

Figure 2-8. The timeline of satellite altimetry missions since 1991 (Credit: DUACS). ... 18

Figure 2-9. Current Cryosat-2 Mode Mask (version 4.0, since Sep 2019; Credit: ESA). 21

Figure 2-10. Beam pattern of ICESat-2 (Credit: NASA)...... 22

Figure 3-1. The location of the Laurentian Great Lakes, the largest freshwater lakes

(94,250 square miles) in the world, comprising Lakes Superior, Michigan, Huron, Erie, and Ontario...... 26

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Figure 3-2. Cryosat-2 ground track in winter 2019 [including Dec 2018 (black), Jan 2019

(red), Feb 2019 (yellow), Mar 2019 (green), and Apr 2019 (blue)] at Lake Superior. .... 27

Figure 3-3. The retracked height profile of Ocean CFI (black), UCL Land Ice (red), and

OCOG (blue), along latitude on Feb 19th, 2014, at Lake Superior...... 28

Figure 3-4. ICESat-2 GT1L ground track in winter 2019 [including Dec 2018 (black), Jan

2019 (red), Feb 2019 (yellow), Mar 2019 (green), and Apr 2019 (blue)] in Lake Superior.

...... 29

Figure 3-5. Snow depth data comparison between GHCN-D (A & B), HRRR (C & D), and SNODAS (E & F) on February 5th and 6th, 2018...... 32

Figure 3-6. Location of in-situ mooring (green) and water level gauge (yellow dots: CO-

OPS stations, red dots: CHS stations). The in-situ mooring is shown as a green rectangle in Lake Superior. The number is corresponding to Index column in Table 3-2...... 33

Figure 3-7. Timeline of data evolution and frequency...... 36

Figure 3-8. Location of selected GHCN-D (blue dots) for AFDD derivation. The number is corresponding to the Index column in Table 3-4...... 37

Figure 3-9. Flowchart of Cryosat-2 lake ice retrieval algorithm...... 39

Figure 3-10. LEW comparison between Ocean CFI model output (gray line) and difference of Threshold retracked gate (black line) on August 10th, 2014 at Lake

Michigan. The black line in each picture is difference of retracked gate between

Threshold 30% and (A) Threshold 50%, (B) Threshold 60%, and (C) Threshold 70%... 41

xiv

Figure 3-11. Demonstration of filtering results is Lake Michigan on February 8th, 2013.

Gray line is original altimetry OCOG height profile along latitude, blue/red/green lines are height profile after first/second/third filtering criteria...... 42

Figure 3-12. Time series of PP with respect to four groups in each Lake. Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and

Group 3 (red) represent the altimetry over the lake ice region...... 45

Figure 3-13. Time series of OCOG width with respect to four groups in each Lake.

Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2

(gray) and Group 3 (red) represent the altimetry over the lake ice region...... 46

Figure 3-14. Schematics of ice freeboard and thickness estimate methods using radar and laser altimetry...... 49

Figure 3-15. Flowchart of ICESat-2 lake ice retrieval algorithm...... 50

Figure 3-16. Upper: The location of in-situ mooring and Cryosat-2 track on Feb. 19th,

2014 and Mar. 2nd, 2014. Lower: Comparison of ice thickness profile at Lake Superior on Feb. 19th, 2014 (left, Threshold 40% results) and Mar. 2nd, 2014 (right, Threshold 70% results)...... 53

Figure 3-17. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Superior...... 56

Figure 3-18. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Michigan...... 57

Figure 3-19. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Huron...... 58

Figure 3-20. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Erie...... 59

Figure 3-21. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Ontario...... 60

Figure 3-22. Scatter plot of ice thickness (Threshold 40%) on X axis and AFDD (top- left), AMIC (top-right), ice duration (bottom-left), and snow depth (bottom-right) on Y axis...... 61

Figure 3-23. Time series of Cryosat-2 and ICESat-2 ice thickness at Lake Superior and

Lake Michigan in winter 2019...... 64

Figure 3-24. Time series of Cryosat-2 and ICESat-2 ice thickness at Lake Huron, Lake

Erie and Lake Ontario in winter 2019...... 65

xvi

Figure 3-25. Ice thickness comparison between altimetry-derived (dotted points in the lower panel of figures), and the USCG estimated ice thickness (background) on February

12th, 2019...... 67

Figure 3-26. Ice thickness comparison between altimetry-derived (dotted points in the lower panel of figures), and the USCG estimated ice thickness (background) on February

26th, 2019...... 68

Figure 3-27. Ice thickness comparison between altimetry-derived (dotted points in the lower panel of figures), and the USCG estimated ice thickness (background) on March

19th, 2019...... 69

Figure 3-28. Time series comparison between Cryosat-2 derived water height (blue dots), and in-situ water level gauge (red line) at Lake Superior (A) and Lake Michigan (B). ... 71

Figure 3-29. Time series comparison between Cryosat-2 derived water level height (blue dots), and in-situ water level gauge (red line) at Lake Huron (A) and Lake Erie (B)...... 72

Figure 3-30. Time series comparison between Cryosat-2 derived water level height (blue dots), and in-situ water level gauge (red line) at Lake Ontario...... 73

Figure 3-31. Time series comparison between ICESat-2 derived water level height (blue dots) and in-situ water level gauge (red line) at Lake Superior...... 73

Figure 3-32. Time series comparison between ICESat-2 derived water height (blue dots) and in-situ water level gauge (red line) at Lake Michigan (A) and Lake Huron (B)...... 74

Figure 3-33. Time series comparison between ICESat-2 derived water height (blue dots) and in-situ water level gauge (red line) at Lake Erie (A) and Lake Ontario (B)...... 75 xvii

Figure 3-34. Time series of snow density in winter 2014...... 76

Figure 3-35. Time series of snow density at Lake Ontario in winter 2014...... 77

Figure 3-36. Comparison between classification results with PlanetScope image. Top:

The location of comparison area, the waveforms of points with respect to the numbers in the right panel shown in Figure 3-37. Bottom: The classifying results using PP threshold

(right), and OCOG width (center). The bottom right figure is the GLERL ice cover data.

...... 78

Figure 3-37. The altimetry waveforms over ice (A and B), and ice with partial water (C to

F). The locations of each waveform are show in Figure 3-36...... 79

Figure 3-38. The altimetry waveforms over water (A), ice (B), and shoreline (C). The locations of each waveform are show in Figure 3-36...... 80

Figure 3-39. The ice thickness variation due to various snow depth (top-left), snow density (top-right), ice density (bottom-left; between 750 ~ 950 kg/m3), and ice density

(bottom-right; between 890 ~ 930 kg/m3). The function in each figure shows the linear relationship between ice thickness and related variable. The fixed variables are also shown in each figure...... 83

Figure 3-40. The schematic of theoretic and actual range measurement of ICESat-2

(laser) and Cryosat-2 (radar)...... 84

Figure 3-41. The ice thickness variation due to changes of ice freeboard. The function in figure shows the linear relationship between ice thickness and ice freeboard. The fixed variables are also shown in figure...... 84

xviii

Figure 4-1. Study region. The backgrounds are the USGS 3DEP Bare Earth DEM

(Arundel et al., 2015), and Blue Marble satellite image. Blue lines are Envisat ground track, brown line is Jason-2 and Jason-3 track. The number on each track is pass number.

Red triangles are GPS stations...... 89

Figure 4-2. Study region. The backgrounds are Global Land Cover – Share (GLC-

SHARE) crop coverage and Blue Marble satellite image. Brown line is California High-

Speed Rail (CHSR), and blue lines are national or state freeways...... 90

Figure 4-3. The flowchart of multi-mission radar altimetry, Envisat, Jason-2 and Jason-3

(left panel), and Cryosat-2 (right panel) derived evolution of land surface rate estimates.

...... 94

Figure 4-4. Example of Envisat height profile of Sub-waveform retracker (magenta solid line)...... 96

Figure 4-5. The nominal track of Jason Track 43 interpolation result...... 97

Figure 4-6. The example of before (gray line) and after (black line) filtering using 3DEP

DEM (red line) and GKR (green line) on April 3rd, 2014...... 99

Figure 4-7. The schematic of Cryosat-2 surface interpolation...... 99

Figure 4-8. The Cryosat-2 interpolated height (background) and used altimetry data (dot).

...... 100

Figure 4-9. Comparison among Cryosat-2 (grid), Jason-2 (circles), and GPS (Triangles).

Cryosat-2 and Jason-2 all used the Threshold 10% retracker to process altimetry data, and the subsidence rate is computed using data from 2010 to 2015...... 102 xix

Figure 4-10. Comparison among Cryosat-2 (grid), Jason-2 (circles), and GPS (Triangles).

Cryosat-2 and Jason-2 all used the Modified Threshold 10% retracker to process altimetry data, and the subsidence rate is computed using data from 2010 to 2015...... 103

Figure 4-11. Comparison among JPL InSAR (background image), Jason-2 (circles), and

GPS (Triangles). In figure, we use Jason-2 and Jason-3 Modified Threshold 10% results.

The subsidence rate of GPS and altimetry is derived in period from March 2015 to May

2017...... 104

Figure 4-12. The subsidence rate along latitude. JPL InSAR (black line) and Cryosat-2

Modified Threshold (red line) results are interpolated using Jason-2 and Jason-3 ground tracks. For Jason mission, we compute subsidence rate in the period of 2015 to 2017

(green line) and period of 2010-2015 (blue line), to compare with InSAR and Cryosat-2 rates...... 105

Figure 4-13. (A) The cumulative groundwater level drop during October 2011 to October

2015 (Credit: Ojha et al., 2019), (B) The Cryosat-2 Modified Threshold 10% derived subsidence rate during December 2010 to September 2015. The black polygons are

California Bulletin 118 Groundwater Basins...... 106

Figure 4-14. Time series comparison between Cryosat-2 (gray) and Jason-2 (blue). .... 107

Figure 4-15. The profile of land subsidence rate along latitude. Blue/red/black line is

Envisat Track 153 (top) and 226 (bottom) Threshold 10% / Modified Threshold 10% /

Unretracked results, gray dots are GPS subsidence rate...... 111

Figure 4-16. The profile of land subsidence rate along latitude. Blue/red/black line is

Envisat Track 611 (top) and 684 (bottom) Threshold 10% / Modified Threshold 10% /

Unretracked results, gray dots are GPS subsidence rate...... 112

Figure 4-17. The profile of land subsidence rate along latitude. Blue/red/black line is

Jason-2 and Jason-3 Track 43 Threshold 10% / Modified Threshold 10% / Unretracked results, gray dots are GPS subsidence rate ...... 113

Figure 4-18. Time series comparison of surface height anomaly between the CRCN GPS station (green line), and the closest altimetry (Jason-2 and Jason-3) point (blue and red lines). Gray line is the total monthly precipitation larger than 50 mm, from the Global

Summary of the Month (GSOM) data...... 113

Figure 4-19. Time series comparison of surface height anomaly between LEMA GPS station (green line), and the closest altimetry (Jason-2 and Jason-3) point (blue and red lines). Gray line is the total monthly precipitation larger than 50 mm, from the Global

Summary of the Month (GSOM) data...... 114

Figure 4-20. The detrended time series of Jason-2, Jason-3 (blue line), and CRCN GPS site (green line). The solid black line is the start of rainy season (Oct.), and dashed line is the end of rainy season (Apr.). Blue rectangle is the period of 2017 California flood. . 114

Figure 4-21. The time series of surface height obtained from (A) Sub-waveform retracker

(Hwang et al., 2016), (B) Threshold 10%, (C) Modified Threshold 10%, (D) unretracked results, and (E) GPS. Red rectangles are drought period in California. In (A) ~ (D), black line is Envisat, red line is Jason-2, and blue line is Jason-3 results...... 116

xxi

Figure A-1. Time series of PPL with respect to four groups in each Lake. Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and

Group 3 (red) represent the altimetry over Lake ice region ...... 135

Figure A-2. Time series of PPR with respect to four groups in each Lake. Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and

Group 3 (red) represent the altimetry over Lake ice region ...... 136

Figure A-3. Time series of gate of max power (MaxP) with respect to four groups in each lake. Group 1 (blue) and Group 4 (black) represent the altimetry data over water area,

Group 2 (gray) and Group 3 (red) represent the altimetry over Lake ice region ...... 137

Figure A-4. Time series of max power value with respect to four groups in each Lake.

Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2

(gray) and Group 3 (red) represent the altimetry over ice region ...... 138

Figure A-5. Time series of LEW with respect to four groups in each Lake. Group 1

(blue) and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and Group 3 (red) represent the altimetry over ice region ...... 139

xxii

Chapter 1: Introduction

1.1 Satellite Altimetry and its Applications over Non-Ocean Surface

Satellite altimetry is a spaceborne sensor for measuring surface height, and was originally designed for monitoring global ocean surface topography. Since the first Skylab radar altimetry was launched in 1973, the altimetric technology has advanced and enable innovative Earth sciences applications, including sea level rise (Church et al., 2004), global marine bathymetry (Smith et al., 1994), ocean circulation (Fu et al., 1996), and derivation of wave height and wind speed (Fedor and Brown, 1982). Beyond the core of mission objectives, variety applications have been demonstrated over non-ocean surfaces

(Shum et al., 1995; Fu & Cazenave, 2000), such as Antarctic or Greenland ice sheet elevation changes (Fricker and Padman, 2012; Zwally et al., 1989), glacier and ice caps monitoring (Moholdt et al., 2010), inland or coastal water level monitoring (Frappart et al., 2006; Lee et al., 2009; Tseng et al., 2013), and detections of solid Earth deformation

(Lee et al., 2008a, 2008b; Kuo et al., 2015; Hwang et al., 2016). To further explore the potential and capability of altimetry, we focus on lake ice thickness retrieval in

Laurentian Great Lakes and anthropogenic land subsidence detection in San Joaquin

Valley, California, USA. Both scientific research topics are crucial and timely societal relevance problems, so improved understanding is required towards addressing these problems. 1

1.2 Motivation of This Study and Literature Review

1.2.1 Lake Ice Thickness Retrieval in Great Lakes

In the Great Lakes region, accurate knowledge of ice cover and ice thickness is crucial for variety purposes, including shipping safety, emergency and rescue missions, biological activities (Zhang et al., 2018), and decadal climate changes (Wang et al., 2017;

Wang et al., 2018; Mason et al., 2016). In addition, lake ice is an important input parameter for lake forecast models (Hawley et al., 2018), which can support stakeholders’ or mariners’ decision-making during the winter season (Fujisaki-Manome et al., 2019). Ice cover has been fully collected and analyzed based on integration of remote sensing sensors, Synthetic Aperture Radar (SAR) and visible/infrared imagery, since 1973, and has been widely used in diverse scientific research and applications

(Yang et al., 2020). Unlike ice cover, there is not yet a robust satellite-based ice thickness observed system in the Great Lakes area. Few studies (Titze & Austin, 2016;

Leshkevich et al., 2016; Hawley et al., 2018) measured ice thickness using mooring observations or airborne ground penetrating radar, however, both spatial and temporal resolutions of data are sparse and limited. Therefore, our goal is demonstrating accurate derivation of the lake ice thickness observations from satellite altimetry, which can offer comprehensive, repeatedly measured, and long-term dataset in whole Great Lakes region.

To explore the possibilities of lake ice thickness retrieval using satellite altimetry,

Beckers et al. (2017) used Cryosat-2 Synthetic Aperture Radar Interferometric (SARIn) mode data to derive the height differences between snow-ice and ice-water interfaces from Great Slave Lake and Great Bear Lake in Canada. The obtained ice thickness data

2 closely match with in-situ measurements, the correlation can reach up to 0.65 and the

Root-mean-square Deviation (RMSE) is less than ± 0.33 meter (m). However, there are too many assumptions for pulse penetration through snow and ice, and this method only can measure 4.9~8.4 m ice thickness due to radar wave maximum penetration depth.

Furthermore, there is no Cryosat-2 SARIn mode data in the Great Lakes region.

Consequently, we employ Cryosat-2 Low Resolution Mode (LRM) and ICESat-2 Inland

Water Elevation (ATL13) data products using the sea ice freeboard method, which has already been proven and widely used to retrieve sea ice thickness changes in the polar region (Connor et al., 2009; Hvidegaard & Forsberg, 2002), to retrieve the ice thickness changes over the entire Great Lakes.

1.2.2 Land Subsidence Detection in San Joaquin Valley, California, US

By 2025, two-thirds of the world’s population will face water scarcity problem (Bremere et al., 2001), which could be manifested as national security concern in the regions, where would endure severe droughts and extremely high demand of freshwater (Fenton,

2014). Since the 1930s, increasing population growth and severe droughts in California, have been causing the needs of groundwater to be dramatically increasing. The extensive groundwater withdrawal causes significantly land subsidence, which has cost the government more than billions of dollars to fix the destroyed infrastructure (Hanak et al.,

2015), and has reduced the flow capacity of canals that deliver irrigation water and disperse floodwater (Sneed et al., 2013). To investigate the magnitude and location of land deformation, several techniques have been developed and applied in California, including Interferometric Synthetic Aperture Radar (InSAR), Global Positioning System 3

(GPS), extensometers, and geodetic leveling survey. Although GPS, extensometers, and leveling survey can offer accurate land deformation measurements, the spatial or temporal sampling is sparse as well as data collection and instrument maintenance are time consuming and relatively high cost. On the contrary, InSAR has high spatial sampling and moderate temporal sampling rate (Wei et al., 2010), but the growing crops, snowfall, hydrology, and/or other processes that cause significantly ground cover changes may lead to unreliable InSAR observations (McCormack et al., 2011). In addition, there are temporal InSAR data gap in California during 2010 to 2015. The current available products for San Joaquin Valley region are ALOS (2007 ~ 2010) and Sentinel-1a and -1b

(2015 ~ present) satellite missions, other historical InSAR missions (Radarsat, ERS-1,

ERS-2) were not optimized to generate continuous deformation time series.

To complement current existing land subsidence monitoring system, several researches have innovated approaches to monitor the vertical land deformation using satellite altimetry. Lee et al. (2008a, 2008b) utilized Modified Threshold Retracker with TOPEX

/POSEIDON (TP) data, successfully estimated the average vertical motion (VM) rate associated with the glacial isostatic adjustment (GIA) process in the land regions of the

Hudson Bay, the location of the principal ancient Laurentide Ice Sheet during the

Pleistocene. The estimated TP altimetry derived VM is up to 10 ~ 15 mm/yr with an estimated uncertainty of ± 2.9 mm/yr, agreeing with the nearby GPS vertical rate. Kuo et al. (2015) used TP and Jason-2 data, retrieved by Threshold and Modified Threshold

Retracker, to successfully detect the vertical land motion in Southwestern Taiwan. The correlation coefficient of estimated VM rate and precise leveling measurements reach 96

%, with mean differences of 0.43 cm/yr. The most recent study, Hwang et al. (2016) combined multiple satellite missions (TP, Jason-1, Jason-2, and Envisat), to monitor long-term land subsidence in San Joaquin Valley, Central Taiwan, and North China Plain using the Sub-waveform Retracker (Yang et al., 2011). Their results closely matched

Global Navigation Satellite System (GNSS) and leveling measurements derived vertical rate estimations. In spite of that, their spatial sampling location is all limited to underneath the satellite ground track, and cannot estimate and quantify the two- dimension (2D) land subsidence spatial pattern in the study region. In our experiment, we use Cryosat-2 data with spatial interpolation, to derive the 2D land subsidence rate in

San Joaquin Valley. Data from other altimetry missions (Envisat, Jason-2, and Jason-3) are also processed using Kuo et al.’s (2015) method, to validate Cryosat-2 estimated land subsidence rate.

1.3 Summary of Chapters

In Chapter 2, we introduce principle and data processing of satellite altimetry. The introduction of used data from multiple altimetry missions (Envisat, Jason-2, Jason-3,

Cryosat-2, and ICESat-2) are presented as well in this chapter.

Chapter 3 shows the examination of ice thickness retrieval using Cryosat-2 and ICESat-2 missions in Great Lakes. We first introduce the in-situ ice thickness and other used dataset (snow depth, snow density and water level). The procedure of getting the ice thickness is then described along with comparison between two satellite missions and validation with in-situ and estimated ice thickness.

Chapter 4 examines the land subsidence rate derivation using Cryosat-2 data with spatial interpolation method over San Joaquin Valley, California. The estimated VM rate is compared with other altimetry missions (Envisat, Jason-2 and Jason-3), GPS, NASA JPL

InSAR result and groundwater well.

Chapter 5 concludes the dissertation, presents results and recommendation of future studies.

Chapter 2: The Principle and Waveform Retracking of Satellite Altimetry

2.1 Principle of Satellite Altimetry

Satellite altimetry, a spaceborne instrument that emits a short microwave pulse in the nadir direction, and the echo reflected from the Earth surface is received by sensor onboard the satellite orbiting the Earth. The two-way travelling time of pulse is transferred to vertical range measurement (h in Figure 2-1) between satellite and surface using and Eq. (2-1). This range measurement, when combine with precise knowledge of the satellite orbit (H in Figure 2-1), allows the determination of surface height (SH) from

Eq. (2-2).

ct h = (2-1) 2

SH=− H h (2-2) where t is the two-way traveling time, and c is the speed of light (Gommenginger et al.,

2011).

To obtain a better estimation of surface height, three types of corrections are applied to the range measurement h: 1) decreasing inhomogeneous effects in the media, 2) eliminating the error and bias in the instrument, and 3) correcting geophysical effects

(Tseng, 2012). These corrections are summarized in Figure 2-2, which is an example over inland water and land surface. The updated Eq. (2-2) and utilized corrections are

7 outlined in Eq. (2-3), the model or method used in each correction are listed in Table 2-2.

The range of Cryosat-2 range corrections are in Table 2-1.

SHHhhhhhh= − −()Int + ion + wet + dry + SET + h PT −  R (2-3)

where hInt is instrument correction, hion is ionosphere delay correction, hwet is wet

tropospheric correction, hdry is dry tropospheric correction, hSET is solid earth tide

correction, hPT is pole tide correction, and R is waveform retracking correction (Eq.

(2-11)). For the applications of satellite altimetry over the Great Lakes and land surface, we do not apply ocean tides correction, dynamic atmosphere correction (DAC), nor the electromagnetic or sea state bias correction. In addition, the ionosphere and dry/wet troposphere delays are corrected by model predicted values. The description of each of these corrections is documented by Fu & Cazenave (2000).

Table 2-1. The range of Cryosat-2 corrections (Bouzinac, 2012)

Corrections Range (cm) Dry tropospheric 170 ~ 250 Wet tropospheric 0 ~ 50 Ionospheric 6 ~ 12 Solid Earth tide -30 ~ 30 Polar tide -2 ~ 2

Figure 2-1. Diagram of satellite altimetry theory (Credit: ESA).

Figure 2-2. The required corrections for altimetry over inland area (Credit: ESA). 9

2.2 Waveform Retracking

Unlike smoother ocean surface, the land or ice surfaces are more complex and nonuniform. The signal reflected from complex topography, contaminates the waveform and causes the accuracy of observations quickly degenerated. Therefore, several algorithms called waveform retracking, have been developed to reprocess waveforms and to optimally derive the range measurement over various non-ocean surfaces. In this section, we will explain the definition of waveform and adopted waveform retrackers in our study.

2.2.1 Waveform

The satellite altimetry transmits a pulse from on-board antenna toward surface, the reflected signal then be captured by sensor and be recorded as measurement of power with a function of time. This temporal profile of received power, which is referred to the altimeter waveform, is shown in Figure 2-3.

Figure 2-3. Waveform generation process over ocean surface (Credit: AVISO). 10

The waveform contains three parts: thermal noise, leading edge and trailing edge, and be sampled by 128 (Envisat and Cryosat-2) and 104 (Jason-2 and Jason-3) gates. The midpoint of the leading edge is the two-way travel time of the pulse, which provides the range measurement between the satellite and reflected surface. In addition to surface height, the waveform can also provide other oceanic parameters, including significant wave height from leading edge rising time, backscatter or wind speed from maximum amplitude, and mis-pointing angle through trailing edge slope (Figure 2-4).

To minimizing the inherent noise in waveform, the on-board tracking system is designed and applied to returned waveform. The on-board tracker keeps the returned signal within analysis window (Gommenginger et al., 2011), and keep the half-power point, as known as nominal tracking point, of the leading edge at the specific frequency (Lee, 2008). The nominal tracking point of each altimetry mission is listed in Table 2-2.

Figure 2-4. Characteristics of an ocean waveform (Credit: Passaro et al., 2014). 11

2.2.2 Waveform Retracking

In Figure 2-3 and Figure 2-4, the presented waveforms are all ocean waveform. As the name implies, the ocean waveform is the reflected signal from ocean surface and be expressed or fitted by Brown (1977) model. While satellite altimetry flies through non- ocean surface, the waveform shape changes due to complicated topography or diverse characteristic of surface (Figure 2-5). However, the onboard tracker is designed by the

Brown model (Lee, 2008), which is not suitable for non-ocean surface. The predicted mid-point of the leading edge may not be at the actual location. This tracker offset causes the erroneous range measurement and decreases the accuracy of altimetry over non-ocean surface. Several approaches called waveform retracker were developed to retrack the waveform for reprocessing the complex waveforms and obtaining the correct mid-point of the leading edge. The aim of retracking is to fit a model or function to waveforms (Gommenginger et al., 2011), based on empirical or physical methods. In following paragraph, we only introduce adopted retrackers: Threshold, Modified

Threshold, and OCOG. Other retrackers are described in Gommenginger et al. (2011).

Figure 2-5. Waveform examples of Cryosat-2 for different types of surface.

A. Threshold Retracker (Davis, 1997)

The threshold retracking algorithm was primarily developed for measuring ice sheet elevation changes (Davis, 1997), and was widely used and proven over land (Lee et al.,

2008a, 2008b) and sea ice areas (Laxon, 1994). The true leading edge position (Rg) is determined by locating the first waveform gate (Rk) that exceed the percentage (TCOEFF,

Threshold Level) of maximum amplitude (Amax), and be retrieved using linear interpolation (Eq. (2-7)). Because Davis (1977) discovered a bias problem within thermal noise in the Seasat and Geosat missions, the pre-leading edge thermal noise (DC) is computed by Eq. (2-5) and be removed in Eq. (2-7). The schematic of Threshold retracker is shown in Figure 2-6 (A). In land study, we apply 10% as threshold level, and

10% ~ 70% with incremental 10% in lake ice study.

Amax = max( Pi ( t )) (2-4)

1 7 DC=  Pi () t (2-5) 3 i=5

TL= DC + TCOEFF () Amax − DC (2-6)

TL− Pk −1() t RRgk=( − 1) + (2-7) Pkk()() t− P−1 t

where Pti ( ) is the power at i gate, Amax is maximum waveform amplitude, DC is

thermal noise or DC level, Tcoeff is threshold level, TL is power of retracked gate, Rk

th is the k gate, which k satisfy the power of Rk is bigger than TL and power of Rk−1 is

smaller than (Pk−1  TL  Pk ) , and Rg is retracked gate.

Figure 2-6. A schematic of Threshold (A) and Modified Threshold Retracker (B, Credit:

Lee, 2008). In Figure 2-6(B), (a) Red solid line is the original gate of Threshold 10%, and red dashed line is the retracked gate from Modified Threshold 10%, (b) An example

of Difference I., (c) An example of Difference II.

B. Modified Threshold Retracker (Lee, 2008)

In coastal or inland regions, the accuracy of Threshold retracker might decrease due to 1) bump in thermal noise causing wrong DC value (DC in Eq. (2-5)) derivation, or 2) the

14 maximum amplitude (Amax in Eq. (2-4)) might not be at around leading edge (see Figure

2-6 (B) (a)). To improve the Threshold retracker accuracy over land, Lee (2008) modified the derivation of DC and Amax in Threshold Retracker through differenced waveform Difference I and Difference II (Pi(t) is the power at i gate).

Difference I(i)=− Pii+1 (t) P (t) (2-8)

Difference II(i)=− Pii+2 (t) P (t) (2-9)

The DC value is selected through the first gate which Difference I is negative and becomes positive at the next gate. For Amax, first finding the apparent leading edge by searching the maximum gate (imax) in Difference II. From gate imax, searching the first negative value (gate in) in Difference II. If value of Difference I at gate in is also negative, the Amax is the power value of gate in. If value of Difference I at gate in is positive, the Amax is the power value of gate in+1. After getting DC and Amax, the retracked gate Rg can be derived by Eq. (2-6) and Eq. (2-7).

C. Offset Center of Gravity (OCOG, Wingham et al., 1986)

Wingham et al. (1986) used the empirical method to compute the Amplitude (A), Width

(W) and center of gravity (COG) of waveform to retrack the mid-point of the leading edge. The OCOG algorithm was developed for monitoring ice sheet change, and is common used for estimating amplitude in Threshold retracker (Bamber, 1994). In

Cryosat-2 built-in algorithm, the used OCOG algorithm is a variant of that used for

Envisat. It first computes the amplitude of waveform using Eq. (2-10), then find the retracked gate using Eq. (2-6) and Eq. (2-7). The thermal noise (DC) is not considered in 15 their process. In our lake ice experiment, the OCOG is employed to retrieve lake water height, because the quality of observation from ocean model is mostly bad during winter season.

N−− n N n 42 (2-10) A = Pii (t) P (t) i=11 + n i = + n where Pi(t) is the power at i gate, N is the total number of gate, n is the number of gate at beginning and end of the waveform, which should be removed due to noise signal contain.

Figure 2-7. Schematic of OCOG (Credit: Lee, 2008).

2.2.3 Retracking Correction

After deriving retracked gate Rg from retracker, the retracking correction (∆R in Eq. (2-

3)) can be computed by:

R =( Rgg − T)  d (2-11)

CG =d a (2-12) 2 where ∆d is the gate spacing, ∆Ga is the pulse duration, Tg is the nominal tracking point.

2.3 Overview of Satellite Altimetry

The idea of using satellite altimetry to monitor ocean parameters was first proposed in

1969 (Kaula, 1969), and was preliminary confirmed by first launched satellite altimetry,

Skylab in 1973. This National Aeronautics and Space Administration (NASA) operated mission, Skylab, though the accuracy is 15 m (AVISO), it can roughly measure the global ocean geoid. After that, NASA launched GEOS-3 and Seasat in 1975 and 1978, these two experimental missions provided many ocean information to Geodesy, Geophysics and Oceanography researches. In 1985, U.S. Navy launched Geosat, which was the first mission that operated the Exact Repeat Mission (ERM), became the first altimetry mission that provide long-term, high-precision, and repeated observations.

Since 1991, NASA, Centre National d’Etudes Spatiales (CNES), and European Space

Agency (ESA) have successfully developed and launched ERS-1, Topex/Poseidon (TP),

ERS-2, GFO, Jason-1, Jason-2, Envisat, ICESat, Jason-3, Cryosat-2, and ICESat-2

(timeline is shown in Figure 2-8). As the error of orbit determination and instrument noise has reduced, the accuracy of satellite altimetry reaches up to 2 cm (Peng et al.,

2009). In addition, some follow-on missions remain same orbit parameters as previous

17 missions (e.g. Jason-3 follows Jason-2, Jason-1, and T/P), to maintain and expand the repeat observations at same point more than 25 years.

Because the footprint of radar pulse is large (around 2 to 5 km), it’s difficult to obtain the accurate ice sheet, cloud and land elevation measurements. ICESat-2 and Cryosat-2 replace traditional radar altimetry with laser or SARIn technique, to offer high precision observations over non-ocean surface.

Figure 2-8. The timeline of satellite altimetry missions since 1991 (Credit: DUACS).

2.4 Brief Introduction of Utilized Satellite Altimetry Missions

In Great Lakes ice thickness retrieval, we use data from Cryosat-2 LRM radar altimetry and ICESat-2 laser altimetry missions. For the San Joaquin Valley land subsidence rate detection, we adopt Envisat, Jason-2, Jason-3 and Cryosat-2 LRM data products. All operating characteristics are organized in Table 2-2.

2.4.1 Envisat

Developed by ESA, Envisat was a follow-on altimetry mission to ERS-1 and ERS-2. In our study, we use RA-2 Level-2 Sensor and Geophysical Data Record (SGDR) Version 3

Ku band altimetry data (Soussi et al., 2018), which contains most precise instrument calibrations, orbit solution, geophysical corrections, and waveforms. The data and waveform are downloaded through ESA FTP data archive

(ftp://ra2_data:[email protected]). After its orbit was changed to a lower inclination for mission extension (Phase E) in October 2010, there is no orbit maintenance during this new 30-day repeat mission

(https://earth.esa.int/web/eoportal/satellite-missions/e/envisat, accessed June 15, 2020).

With degraded altimeter data accuracy, we did not use the Envisat data after degradation in our study.

2.4.2 Jason-2 and Jason-3

Jason-2 and Jason-3 are both operated and maintained by CNES, NASA, National

Oceanic and Atmospheric Administration (NOAA), and European Organization for the

Exploitation of Meteorological Satellites (EUMETSAT), they take over and continue TP and Jason-1 mission since 2008. In our study, we use Jason-2 Poseidon-3 (Dumont et al.,

2009) and Jason-3 Poseidon-3B (Dumont et al., 2016) Level-2 SGDR Version D Ku band altimetry data. The data and waveform can be derived from NOAA National Centers for

Environmental Information (NCEI) Jason-2 and Jason-3 satellite products archive

(https://www.nodc.noaa.gov/SatelliteData/jason/). In October 2016, Jason-2 entered its

19 extended mission phase to move to an interleaved orbit with Jason-3, and then began the geodetic mission phase with a long or non-repeat orbit commencing in July 2017

(https://directory.eoportal.org/web/eoportal/satellite-missions/j/jason-2, accessed June 15,

2020). As a result, we did not use the Jason-2 altimeter data after October 2016 in our study.

2.4.3 Cryosat-2

Cryosat-2 mission is operated by ESA and launched in April 2010, it replaces the first

Cryosat mission, which was lost due to launcher failure on 8 October 2005. Unlike the conventional radar altimeter, which interval between pulse is about 500.25 seconds, the

Cryosat-2 on-board altimeter, a SAR/Interferometry radar altimeter instrument (SIRAL), can emit a pulse every 50.25 seconds (ESA). Combine short pulse interval with Doppler properties of pulse and dual SIRAL payload, Cryosat-2 not only provides conventional

LRM (Low Resolution Mode), but also offers SAR and SARIn mode data, where footprint diameter can reduce to 400 m in along-track direction. The small footprint significantly improves the accuracy of measurement over floating sea ice or mountain glacier regions. However, three modes can only operate at one time, SAR and SARIn mode data are available in certain areas of the world based on user requirements. There is only LRM mode data in the Great Lakes region (Figure 2-9). Thus, we only adopt

LRM Version C Level-2I and Level-1B data (Bouzinac, 2012), which are generated by

Cryosat Ice Processor, in our experiments. All dataset can be downloaded through ESA web interface at http://science-pds.cryosat.esa.int/.

Figure 2-9. Current Cryosat-2 Mode Mask (version 4.0, since Sep 2019; Credit: ESA).

2.4.4 ICESat-2

ICESat-2 is a follow-on to the ICESat mission and part of NASA’s Earth Observing

System, projected to lunch in Sep 2018. ICESat-2 carry a laser altimeter system,

Advanced Topographic Laser Altimeter System (ATLAS), which has a single laser and be split into three pairs (see Figure 2-10). Each pair is composed by a strong energy beam and a low energy beam, and two beams are separated by about 90m. Compare with footprint of radar pulse (2~5 km), ICESat-2 footprint size is much smaller (14 m), leading good performance in ice sheet and land topography monitoring. Although ICESat-2 sea ice mask includes Great Lakes region, there is no sea ice thickness product (ATL07) in our research region. Therefore, inland water data product (ATL13) Version 2 is used in our study (Jasinski et al., 2019). The data archive is at NOAA National Snow and Ice

Data Center (NSIDC, https://nsidc.org/data/ATL03/versions/2).

Figure 2-10. Beam pattern of ICESat-2 (Credit: NASA).

Table 2-2 lists all operating characteristics of altimetry missions. It is noted that Envisat,

Jason-2 and Jason-3 are all dual-frequency altimeters (Ku and C band for Jason, Ku-band and S-band for Envisat). C or S-band ranges are used to remove first order ionosphere delays, however, S-band on Envisat failed shortly after launch. Since Ku band is higher resolution and long-lasting, we only choose Ku band data in our processing. For consistency, we use the GIM (GPS Ionosphere Map) model to do the ionosphere correction for all altimetry missions. In Table 2-2, we only list the information with respect to Ku band.

Table 2-2. Operating characteristics of satellite altimeters used in the study

Envisat Jason-2 Jason-3 Cryosat-2 ICESat-2 Launch - Mar 2002 - Jun 2008 - Jan 2016 - Apr 2010 - Sep 2018 - End June 2012 Oct 2019 Present Present Present Altitude (km) 784 1336 1336 717 480 Inclination (°) 98 66 66 92 92 Nominal Repeat cycle 35 10 10 369 91 Mission (days) Orbit Ground track spacing at the 90 315 315 8 30 equator(km) Along track 350 350 350 300 0.7 interval (m) (20Hz) (20Hz) (20Hz) 1.65 km Footprint size 2~5 km 2~5 km 2~5 km 13 m Beam (LRM) Band Ku (Radar) X (Laser) Number of 128 104 104 128 waveform gates N\A Nominal Waveform 46 32 32 65 tracking point Pulse duration 3.125 3.125 3.125 3.125 1.5 (ns) Ionospheric Global Ionosphere Maps (GIM) model IERS 2010 Dry Tropo. GEOS- European Centre for Medium-Range Weather FPIT Range Wet Tropo. Forecasts (ECMWF) model model Corrections Solid Earth Cartwright & Taylor (1973) tidal potential Tide Pole Tide Wahr (1985) LRM VC SGDR V3 SGDR VD SGDR VD Version Level-2I, ATL13 V2 Level-2 Level-2 Level-2 Data 1B Jun 2002 - Aug 2008 - Mar 2016 - Jul 2010 - Oct 2018 - Period Jul 2010 Aug 2016 Oct 2019 Apr 2019 Sep 2019

Chapter 3: Lake Ice Thickness Retrieval in the Great Lakes

3.1 Introduction

The report of the 2019 Great Lakes Ice Forecast Workshop (Fujisaki-Manome et al.,

2019) reveals that the ice information, ice cover and thickness, is crucial for U.S. Coast

Guard (USCG), vessel operators, and the National Weather Service, to improve their decision-making during winter season. The stakeholders indicate that these lake ice data have significant impact on navigation safety, regional climate, lake effect weather forecasting, and emergency or rescue response. Through the cooperation among the U.S.

National Ice Center (USNIC), Canadian Ice Service (CIS), and NOAA’s Great Lakes

Environmental Research Laboratory (GLERL), the consistent and accurate ice cover data have been created by satellite-based measurements, and been maintained since 1973

(Yang et al., 2020). Unlike ice cover, there are only estimated or model-based ice thickness data available for the public, because the in-situ data is difficult to gather and there has not yet a satellite-based observing system to monitor lake ice thickness developed in the Laurentian Great Lakes.

To explore the possibility and capability of lake ice thickness retrieval using satellite altimetry, we adopt the sea ice freeboard method, which has been proven and widely used for sea ice thickness retrieval in the polar region, along with the use of Cryosat-2 Low

Resolution Mode (LRM) radar altimetry data and the ICESat-2 laser altimeter data. The 24 ice freeboard method is based on the assumption that the floating lake ice is in isostatic balance (or hydrostatic equilibrium), which means that the relationship among ice thickness, ice freeboard, and snow depth can be represented by the scaling of ice, snow and water density. In our data processing, we utilize satellite radar altimetry to derive lake ice freeboard height, the height between snow/ice interface (or air/snow interface for laser altimetry) and water surface, and use the Snow Data Assimilation System

(SNODAS) model data to obtain the snow depth and snow density. With the assumption of ice density, the lake ice thickness can be estimated over the Great Lakes (the location of Great Lakes is shown in Figure 3-1). The derived ice thickness is then validated against the available in-situ ice thickness data (Titze et al., 2016), the USCG 9th District estimated ice thickness, and the ICESat-2 multi-beam laser altimeter derived ice thickness estimates. As we know several environmental parameters have correlations with each other, thus we compare interannual variability between lake ice duration, annual maximum ice cover (AMIC), and accumulative freezing degree days (AFDD), with our ice thickness results in our validation.

Figure 3-1. The location of the Laurentian Great Lakes, the largest freshwater lakes

(94,250 square miles) in the world, comprising Lakes Superior, Michigan, Huron, Erie,

and Ontario.

The Laurentian Great Lakes provide the natural border between U.S. and Canada (Figure

3-1, left), and bordering the seven states (red boundaries in Figure 3-1 right figure) in the

United States, and one Canada Province (blue outline in Figure 3-1 right figure). A Blue

Marble image (Stöckli et al., 2005) in the background shows the extent of Great Lakes water surface (dark tones in Figure 3-1 right figure).

3.2 Data

3.2.1 Cryosat-2 Radar Altimetry LRM Data

ESA’s radar altimetry mission, Cryosat-2, was launched in Apr 2010 and is still in operation at present. In spite of repeat cycle of Cryosat-2 is about one year (369 days with 30 days sub-cycle), its footprint size is merely 2.15 km2 (with the diameter at 1.65 26 km) and the density or coverage of ground track (Figure 3-2) is higher than previous or other current missions. Therefore, we choose Cryosat-2 as our experimental altimetry data source, to demonstrate that lake ice derivation using altimetry is plausible. The Ku band unretracked height and range corrections are downloaded from the LRM Level-2I dataset, the corresponding waveform data is retrieved from the LRM Level-1B dataset.

There are three built-in retracked heights, the Ocean CFI model fit, the UCL Land Ice, and the Offset Centre of Gravity (OCOG) retrackers, are available in the Level-2I data product. Nevertheless, the Ocean and Land Ice retracked heights have large variance and error during winter season (Figure 3-3) due to lake ice influence. In our study, we use the

OCOG retracked height as our preferred water level height, and apply the Threshold retracker to unretracked height, to derive the ellipsoidal height of the lake snow/ice interface.

Figure 3-2. Cryosat-2 ground track in winter 2019 [including Dec 2018 (black), Jan 2019

(red), Feb 2019 (yellow), Mar 2019 (green), and Apr 2019 (blue)] at Lake Superior.

Figure 3-3. The retracked height profile of Ocean CFI (black), UCL Land Ice (red), and

OCOG (blue), along latitude on Feb 19th, 2014, at Lake Superior.

3.2.2 ICESat-2 Laser Altimetry ATL13 Data Product

NASA’s multi-beam laser altimetry mission, ICESat-2, was launched in Sep 2018 and is currently operational. Compared with radar altimetry, the footprint size of ICESat-2 is much smaller (about 250 m2). That is the main reason why ICESat-2 is an important mission for mountain glacier, ice caps, and ice sheets mass balance studies. Because there is no lake ice nor sea ice data product in the Great Lakes, we employ the ATL13 product, which provides the estimation of inland water surface height, to retrieve lake ice thickness in our experiment. There is no waveform retracking process for the ICESat-2 data, since the ATL13 product has already conducted the model fitting from original photon data. In each emission, 6 beams are transmitted from ICESat’s altimeter instrument, the Advanced Topographic Laser Altimeter System (ATLAS). These 6 beams are grouped into 3 pairs, consists by a strong energy beam and a low energy beam,

28 and two beams are separated by about 90 m (see Figure 2-10). Because the low power beams have few collected data during the winter season, we only exploit the high energy beams of each pair, called GT1L, GT2L and GT3L. In addition, the distance of each pairs is 3 km, we do not combine three data together but process them separately. The ground track of ICESat-2 GT1L is shown in Figure 3-4.

Figure 3-4. ICESat-2 GT1L ground track in winter 2019 [including Dec 2018 (black), Jan

2019 (red), Feb 2019 (yellow), Mar 2019 (green), and Apr 2019 (blue)] in Lake Superior.

3.2.3 In-Situ Ice Thickness Data (in winter 2014)

The only in-situ data we have is kindly provided by Titze and Austin (2016). The data were collected from the Western Mooring in Lake Superior (47° 19.02' N, 89° 48.52' W; location of mooring is shown in Figure 3-6), depth or lake bottom pressure values were measured every minute during winter 2014. The time-series of ice thickness corresponds to the depth of the pressure sensor, and is derived by subtracting the atmospheric pressure from a nearby station and then computed using the hydrostatic assumption and equation.

3.2.4 SNODAS Snow Depth and Snow Density Data

Although the Global Historical Climatology Network Daily (GHCN-D) data product supplies in-situ snow data along the Great Lakes shoreline, the number of stations at

Canada side is relatively sparse and the spatial interpolation over Great Lakes surface contains large errors due to wide-spread lake-effect snows. Currently, two models provide snow data in Great Lakes, one is the High-Resolution Rapid Refresh (HRRR), and the other one is the Snow Data Assimilation System (SNODAS). HRRR offers snow model predicted or nowcasted data in the Great Lakes, so there is no need to do spatial interpolation over the Great Lakes ice surface. However, the HRRR model data is only available after September 2014, thus we choose SNODAS as our snow data source.

SNODAS is a modeling and data assimilation system (Barrett A., 2003), which is developed by the National Operational Hydrological Remote Sensing Center (NOHRSC).

The data archived is at the National Snow and Ice Data Center (NSIDC, https://nsidc.org/data/g02158). The unmasked (covering part of Canada) SNODAS provides several snow-related parameters since December 2009, here we use the snow water equivalent (SWE) and snow depth grid data to obtain the snow density (Eq. (3-8)) and snow depth (SD). Both spatial resolutions of SWE and snow depth are 1 km, and they represent the model state at 06:00 UTC (Coordinated Universal Time).

Because no SNODAS data are available over Great Lakes water/ice surface, we adopt

Triangulation-based natural neighbor interpolation to perform 2D spatial interpolation over the lake ice/water surface. The spatial resolution of the interpolated SNODAS is

0.01 degree. To evaluate our spatial interpolation results, we compare the interpolated

SNODAS snow depth with GHCN-D (Menne et al., 2012), and HRRR (Smith et al.,

2008) snow depth data on February 5th and 6th, 2018. Same as SNODAS, we perform 2D spatial interpolation for GHCN-D as well. Through comparison, the SNODAS grid data

(Figure 3-5 (E) and (F)) match well with most of the GHCN-D stations. Over the lake surface, the spatial patterns of SNODAS and HRRR look similar in the whole Great

Lakes, indicating that our spatial interpolation method is valid and the interpolated snow parameters are accurate. In addition, we find discrepancies between HRRR and GHCN-

D in the northwest part of Lake Superior. There is a 30~50 cm difference between

HRRR and GHCND. In same region, SNODAS is more accurate as compared with

GHCN-D in-situ data. In Figure 3-5 (A) and (B), they show how lake-effect snow affects

GHCN-D interpolated grids. The lake-effect snow occurs when the cold air from Canada passes over the unfrozen and warm water surface, causing the clouds form, grow and produce the heavy snow falls on the southern and eastern shores of Great Lakes (Niziol et al., 1995). Therefore, the snow depth in Lake Superior should be close to zero in Figure

3-5, the GHCN-D interpolated snow depth is around 70 cm in the south part of Lake

Superior.

Table 3-1. Main characteristics of GHCN-D, SNODAS and HRRR

GHCN-D SNODAS (Unmasked) HRRR Period Since 1763 Since Dec. 2009 Since Sept. 2014 Spatial Point observations, be 1 km, be interpolated to 3 km Resolution interpolated to 0.1 deg grid 0.01 deg grid Frequency Daily Daily Hourly Operator NOAA NCEI NOAA NOHRSC NOAA/ESRL/GSD

Figure 3-5. Snow depth data comparison between GHCN-D (A & B), HRRR (C & D),

and SNODAS (E & F) on February 5th and 6th, 2018. 32

3.2.5 CO-OPS and CHS Water Level Gauge

Two types of daily water level data are downloaded and used for water level validation, as the Great Lakes region is partially over US and partially over Canada. The US water level data source is the Center for Operational Oceanographic Products and Services

(CO-OPS, https://tidesandcurrents.noaa.gov), operated by NOAA National Ocean

Service (NOS). The Canadian water level data source is the Canadian Hydrographic

Service (CHS, https://www.waterlevels.gc.ca/eng), which is managed by Department of

Fisheries and Oceans (DFO). The locations of each station are shown in Figure 3-6.

There are 58 selected stations, among them, 22 sites are CHS stations, and 35 sites are

CO-OPS stations. Because the CHS only has daily data, only daily water level data from both CO-OPS and CHS are utilized in our validation study.

Figure 3-6. Location of in-situ mooring (green) and water level gauge (yellow dots: CO-

OPS stations, red dots: CHS stations). The in-situ mooring is shown as a green rectangle

in Lake Superior. The number is corresponding to Index column in Table 3-2.

Table 3-2. List of selected water level gauges

Index ID Name Lat Long Index ID Name Lat Long 0 10050 THUNDER BAY 48.41 -89.22 29 9063028 Sturgeon Point 42.69 -79.05 1 10220 ROSSPORT 48.83 -87.52 30 9063038 Erie 42.15 -80.09 2 10750 MICHIPICOTEN 47.96 -84.90 31 9063053 Fairport 41.76 -81.28 3 10920 GROS CAP 46.53 -84.59 32 9063063 Cleveland 41.54 -81.64 4 11070 THESSALON 46.25 -83.55 33 9063079 Marblehead 41.54 -82.73 LITTLE 5 11195 45.98 -81.93 34 9063085 Toledo 41.69 -83.47 CURRENT 6 11375 PARRY SOUND 45.34 -80.04 35 9063090 Fermi Power Plant 41.96 -83.26 7 11690 TOBERMORY 45.26 -81.66 36 9075002 Lakeport 43.14 -82.49 8 11445 MIDLAND 44.75 -79.89 37 9075014 Harbor Beach 43.85 -82.64 9 11500 COLLINGWOOD 44.51 -80.22 38 9075035 Essexville 43.64 -83.85 10 11860 GODERICH 43.75 -81.73 39 9075065 Alpena 45.06 -83.43 11 12005 BAR POINT 42.06 -83.11 40 9075080 Mackinaw City 45.80 -84.72 12 12065 KINGSVILLE 42.03 -82.73 41 9075099 De Tour Village 45.99 -83.90 13 12250 ERIEAU 42.26 -81.91 42 9076024 Rock Cut 46.26 -84.19 14 12400 PORT STANLEY 42.66 -81.21 43 9087023 Ludington 43.95 -86.44 15 12710 PORT DOVER 42.78 -80.20 44 9087031 Holland 42.77 -86.21 PORT 16 12865 42.87 -79.25 45 9087044 Calumet Harbor 41.73 -87.54 COLBORNE 17 13030 PORT WELLER 43.24 -79.22 46 9087057 Milwaukee 43.00 -87.89 18 13150 BURLINGTON 43.30 -79.79 47 9087068 Kewaunee 44.46 -87.50 19 13320 TORONTO 43.64 -79.38 48 9087072 Sturgeon Bay Canal 44.80 -87.31 20 13590 COBOURG 43.96 -78.16 49 9087079 Green Bay 44.54 -88.01 21 13988 KINGSTON 44.22 -76.52 50 9087088 Menominee 45.10 -87.59 22 9014098 Fort Gratiot 43.01 -82.42 51 9087096 Port Inland 45.97 -85.87 23 9044020 Gibraltar 42.09 -83.19 52 9099004 Point Iroquois 46.48 -84.63 24 9052000 Cape Vincent 44.13 -76.33 53 9099018 Marquette C.G. 46.55 -87.38 25 9052030 Oswego 43.46 -76.51 54 9099044 Ontonagon 46.87 -89.32 26 9052058 Rochester 43.27 -77.63 55 9099064 Duluth 46.78 -92.09 27 9052076 Olcott 43.34 -78.73 56 9099090 Grand Marais 47.75 -90.34 28 9063020 Buffalo 42.88 -78.89

Note: Lat and Long represent the geodetic latitude and longitude of water level gauge stations, the units are degree.

3.2.6 NOAA GLERL Ice Cover: AMIC and Ice Duration

In the Great Lakes Ice Cover (GLIC) dataset, ice cover values are projected on a 2D square grid, and categorized in 21 levels (between 0 to 100 with 5 interval, before winter

1983) and 13 levels (0, 5, 10, 20, …, 90, 95, and 100, since winter 1983). GLIC represents the percentage of ice cover for each grid cell since winter 1973. Throughout this long history, GLIC dataset has been upgraded several times in both spatial and temporal resolutions (Figure 3-7). In order to make those data sets consistent, we reprocess the GLIC dataset to generate pseudo-daily 1024 x1024 grid (1.8 km spatial resolution) using projection with Nearest Neighbor Search (NNS) for spatial interpolation, and linear interpolation with categorization for temporal interpolation

(Yang et al., 2020). The improved data archive is available at https://doi.org/10.7265/krkb-f591.

Ice duration is obtained by subtracting the freeze-up date by the break-up date. The free- up and break-up date are determined if this is the first/last date when the mean of ice cover greater than or equal to 10%. The AMIC (Annual Maximum Ice Cover) is derived by computing the mean of ice cover for each lake per observed date and assigning the maximum mean as AMIC. To be consistent with the altimetry data, we only count the ice duration and AMIC between December 1st to April 30th. The derived ice duration and

AMIC for each lake are listed in Table 3-3.

Figure 3-7. Timeline of data evolution and frequency.

Table 3-3. AMIC and ice duration of each lake from winter 2011 to winter 2019

Year Superior Michigan Huron Erie Ontario AMIC (%) 2011 33.65 29.33 63.91 95.84 32.29 2012 8.51 16.71 23.37 13.98 3.39 2013 38.66 24.42 48.03 83.75 17.07 2014 95.82 93.32 96.43 96.46 61.61 2015 95.65 72.91 96.42 98.15 82.71 2016 22.70 26.73 48.14 78.75 24.61 2017 18.72 18.18 35.55 35.57 6.80 2018 77.17 51.30 81.45 95.12 25.93 2019 94.91 55.82 95.71 94.28 39.78 Ice Duration (days) 2011 74 99 117 109 50 2012 0 46 53 26 0 2013 65 61 74 50 23 2014 121 137 140 132 96 2015 113 97 124 102 89 2016 24 49 63 49 22 2017 29 75 85 54 0 2018 108 84 110 95 57 2019 89 83 112 71 49 36

3.2.7 GHCN-D Air Temperature: AFDD

The air temperature data are downloaded from GHCN-D, which is an integrated database of daily climate information from land-based stations. The data archive is at ftp://ftp.ncdc.noaa.gov/pub/data/ghcn/daily/by_year/, the location and information of the selected stations are shown in Figure 3-8 and Table 3-4. Because the data coverage of the daily average air temperature is sparse in most of stations, we use maximum and minimum temperature and average these two variables to derive the daily average temperatures. To get the Accumulative Freezing Degree Days (AFDD) of each lake, we average the temperature of each lake and count how many days that average temperature is less than or equal to 0 °C . To consistent with altimetry data, we only count the AFDD between December 1st to April 30th. The obtained AFDD is listed in Table 3-5.

Figure 3-8. Location of selected GHCN-D (blue dots) for AFDD derivation. The number

is corresponding to the Index column in Table 3-4.

Table 3-4. List of selected GHCN-D air temperature stations

Lat Long Time Data Region Index Station ID (deg) (deg) Span Coverage (%) 0 CA006046768 48.60 -86.28 2011-2020 98 1 CA006049443 48.37 -89.12 1967-2020 55 2 USC00205690 46.41 -86.66 1911-2020 95 3 USC00208043 46.60 -85.22 1968-2019 95 Superior 4 USC00213282 47.75 -90.33 1913-2020 96 5 USC00474953 46.78 -90.77 1944-2020 95 6 USC00478349 46.73 -92.07 1909-2020 97 7 USW00014858 47.17 -88.49 1948-2020 85 8 USC00124244 41.63 -87.09 1989-2020 97 9 USC00201896 45.64 -85.01 1969-2019 97 10 USC00205065 44.21 -86.29 1888-2019 92 11 USC00207690 42.40 -86.28 1895-2019 93 Michigan 12 USC00473271 44.53 -88.10 1999-2020 91 13 USC00478905 45.36 -86.89 1944-2020 99 14 USW00014839 42.95 -87.90 1938-2020 100 15 USW00014840 43.17 -86.24 1896-2020 100 16 USW00014850 44.74 -85.58 1896-2020 100 17 CA006092920 45.88 -82.57 2010-2020 96 18 CA006111792 44.50 -80.22 1994-2020 98 19 CA006116257 45.35 -80.05 2002-2020 97 20 CA006122847 43.77 -81.72 1981-2020 71 21 CA006128330 45.23 -81.63 2007-2020 98 Huron 22 USC00200361 43.63 -84.02 2004-2020 91 23 USC00201492 45.65 -84.47 1891-2020 93 24 USC00206680 42.98 -82.42 1933-2020 97 25 USW00014814 45.06 -83.43 1948-2019 98 26 USW00014847 46.48 -84.36 1931-2020 100 27 USW00094898 44.02 -82.79 1999-2020 96 28 CA006134190 42.05 -82.67 1968-2020 96 29 CA006135583 42.52 -81.63 1957-2020 99 30 CA006136606 42.88 -79.25 1964-2020 97 Erie 31 USC00336389 41.75 -81.30 1950-2019 99 32 USW00014846 41.45 -82.72 1936-2019 97 33 USW00014860 42.08 -80.18 1926-2020 100 34 CA006151061 43.30 -79.80 1992-2020 92 35 CA006155878 43.87 -78.83 1969-2020 98 36 CA006156559 43.83 -77.15 1992-2020 88 Ontario 37 USC00306314 43.46 -76.49 1926-2019 100 38 USC00309049 43.24 -77.39 2009-2020 100 39 USC00309690 43.27 -79.01 2004-2019 99 40 USW00094790 43.99 -76.02 1949-2020 100

Table 3-5. AFDD (unit: days) of each lake from winter 2011 to winter 2019

Year Superior Michigan Huron Erie Ontario 2011 117 96 109 91 94 2012 98 53 69 32 44 2013 129 85 93 66 61 2014 131 105 112 84 91 2015 115 89 102 77 89 2016 105 62 73 39 58 2017 95 66 72 43 56 2018 130 95 106 72 77 2019 119 89 96 62 77

Figure 3-9. Flowchart of Cryosat-2 lake ice retrieval algorithm. 39

3.3 Methodology

3.3.1 Procedure for Cryosat-2 Altimetry Data

In addition to the hypothesis that floating lake ice is in hydrostatic equilibrium, we also assume that Ku band radar can penetrate dry and cold snow (Beaven et al., 1995). Figure

3-14 shows the diagram of ice freeboard and thickness method. In our study, we use built-in OCOG retracked height or water level gauge data, to derive the water level height

(Rw). The unretracked height is processed by using waveform retracking for deriving the snow/ice interface height (Rri). The detail processing steps are depicted in following paragraphs.

Step 1: Filter out bad quality data using LEW, MaxP and median of OCOG Height

We use three criteria to remove the outliers in the CryoSat-2 LRM altimetry data:

1. Leading Edge Width [LEW; Eq. (3-1)] > 3: A wide LEW may be due to off-nadir

reflection or reflection from rough surface (Tilling et al., 2019)

2. Bin of maximum power of waveform (MaxP) is not within 30-80 bin: if MaxP exists

in front/rear end of waveform, the signal might be reflected from land surface

3. The differences between measurement and median of OCOG height is larger than 20

m or lower than -10 m

LEW = Retracked gate of Threshold 60% - Retracked gate of Threshold 30% (3-1)

The definition of LEW in Tilling et al. (2019) is difference of retracked gate between

Threshold 70% and Threshold 30% in Arctic sea ice region. To confirm whether this definition is appropriate in our study area, we compare the LEW between Cryosat-2 built-

40 in Ocean CFI model output and difference of retracked gate from Threshold retracker during summer 2014. Unlike Tilling et al. (2019), we find that the difference of retracked gate between Threshold 60% and Threshold 30% agrees well with Ocean CFI model

LEW, in most of the track (Figure 3-10). Thus, we slightly change the LEW definition for better performance in our study region.

Figure 3-10. LEW comparison between Ocean CFI model output (gray line) and

difference of Threshold retracked gate (black line) on August 10th, 2014 at Lake

Michigan. The black line in each picture is difference of retracked gate between

Threshold 30% and (A) Threshold 50%, (B) Threshold 60%, and (C) Threshold 70%.

Figure 3-11 demonstrates our filtering result, which reveals that our filtering criteria can perfectly remove the error or outliers in our data. Figure 3-11 shows that the LEW criteria can eliminate the large variance data between latitude 44.9 ~ 45°, and outliers around 45°, 45.15° and 45.9° are eliminated through MaxP criteria. Since the variance of water level should not be too large, we use median of OCOG height to remove the bad data (red line around 44.9°).

Figure 3-11. Demonstration of filtering results is Lake Michigan on February 8th, 2013.

Gray line is original altimetry OCOG height profile along latitude, blue/red/green lines

are height profile after first/second/third filtering criteria.

Step 2: Reference to EGM2008 model geoid height

We convert altimetry ellipsoid height, WGS84, to orthometric height using EGM2008 model, to eliminate the dominant component of height signal (Connor et al., 2009). The small-scale ice freeboard height will be easy to detect in following procedure.

Step 3: Identify surface types ‘ice’ or ‘water’ using waveform characteristics

We classify the altimetry data using Pulse Peakiness (PP) and OCOG width, the thresholds are listed in Table 3-6.

Table 3-6. Threshold used to identify between surface types ‘ice’ or ‘water’

Ice Water PP > 20 < 5 OCOG Width < 20 45 ~ 65

To determine the threshold and which waveform parameters can be used in our classifying algorithm, we test several parameters, including PP, peakiness left of the max power (PPL; Ricker et al., 2014), peakiness right of the max power (PPR; Ricker et al.,

2014), bin of max power (MaxP), max power value, LEW, and OCOG width (provided by Cryosat-2 database), with GLERL ice cover (IC) data. The equations for each parameter are written in Eq. (3-2) ~ Eq. (3-5). Each variable is categorized according to corresponding ice cover and observed date. Group 1 to Group 3 are wintertime period

(December, January, February, March, April) with IC <= 25%, 25% < IC < 75%, IC >=

75, and Group 4 is summer period (June, July, August, September). The mean of each variable in each group is then computed per year. Here, we find that only PP (Figure 3-

12) and OCOG width (Figure 3-13) can effectively classify surface type. The time series of other variables can be found in Appendix A.

NWF max(WF ) PP= NWF (3-2) i=1 WF

MaxP−1 PPL=max( WF) mean WFi 3 (3-3) i=− MaxP 3

MaxP+3 PPR=max( WF) mean WFi 3 (3-4) i=+ MaxP 1

2 NWF−− n N WF n 24 OCOG Width=  WFii WF (3-5) i=11 + n i = + n where WF is the altimetry waveform values, and NWF is the number of waveform gates

(128 gates for Cryosat-2).

In Figure 3-12 and Figure 3-13, Group 1 (blue line) and Group 4 (black line) represent the altimetry data over water area, Group 2 (gray line) and Group 3 (red line) represent the altimetry over ice region. Both figures show PP and OCOG width have significant different when data point is over ice or water surface. The verification of our classification results is described in Chapter 3.4.7.

Step 4: Derive snow/ice interface height using Threshold retracker

After applying range corrections (instrument, ionospheric, wet and dry tropospheric, solid

Earth tide and pole tide) to the Cryosat-2 unretracked height, we perform waveform retracking using Threshold algorithm. It should be note that the conventional ocean corrections, including Dynamic Atmosphere Correction (DAC), ocean tides, and the electromagnetic or sea state bias are not applied in this study. For the threshold level (see

Chapter 2.2.2), Nilsson et al. (2016) use 20% to obtain Greenland ice sheet surface height, Ricker et al. (2014) apply 40%, 50% and 80% in Arctic sea ice region. There is no existing suggestion for threshold level to retrieval lake ice freeboard height.

Therefore, we test 7 threshold level (10%, 20%, …, 60%, and 70%) in the Great Lakes, to find the most appropriate algorithm and derive the lake ice freeboard height. 44

Figure 3-12. Time series of PP with respect to four groups in each Lake. Group 1 (blue)

and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and

Group 3 (red) represent the altimetry over the lake ice region. 45

Figure 3-13. Time series of OCOG width with respect to four groups in each Lake.

Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2

(gray) and Group 3 (red) represent the altimetry over the lake ice region. 46

Step 5: Obtain water level from altimetry OCOG retracked height or water level gauge

In each cycle, if the number of altimetry data points over water is larger than 10, we use altimetry OCOG retracked height to get water level height. To remove the outlier, the differences between OCOG height and its median larger than three times of Median

Absolute Deviation (MAD) are filter out in our data processing (Jia et al., 2018).

If the number of altimetry points over water is less than 10, the water level gauge record replaces the altimetry derived water level. However, the datums of water level gauge are all referenced to the International Great Lakes Datum 1985 (IGLD85), altimetry coordinate system is WGS84. For data consistency, we first convert altimetry ellipsoidal height to orthometric height using Earth Gravitational Model 2008 (EGM2008) model (in

Step 2). The mean of differences between water level gauge IGLD85 and altimetry

EGM2008 height then be computed during the summer season (June, July, August,

September) from 2011 to 2018. Last, the water level gauge IGLD85 height is transferred to EGM2008 height using the derived bias (Table 3-7).

Table 3-7. The differences and its STD between IGLD85 and EGM08 height (Cryosat-2)

Differences and STD Lake between IGLD85 and EGM08 (Unit: m) Superior -0.535 ± 0.014 Michigan -0.391 ± 0.023 Huron -0.355 ± 0.010 Erie -0.317 ± 0.009 Ontario -0.277 ± 0.015

Step 6: Derive the bias between Threshold and OCOG retracker

The biases exist between different retrackers, due to various models and methods for convolution in each of the retrackers. To estimate and eliminate the biases, time series of both retrackers are compared in summer season (June, July, August, September) from

2011 to 2018. The results are shown in Table 3-8. This bias is eliminated when we compute the ice freeboard.

Table 3-8. Bias and its STD (unit: m) between Threshold and OCOG retracker

Superior Michigan Huron Erie Ontario Thre10-OCOG 0.102±0.004 0.117±0.008 0.106±0.006 0.107±0.008 0.099±0.020 Thre20-OCOG -0.028±0.004 -0.027±0.006 -0.028±0.002 -0.030±0.005 -0.036±0.017 Thre30-OCOG -0.128±0.005 -0.132±0.008 -0.127±0.009 -0.133±0.004 -0.139±0.016 Thre40-OCOG -0.220±0.007 -0.223±0.008 -0.221±0.010 -0.226±0.005 -0.234±0.017 Thre50-OCOG -0.312±0.008 -0.315±0.011 -0.313±0.009 -0.321±0.006 -0.329±0.019 Thre60-OCOG -0.415±0.007 -0.422±0.014 -0.418±0.012 -0.422±0.005 -0.439±0.021 Thre70-OCOG -0.584±0.007 -0.602±0.025 -0.609±0.015 -0.591±0.020 -0.626±0.027

Step 7: Calculate the ice freeboard and ice thickness

After getting the height of snow/ice interface and water surface, we use Eq. (3-6) and Eq.

(3-7) to calculate the ice freeboard (hfi) and ice thickness (hi). Figure 3-14 is schematic of parameters involved in equations (Ricker et al., 2014). In our study, ice and water density are constant, which are 915 and 1000 kg/m3 (Wadhams et al., 1992).

hfi= R w − R ri = H ri − H w (3-6)

hhfi w+ fs s hi = (3-7) wi−

48 where Rw and Rri (or Hw and Hri) are altimetry range measurements (or height) over water and snow/ice surface, hfs is snow depth, ρi, ρw, ρs are ice, water, snow density.

In Eq. (3-7), the snow density is calculated from SNODAS SWE and snow depth (SD) using Eq. (3-8). Because the units of SNODAS SWE and SD are all in meter, we multiply the water density by 1000 kg/m3 in Eq. (3-8).

3 s =SWE SD1000 kg / m (3-8)

After obtaining the ice thickness, three times MAD is used to remove the outliers. We also remove the ice thickness, which is larger than 15 m, since the value is not reasonable in Great Lakes.

Figure 3-14. Schematics of ice freeboard and thickness estimate methods using radar and

laser altimetry. 49

Figure 3-15. Flowchart of ICESat-2 lake ice retrieval algorithm.

3.3.2 Procedure for ICESat-2 Data Processing

Step 1: Remove altimetry points over non-ice surface using GLERL ice cover

In our experiment, we use ICESat-2 ATL13 orthometric height EGM2008 converted from ellipsoidal height WGS84. Because ICESat-2 waveform is not available, we use

GLERL ice cover record to filter out the non-ice surface type data. If the ice cover data larger than or equal to 75%, we define this point is over ice surface. After that, we remove the outliers using three times MAD.

Step 2: Derive water level height from water level gauge stations

Because the number of ICESat-2 points over water surface is low, we use water level gauge records to derive the water level height. The differences between EGM2008 and

IGLD85 are also computed in summer 2018 (Table 3-9). Since Cryosat-2 and ICESat-2 use different model to obtain the water level height, the differences are slightly distinct. 50

Table 3-9. The differences and its STD between IGLD85 and EGM08 height (ICESat-2)

Differences and STD Lake between IGLD85 and EGM08 (Unit: m) Superior -0.596 ± 0.057 Michigan -0.480 ± 0.101 Huron -0.443 ± 0.059 Erie -0.451 ± 0.063 Ontario -0.399 ± 0.048

Step 3: Calculate ice freeboard and ice thickness

Unlike Cryosat-2, ICESat-2 measures air/snow interface instead of snow/ice interface.

Although the ICESat-2 green laser (wavelength is 532 nm) might penetrate snow

(Harding et al., 2015), we assume the penetration is small and negligible. Thus, the equation of ice thickness calculation for ICESat-2 is slightly different from Eq. (3-7), since what ICESat-2 measures is total freeboard (hf) not ice freeboard (hf). The total freeboard and ice thickness can be estimated by Eq. (3-9) and Eq. (3-10), based on assumption that the floating lake ice is in hydrostatic equilibrium (Giles et al., 2007).

hf= R w − R li = H li − H w (3-9)

hhf w−− fs(  w  s ) hi = (3-10) wi− where Rw and Rli (or Hw and Hli) are altimetry range measurements (or height) over water and air/snow surface, hfs is snow depth, ρi, ρw, ρs are ice, water, snow density. Same as

Cryosat-2, snow depth and density are obtained from SNODAS and Eq. (3-8), and ice/water density are constant, 915 and 1000 kg/m3, respectively.

3.4 Results and Validations

3.4.1 Validation using In-Situ Ice Thickness Data in Lake Superior, Winter 2014

Figure 3-16 shows the comparison between our ice thickness results with Titze et al.

(2016) in-situ data. Because there are only two altimetry tracks near the mooring location (Upper figure in Figure 3-16.) during the whole winter 2014, we only have a two-day comparison. For Cryosat-2 derived ice thickness, we compute the mean of altimetry data points, which are within the 10 x 10 km2 area around the in-situ mooring.

For the in-situ ice thickness, we average the data before and after three minutes of epoch when altimetry passed the mooring, to represent the ice depth. Their differences are then computed, and the results are in Table 3-10 and Figure 3-16. The validation indicates that Threshold 40% (or 50%) and Threshold 70% are best performances in each observed day, the differences of former one even reaches to 0.2 m. However, there is only two days of data can be used to compare, and the in-situ ice thickness data, which is generated from pressure data based on some certain assumptions, contains measurement errors. As a result, the validation results are thought to be not truly reliable. Further study is needed using additional in-situ data with better temporal and spatial coverage.

Table 3-10. Differences between mean of altimetry-derived and in-situ ice thickness

2014-02-19 (unit: m) 2014-03-02 (unit: m) Threshold 10% -1.444 -2.005 Threshold 20% -1.000 -1.989 Threshold 30% -0.279 -1.955 Threshold 40% -0.199 -1.920 Threshold 50% 0.198 -1.726 Threshold 60% 0.729 -1.492 Threshold 70% 1.685 -0.732

Figure 3-16. Upper: The location of in-situ mooring and Cryosat-2 track on Feb. 19th,

2014 and Mar. 2nd, 2014. Lower: Comparison of ice thickness profile at Lake Superior on Feb. 19th, 2014 (left, Threshold 40% results) and Mar. 2nd, 2014 (right, Threshold 70%

results). 53

3.4.2 Compare Derived Ice Thickness with Ice Duration, AMIC, AFDD, and snow depth

As we know several environmental parameters have correlation with each other, thus we compare interannual variability between ice duration, AMIC, AFDD and snow depth with our ice thickness estimates to validate our experiment results. Although snow depth is one of the variables to derive the ice thickness, it can represent the severity of winter.

In this comparison, we compute and utilize the yearly average snow depth of each lake.

Table 3-11 lists the correlation coefficient between yearly average Cryosat-2 derived ice thickness with ice duration (ID), AMIC, AFDD, and snow depth. Compared with ID,

AMIC, AFDD, the correlations are all higher than 70% (gray-color-filled in Table 3-11) in Lake Superior, Erie and Ontario, the time series of altimetry derived ice thickness

(Figure 3-17 to Figure 3-21) match well with ID, AMIC, and AFDD time series.

However, the correlation coefficients of Lake Michigan and Huron all less than 70%.

Compared with snow depth, the correlation in Lake Michigan and Huron get better performance, the coefficients are all larger than 85 %. The snow depth comparison results are totally opposite with other three variables. Further research is needed to analyze this comparison. The performance for each threshold retracker setting is similar, the mean of correlation coefficient all within 72~73 %. The results prove the interannual variability signal in our derived ice thickness is correct, but cannot validate the amplitude of ice thickness. Further in-situ ice thickness data are needed to confirm our results.

Table 3-11. Correlation coefficient between altimetry-derived ice thickness and ice

duration (ID), AMIC, AFDD, and snow depth (SD*). Table that correlation larger than

70% is filled in gray color.

Pearson Correlation Coefficient (%) Lake Variables Thre10 Thre20 Thre30 Thre40 Thre50 Thre60 Thre70 ID 81 82 83 84 85 87 89 AMIC 81 82 84 85 86 88 91 Superior AFDD 74 75 76 76 77 77 78 SD 76 75 73 72 70 68 64 ID 60 58 59 60 59 61 64 AMIC 51 49 50 52 51 51 55 Michigan AFDD 54 53 53 54 54 57 61 SD 91 90 89 89 88 88 88 ID 60 60 60 60 59 59 58 AMIC 52 51 50 49 48 48 48 Huron AFDD 66 64 64 64 64 65 66 SD 94 94 95 95 95 95 95 ID 82 81 81 81 81 82 83 AMIC 84 84 84 85 86 86 87 Erie AFDD 94 94 94 94 94 94 95 SD 60 60 60 60 59 59 59 ID 84 85 85 85 85 85 84 AMIC 95 96 96 96 97 97 97 Ontario AFDD 72 73 74 73 73 73 72 SD 40 40 39 36 36 34 30 Mean 73 72 72 73 72 73 73

* Here, we use yearly average snow depth of each lake for comparison.

Figure 3-17. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Superior.

Figure 3-18. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Michigan.

Figure 3-19. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Huron.

Figure 3-20. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Erie.

Figure 3-21. Time series comparisons between ice thickness (Threshold 40%) with ID

(top-left), AMIC (top-right), AFDD (bottom-left), and snow depth (bottom-right) at Lake

Ontario.

Figure 3-22. Scatter plot of ice thickness (Threshold 40%) on X axis and AFDD (top- left), AMIC (top-right), ice duration (bottom-left), and snow depth (bottom-right) on Y

axis.

Table 3-12. The coefficients of linear regression: y = ax + b, where x is the Threshold

40% ice thickness, y is the ice duration, AMIC, AFDD, and snow depth

Ice Duration AMIC

a b R2 P-value a b R2 P-value R1: Superior 25.882 29.241 0.647 0.000 23.367 24.168 0.654 0.000 Erie, Ontario R2: 24.691 7.172 0.352 0.009 20.078 -12.537 0.239 0.040 Michigan, Huron AFDD Snow Depth

a b R2 P-value a b R2 P-value R1: Superior 13.039 66.474 0.303 0.003 0.087 -0.015 0.390 0.000 Erie, Ontario R2: 14.550 38.884 0.343 0.011 0.146 -0.393 0.790 0.000 Michigan, Huron

Based on the performance of correlation, we separate the data into two groups, one includes Lake Superior, Erie, and Ontario data (Group R1), the other one includes Lake

Michigan and Huron data (Group R2). We then use linear regression to fit Threshold

40% ice thickness results with ice duration, AMIC, AFDD, and snow depth to determine whether they have linear relationships. The results (Table 3-12 and Figure 3-22) indicate that the linear regression model fit well for ice duration and AMIC data in Group R1.

The R2 of both fitting results are all 0.65, showing the small variance of differences between the observation and predicted values. In addition, the p-value of 0.000 is less than the significant level 0.05, which means there are 95% confident that a linear relationship exists. For the AFDD linear regression result, though p-value are all less than 0.05 for both R1 and R2 group but R2 are all less than 0.4, which means the linear relationship between ice thickness and AFDD is weak. The reason may be the used air temperature data is land surface temperature not water surface temperature. Furthermore,

AFDD though is an easy-implement model, it cannot completely represent the surface 62 energy budget and weather pattern (Chang and Hong, 2012). For data in Lake Michigan and Huron (Group R2), the ice thickness values are within 2 to 4 meters no matter how ice duration, AMIC and AFDD changes. However, there is a strong linear relationship between snow data and ice thickness estimation in Lake Michigan and Huron, the R2 of both fitting results are 0.79.

3.4.3 Compare Cryosat-2 Estimated Ice Thickness with ICESat-2 results

Figure 3-23 and Figure 3-24 are time series comparisons of ice thickness between

Cryosat-2 Threshold 10% ~70% and ICESat-2 GT1L, GT2L, and GT3L at each lake in winter 2019. The figures reveal that the estimated ice thickness from Cryosat-2 are higher in whole region, compared with ICESat-2 estimations. The reason might be the signal of Cryosat-2 did not penetrate through snow and reflected in snow layer due to air bubble, causing height measurement is relatively higher than ICESat-2. The other reasons might be ICESat-2 underestimate the ice thickness due to the fact that ICESat’s green (532 nanometer) laser might penetrate snow, leading the total freeboard measurement to be lower than actual height (Figure 3-40).

Figure 3-23. Time series of Cryosat-2 and ICESat-2 ice thickness at Lake Superior and

Lake Michigan in winter 2019.

Figure 3-24. Time series of Cryosat-2 and ICESat-2 ice thickness at Lake Huron, Lake

Erie and Lake Ontario in winter 2019.

3.4.4 Compare Cryosat-2 and ICESat-2 Results with USCG 9th District Estimated Data

We also compare our ice thickness results with US Coast Guard (USCG) 9th District estimated ice thickness, which can be downloaded from USNIC

(https://www.natice.noaa.gov/products/great_lakes.html). The USCG estimates ice thickness using freezing degree days, and groups the derived ice thickness into six groups

(see legend in Figure 3-25). The format of USCG estimated data is image file, we exploit

GIS georeferenced tool to give geoinformation to image data for comparison. The comparison results are displayed in Figure 3-25 to Figure 3-27, in which the Cryosat-2 ice thickness is Threshold 40% results. Because laser altimetry is easily affected by snow depth, the HRRR snow data is applied and compared as well with SNODAS data for

ICESat-2. The figures illustrate that both Cryosat-2 and ICESat-2 estimated ice thickness are higher than USCG estimations in most of regions, especially for Cryosat-2 result.

The reason may be USCG estimated ice thickness is mostly from thermal growth and do not take account of ridging, the values could be lower than actual. For snow data comparison, there is not too much improvement between HRRR and SNODAS, and the number of data points of HRRR is reduced. The reason is that HRRR estimated snow depth is sometimes higher, causing the ice thickness values to be less than zero (snow/ice surface lower than water surface). Since it is physically not possible, those data would be removed by the filter.

Figure 3-25. Ice thickness comparison between altimetry-derived (dotted points in the lower panel of figures), and the USCG estimated ice thickness (background) on February

12th, 2019.

Figure 3-26. Ice thickness comparison between altimetry-derived (dotted points in the lower panel of figures), and the USCG estimated ice thickness (background) on February

26th, 2019.

Figure 3-27. Ice thickness comparison between altimetry-derived (dotted points in the lower panel of figures), and the USCG estimated ice thickness (background) on March

19th, 2019.

3.4.5 Validate Altimetry Derived Water Level Height Using Water Level Gauge Records

To validate the altimetry derived water level, we compare its time series with the water level gauge record. The procedure of Cryosat-2 water surface height derivation is described in Chapter 3.3.1 Step 5. In our comparison, we use Gaussian Kernel

Regression (kernel width is 10) in our last step (dash line in Figure 3-28), to filter out the outlier (Jia et al., 2018). Table 3-13 and Figure 3-28 to Figure 3-30 indicate that Cryosat-

2 derived water surface height agrees well with water level gauge record, the correlation coefficients (CC) between two data sets are all larger than 95% and RMSE are all smaller than ± 0.1 m. The positive results demonstrate that altimetry could complete and even improve current Great Lakes water level monitoring system. Though we do not use

ICESat-2 data to get water level in our data processing, we also compare ICESat-2 derived water surface height with water level gauge records. ICESat-2 shows excellent performance, the CC are all larger than 90% (Table 3-14 and Figure 3-31 to Figure 3-33).

Table 3-13. The correlation and RMSE of Cryosat-2 derived water surface height and

water level gauge records in each lake from July 2010 to April 2019

Superior Michigan Huron Erie Ontario Correlation (%) 97.08 97.64 98.50 94.91 98.32 RMSE (m) 0.065 0.091 0.071 0.092 0.056

Table 3-14. The correlation and RMSE of Cryosat-2 derived water surface height and

water level gauge records in each lake from October 2018 to September 2019

Superior Michigan Huron Erie Ontario Correlation (%) 91.39 91.57 96.78 96.74 99.46 RMSE (m) 0.057 0.102 0.06 0.063 0.049 70

(A) Lake Superior

(B) Lake Michigan

Figure 3-28. Time series comparison between Cryosat-2 derived water height (blue dots),

and in-situ water level gauge (red line) at Lake Superior (A) and Lake Michigan (B). 71

(A) Lake Huron

(B) Lake Erie

Figure 3-29. Time series comparison between Cryosat-2 derived water level height (blue

dots), and in-situ water level gauge (red line) at Lake Huron (A) and Lake Erie (B). 72

Figure 3-30. Time series comparison between Cryosat-2 derived water level height (blue

dots), and in-situ water level gauge (red line) at Lake Ontario.

Figure 3-31. Time series comparison between ICESat-2 derived water level height (blue

dots) and in-situ water level gauge (red line) at Lake Superior. 73

(A) Lake Michigan

(B) Lake Huron

Figure 3-32. Time series comparison between ICESat-2 derived water height (blue dots)

and in-situ water level gauge (red line) at Lake Michigan (A) and Lake Huron (B). 74

(A) Lake Erie

(B) Lake Ontario

Figure 3-33. Time series comparison between ICESat-2 derived water height (blue dots)

and in-situ water level gauge (red line) at Lake Erie (A) and Lake Ontario (B). 75

3.4.6 Corroborate Snow Density

In our study, we use SNODAS SWE and snow depth, to compute the snow density. To verify whether the snow density is correct, we plot the time series of snow density in winter 2014. As we know, fresh snow might have smaller density, around 100-200 kg/m3 or even less, depending on the precipitation type and temperature. Figure 3-34 and

Figure 3-35 show the snow density in all area is all less than 350 kg/m3 and gets higher through time, which is line with normal and reasonable condition.

Figure 3-34. Time series of snow density in winter 2014.

Figure 3-35. Time series of snow density at Lake Ontario in winter 2014.

3.4.7 Validate Surface Type Classification by PlanetScope Satellite Images

To verify the threshold, we compare our classification result with PlanetScope satellite images (Ortho Scene Level 3B, ground sampling is 3.7 m; Team P., 2019) on February

27th, 2008 at Lake Superior. Figure 3-36 reveals that our threshold setting can accurately identify altimetry measurement is water-reflected or ice-reflected. For ice cover between

25~75% (green dots in Figure 3-36, bottom right), those points are in new, thin or undeformed ice region, thus the classified algorithms define those observations are over water.

The altimetry waveforms along Cryosat-2 track are shown in Figure 3-37 and Figure 3-

38. They reveal that the waveforms over ice is specular waveform, and become ocean waveform when data points are over water. The waveforms [Figure 3-37 (C) ~ (F)] of green dots in Figure 3-36 clearly show that the measurements are captured partially over water and partially over ice. 77

Figure 3-36. Comparison between classification results with PlanetScope image. Top:

The location of comparison area, the waveforms of points with respect to the numbers in the right panel shown in Figure 3-37. Bottom: The classifying results using PP threshold

(right), and OCOG width (center). The bottom right figure is the GLERL ice cover data. 78

Figure 3-37. The altimetry waveforms over ice (A and B), and ice with partial water (C to

F). The locations of each waveform are show in Figure 3-36. 79

Figure 3-38. The altimetry waveforms over water (A), ice (B), and shoreline (C). The

locations of each waveform are show in Figure 3-36.

3.5 Error Sources of Ice Thickness Estimation

Because the ice condition or location of each lake varies a lot in the Great Lakes region, due to the differences of wind, wave, and temperature. Therefore, there are some error and uncertainty in our process, including:

1. Whether the lake ice of entire Great Lakes fulfills the hydrostatic equilibrium

assumption? The used ice thickness equations [Eq. (3-7) and Eq. (3-10)] are based on

hydrostatic equilibrium assumption, which means that lake ice is in floating

condition. However, sometimes wind and wave push ice to shore and cause the ice

shove along lake shore, or the ice touch the lake bottom in shallow region. These

situations do not fulfill the hydrostatic equilibrium assumption, leading the wrong ice

thickness estimation.

2. Uncertainty of snow depth, snow density and ice density. Because lack of snow and

ice data over lake surface, we use SNODAS model output as our data source and set

ice density as constant (915 kg/m3). In addition, the SNODAS snow data over lake

surface is interpolated by data over land, the interpolation error is unknown and

should be noted in future work. To see how snow and ice data affect ice thickness

estimation, we change snow depth, snow density and ice density respectively in

Figure 3-39 and fix the remaining variables. For snow depth, 10 cm snow depth error

may cause 0.25 m ice thickness error, based on the assumptions of other variables.

For snow density, 30 kg/m3 snow density error may cause 0.07 m ice thickness error.

For ice density, 30 kg/m3 snow density error may cause 0.55 m ice thickness error

when the ice density is between 890 ~ 930 kg/m3, which is the largest error factor

among three variables. In ice thickness equation, the ice density is denominator, thus

the influence is much larger than snow depth and snow density. More detail and

accurate ice density data is needed in future research.

3. Error of ice freeboard measurement and penetration in snow layer. We assume

Cryosat-2 can penetrate snow and measure the ice freeboard. But air bubble might

cause the radar pulse scatters in snow layer (Beckers et al., 2017), causing the ice

freeboard measurement is higher than actual. The opposite situation occurs to

ICESat-2 that the laser pulse might penetrate to snow, leading the estimated total

freeboard lower than actual (see Figure 3-40). In addition, the speed of light in snow

layer is slightly different from in air, the discrepancy is not considered in our Cryosat-

2 process. Figure 3-41 displays how ice freeboard measurements influence ice

thickness. The ice freeboard error of 10 cm may cause 1.1 m ice thickness error.

This result indicates that how important of accuracy of ice freeboard (or total

freeboard) observation for ice thickness estimation, and proves that the problem of

penetration in snow layer must be solved in future study.

4. Uncertainty of ICESat-2 ATL13 product. In our process, we utilize ICESat-2 ATL13

product, which is the inland water surface product, because there is no ice freeboard

product over Great Lakes. We assume the ATL13 provided height is air/snow

interface height, but this assumption might be wrong and need to be confirmed in

future work.

Figure 3-39. The ice thickness variation due to various snow depth (top-left), snow density (top-right), ice density (bottom-left; between 750 ~ 950 kg/m3), and ice density

(bottom-right; between 890 ~ 930 kg/m3). The function in each figure shows the linear

relationship between ice thickness and related variable. The fixed variables are also

shown in each figure.

Figure 3-40. The schematic of theoretic and actual range measurement of ICESat-2

(laser) and Cryosat-2 (radar).

Figure 3-41. The ice thickness variation due to changes of ice freeboard. The function in

figure shows the linear relationship between ice thickness and ice freeboard. The fixed

variables are also shown in figure. 84

3.6 Conclusion

In our study, we explore the possibility and capability of using satellite radar/laser altimetry, Cryosat-2 and ICESat-2, to measure ice thickness using ice freeboard method.

The results show Cryosat-2 Threshold 40% (or 50%) and Threshold 70% are best performances in each observed day, the differences of former one reaches to 0.2 m.

Through the comparison with ice cover and air temperature, the correlation coefficient between our Cryosat-2 results and these two parameters are all larger than 70%, proving the interannual variability of our estimated ice thickness is correct. Furthermore, we use linear regression to fit the Cryosat-2 Threshold 40% ice thickness results with ice duration, AMIC, AFDD, and snow depth, to determine whether they have linear relationships. The results indicate that the linear regression model fit well for ice duration and AMIC data in Lake Superior, Erie, and Ontario. The R2 of both fitting results are all 0.65, and the p-value of 0.000 is less than the significant level 0.05 (95% confident). This discovery shows the ice thickness has strong linear relationship with ice cover data, and prove the possibility that using ice cover data to predict ice thickness.

The one-year long ICESat-2 dataset is used to obtain ice depth in Great Lakes for validating Cryosat-2 results. The comparison reveals that the Cryosat-2 derived ice thickness is higher than ICESat-2. The reason may be the signal of Cryosat-2 is reflected in snow layer causing ice freeboard measurements are higher than actual, or ICESat-2 total freeboard measurements are lower than actual due to laser pulse penetrate snow (see

Figure 3-40). To prove which mission is correct, we compare Cryosat-2 and ICESat-2 estimated results with USCG estimated ice thickness, but the altimetry derived ice

85 thickness values are all higher than USCG estimations. The reason is USCG estimated ice thickness is mostly from thermal growth and do not take account of ridging, the values could be lower than actual. In general, it is difficult to conclude which sensor

(Cryosat-2 or ICESat-2) is correct or whether altimetry can derive the correct ice thickness in Great Lakes, since we only have one winter in-situ data and the ice condition in Great Lakes region has large variation. More in-situ data are needed to continue this study in the future.

Chapter 4: Land Subsidence Monitoring in San Joaquin Valley

4.1 Introduction

From 2012 to 2017, California experienced one of the worst persistent droughts in history. It resulted in increased anthropogenic withdrawal and depletion of groundwater in the aquifers, causing severe land subsidence in the San Joaquin Valley (Konikow,

2013). The severe land subsidence might lead to increased flood risks in low-lying region and/or infrastructure damage, thus the mapping of spatial and temporal change of land subsidence is imperative. GPS (Hammond et al., 2016), InSAR (Sneed and Brandt,

2015) and leveling survey (Poland et al., 1975) have been well developed and widely applied to monitor topography changes, however, each of these techniques has pros and cons (e.g. sparse spatial or temporal resolution, or easily influenced by ground cover changes). An additional or innovative technique of land vertical motion monitoring system, first proposed by Lee et al. (2008a, 2008b), and then by Kuo et al. (2015), and

Hwang et al. (2016). They developed altimeter waveform retracking algorithms and sophisticated data analysis techniques using satellite radar altimetry, to detect land vertical motion over flat and vegetated land regions. Their results demonstrated the feasibility of this novel method in obtaining reliable land deformation time series, corresponding to the glacial isostatic adjustment geophysical process in the Hudson Bay land region (Lee et al., 2008a, 2008b), and land subsidence due to human excessively 87 extracting groundwater for agricultural irrigations (Kuo et al., 2015; Hwang et al., 2016).

In particular, Hwang et al. (2016) combined multiple altimetry missions (Envisat, TP,

Jason-1, and Jason-2) to detect land subsidence in San Joaquin Valley, Taiwan and North

China Plain using Sub-waveform retracker (Yang et al., 2012) and the least-squares fitting method. However, their results did not produce two-dimensional (2D) land deformation with adequate spatial resolution, to allow interpretations of land subsidence spatial patterns as interferometric synthetic aperture radar (InSAR) data could measure.

This is primarily due to the fact that radar altimetry data are repeated measurements over designed ground tracks at a nominal temporal sampling of 10-days to 35-days, using the so-called repeat orbits (Table 2-2).

In this study, we propose to use Cryosat-2 mission, which was designed to provide very dense ground track (369-day repeat orbit with a sub-cycle of 30 days), with spatial interpolation methods to produce 2D land subsidence patterns and rates in the San

Joaquin Valley (Figure 4-1 and Figure 4-2). The plausible advantage of the satellite radar altimetry constellation data is that, unlike InSAR, altimeter time series can sense seasonal or shorter changes of the vertical land motion (Jason-2, Jason-3 and Envisat), and the 2D land deformation patterns (CryoSat-2) with a spatial (cross-track) resolution of ~4 km, which is much better as compared to GPS.

Our scientific objective is generating 2D land subsidence rate using Cryosat-2 mission

Low Resolution Mode (LRM) data. The estimated land deformation results can complement InSAR and GPS monitoring results, and potentially support agricultural, infrastructure, and disaster mitigation planning and response. The state-of-the-art method

(Kuo et al., 2015) is implemented for processing conventional altimetry missions

(Envisat, Jason-2 and Jason-3), and compare with Cryosat-2 results. GPS and InSAR velocity solutions are then used to evaluate the performance of our radar altimeter deformation results.

Figure 4-1. Study region. The backgrounds are the USGS 3DEP Bare Earth DEM

(Arundel et al., 2015), and Blue Marble satellite image. Blue lines are Envisat ground track, brown line is Jason-2 and Jason-3 track. The number on each track is pass number.

Red triangles are GPS stations. 89

Figure 4-2. Study region. The backgrounds are Global Land Cover – Share (GLC-

SHARE) crop coverage and Blue Marble satellite image. Brown line is California High-

Speed Rail (CHSR), and blue lines are national or state freeways.

Hwang et al. (2016) concluded that the accurate heights over land can be derived if the research region is a flat terrain and covered with short vegetation (e.g. crops). Thus, we use the criteria of low gradient as measured by the USGS 3DEP Bare Earth DEM (Figure

4-1), and use the GLC-Share (Latham et al., 2014) crop coverage larger than 50% to select our research regions (Figure 4-2). 90

4.2 Data

4.2.1 Satellite Radar Altimetry - Envisat, Jason-2, Jason-3 and Cryosat-2 LRM data

For Envisat (May 2002 ~ June 2010; Cycle number: 6 ~ 90), the Ku band Level-2 Sensor

Geophysical Data Record (SGDR) data are downloaded from ESA’s FTP data archive

(ftp://ra2_data:[email protected]). Its footprint size is 2~5 km (based on reflected surface), and the orbital cycle is repeated every 35 days. The ground track of

Envisat is displayed in Figure 4-1.

For Jason-2 (August 2008 to August 2016; Cycle number: 4 ~ 300), and Jason-3 (March

2016 to October 2019; Cycle number: 5 ~135), the Ku band Level-2 SGDR data is downloaded from NOAA NCEI archive

(https://www.nodc.noaa.gov/SatelliteData/jason/). Its footprint size is 2~5 km as well, and the orbit is repeated every 10 days. Compare with Envisat, Jason mission has higher observed frequency, but with ~3 times coarser spatial resolution (Figure 4-1). Frappart et al. (2006) revealed that Jason-1 has proved poor accuracy over land region due to instrument problem, we do not use Jason-1 mission data in our study.

For Cryosat-2 (October 2010 to November 2015), the Ku band LRM (Low Resolution

Mode) Level-2I and -1B data is obtained from ESA (http://science-pds.cryosat.esa.int/).

Although the Cryosat-2 is still in mission now, ESA change the observed mode from

LRM to SARIn mode after December 2015 and change to SAR mode in December 2019

(https://earth.esa.int/web/guest/-/geographical-mode-mask-7107). LRM data are essentially the same as the conventional pulse-limited altimeter data (as Envisat, Jason-2

91 and Jason-3 altimeter data). In our study, we focus on the LRM data, so only data before

December 2015 are used.

All missions’ range measurements are modified using instrument, media (ionospheric, dry and wet tropospheric), and geophysical (solid earth tide and pole tide) corrections provided in the respective altimeter SGDRs (Geophysical Data Records). Here we use the Threshold 10% and the Modified Threshold 10% radar altimeter waveform retracking corrections, to derive the evolution of surface height over land.

4.2.2 USGS 3DEP DEM

Although the designs of the repeat orbit ground track drift for the altimeter missions usually have the criteria to “exactly” repeat within ±1 km at the equator, the ground track shifts by ±1~3 km off the nominal ground tracks in across-track or along-track direction, respectively (Kuo et al., 2015). To adjust the actual track to the nominal track (defined as computed theoretical ground), we use the USGS 3DEP Bare Earth DEM (Arundel et al.,

2015) to correct the terrain gradients of observed radar altimeter land surface ellipsoidal heights. The 1/3 arc-second (approximately 10 m ground spatial sampling) DEM is download from USGS National Map (https://viewer.nationalmap.gov/basic/). The datum of 3DEP is North American Datum of 1983 (NAD83) in horizontal, and North American

Vertical Datum of 1988 (NAVD88) in vertical. To be consistent with satellite altimetry’s datum (WGS84 reference ellipsoid), we convert the DEM datum using NOAA VDatum tool (Hess, 2012).

4.2.3 CORS and Nevada Geodetic Lab GPS

The daily GPS velocity data are used as the validation data in our final process. The

Continuously Operating Reference Station (CORS) time series are downloaded from

NASA Jet Propulsion Laboratory (JPL) and Nevada Geodetic Laboratory (Blewitt et al.,

2018). The locations of the GPS stations are displayed in Figure 4-1, and datum of GPS is

International GNSS Service 14 (IGS14) with ITRF2014 reference frame. Although the reference frame of Envisat, Jason-2 (version D), Jason-3 (data before September 2018), and Cryosat-2 (Version C) are all ITRF2008, the differences between ITRF2008 and

ITRF2014 are minor and may be negligible (Figurski and Nykiel, 2017). In our study, we do not take into account of reference frame differences as they are negligible.

Table 4-1. The list of GPS stations in the study region

Name Lat (°) Long (°) Time Span Source P300 36.304 -120.277 2005 - 2020 P303 37.054 -120.705 2005 - 2020 P304 36.739 -120.357 2004 - 2020 NASA JPL: P307 36.947 -120.058 2005 - 2020 https://sideshow.jpl.nasa.gov/post/series.html P544 35.731 -119.738 2006 - 2020 P565 35.744 -119.237 2005 - 2020 P566 36.324 -119.229 2005 - 2020

CRCN 36.114 -119.568 Nevada Geodetic Lab: 2010 - 2020 LEMA 36.292 -119.782 http://geodesy.unr.edu/index.php

4.2.4 NASA JPL InSAR Measured Subsidence Rate

In a collaboration between NASA’s Jet Propulsion Laboratory (JPL), California Institute of Technology, and the California Department of Water Resources, they generated the interferometric synthetic aperture radar (InSAR) derived vertical surface displacement in

Bulletin 118 groundwater basin (see Figure 4-13.) from Spring 2015 to Summer 2017.

The Geotiff image files of annual land subsidence rate is provided by the California

Natural Resources Agency (https://data.cnra.ca.gov/dataset/nasa-jpl-insar-subsidence).

The image resolution is 0.0008333 degrees (about 92 m in north-south direction and

70~77 m in east-west direction), and the vertical motion is collected by ESA Sentinel-1A satellite InSAR data.

Figure 4-3. The flowchart of multi-mission radar altimetry, Envisat, Jason-2 and Jason-3

(left panel), and Cryosat-2 (right panel) derived evolution of land surface rate estimates. 94

4.3 Methodology

4.3.1 Data processing procedure for Envisat, Jason-2 and Jason-3

Step 1: Filter out bad quality data using PP and MaxP

We use two waveform parameters to remove the outliers in altimetry data:

1. Pulse peakiness [PP; Eq. (4-1)] > 1.8: Because the shape of waveform over land

should be specular waveforms (Figure 2-5, right), which usually have small values of

PP. Here we apply Laxon’s (1994) equation to derive PP, which is different with the

PP used in Chapter 3. [Eq. (3-2)].

2. Bin of maximum power of waveform (MaxP) is not within 10 to NWF-10 bin, where

NWF is number of waveform gates (Envisat is 128, Jason-2 and Jason-3 are 104).

NWF max(WF ) PP = 31.5 (4-1) i=1 WF

Step 2: Waveform retracking

The state-of-the-art Threshold 10% and Modified Threshold 10% retrackers are used in our altimeter waveform processing, the threshold level of 10% is adopted according to

Kuo et al. (2015) recommendation. Though the Sub-waveform retracker is demonstrated or preferred in Hwang et al. (2016) study, we find that the retrieved heights using this retracker have large variance in the height profile (see an example height profile, magenta solid line, in Figure 4-4). Furthermore, Kuo et al. (2015) indicated that the Modified

Threshold and the Sub-waveform perform equally well in Southwestern Taiwan.

Therefore, we do not to apply the Sub-waveform retracker in this study.

Figure 4-4. Example of Envisat height profile of Sub-waveform retracker (magenta solid

line).

Step 3: Terrain gradient corrections

Because altimetry ground track shifts 1 to 3 km cross-track during every repeat cycle, the observations cannot measure the same points during the revisits. Therefore, the terrain gradient corrections are needed to improve the accuracy of the radar altimeter time series.

To derive the long-term measurements, we adjust or correct the height measurements to the nominal point using the USGS 3DEP DEM.

First, we need to generate the nominal track. Here, we utilize the French AVISO altimetry data center provided nominal ground tracks

(https://www.aviso.altimetry.fr/en/data/tools/pass-locator.html) and conduct linear interpolation. The interpolation intervals are 0.0033° and 0.0025° for Envisat and Jason mission data, respectively, based on the actual 18 ~ 20 Hz (~375 m along the altimeter

96 measurement profiles) spatial resolutions. The interpolated result is displayed in Figure

4-5.

Afterwards, 3DEP DEM is used to correct the terrain gradients using linear interpolation method (Kuo et al., 2015), the equation is shown in Eq. (4-2).

SHnom= SH cyc +( DEM nom − DEM cyc ) (4-2) where SHnom/SHcyc is the surface height after/before terrain correction, DEMnom/DEMcyc is the DEM with respect to SHnom/SHcyc measured points.

Figure 4-5. The nominal track of Jason Track 43 interpolation result.

Step 4: Spatial and temporal smoothing

To reduce the noise, Kuo et al. (2015) recommended smoothing the data in both spatial and temporal domain after removing outlier. The outlier in each bin is identified using three times Median Absolute Deviation (MAD). For spatial smoothing, we choose to average surface height within bins that spaced about 3 km (for Jason-2 and Jason-3), and

4 km (for Envisat) in along-track direction. For the temporal smoothing, we utilize moving averages over each window, the window length is about 100 days for both the

Envisat (3 cycles) and the Jason (10 cycles) altimeter data.

4.3.2 Data processing procedure for Cryosat-2

Step 1: Waveform retracking

We apply the Threshold 10% and the Modified Threshold 10% algorithms for altimeter waveform retracking. For used variables in algorithm, the number of Cryosat-2 LRM waveform gate is 128, the nominal tracking gate is 65, and the pulse duration is 3.125 ns.

Step 2: Filter out outliers using 3DEP DEM and GKR

We use two criteria to remove the outlier, the example of before and after filtering is demonstrated in Figure 4-6.

1. The differences between retracked height and DEM is larger (or less) than 10 km.

2. The differences between retracked height and Gaussian Kernel Regression (GKR)

larger (or less) than three times STD.

Figure 4-6. The example of before (gray line) and after (black line) filtering using 3DEP

DEM (red line) and GKR (green line) on April 3rd, 2014.

Step 3: Spatial interpolation

We fit a surface using every five months retracked heights, e.g., the interpolated surface of March 2014 is derived from data during January 2014 to May 2014 (Figure 4-7). The interpolated method is the Triangulation-based cubic interpolation, and the spatial resolution is 0.3 degree. The example of interpolated results and used altimetry data is shown in Figure 4-8.

Figure 4-7. The schematic of Cryosat-2 surface interpolation.

Figure 4-8. The Cryosat-2 interpolated height (background) and used altimetry data (dot).

4.4 Results and Validations

4.4.1 Performance of Cryosat-2: validated by GPS, JPL InSAR, and Jason-2 data

Figure 4-9 and Figure 4-10 show that the Cryosat-2 Threshold 10% and Modified

Threshold 10% retracker derived land subsidence rate during December 2010 to

September 2015, Figure 4-11 show the NASA JPL InSAR estimated subsidence rate during March 2015 to May 2017. Figure 4-9 and Figure 4-10 reveal that our Cryosat-2 results agree well with GPS data and Jason-2 altimeter data derived trends, which prove the capability and possibility of getting 2D land subsidence rate using CryoSat-2 altimetry data. In addition, the largest subsidence bowl is identified near the city of

Corcoran from the Cryosat-2 results, excellent agrees with the JPL InSAR derived 100 subsidence. To compare the deformation rate in this area, we interpolate Cryosat-2 and

JPL InSAR subsidence rate using Jason-2 and Jason-3 ground track and plot the profile along latitude in Figure 4-12. The comparison shows good agreement among Cryosat-2,

JPL InSAR and Jason-2, all have the largest rates, -30 ~ 35 cm/yr, around latitude 36.2°.

The sinking in this region is mainly due to excessive groundwater pumping, the maximum groundwater level drops (> 30m) were observed in Westside, Kings, Tulare

Lake, Kaweah, and Tule (Figure 4-13) sub-basins.

It should be noted that Cryosat-2 altimeter data did not detect the second large subsidence bowl at the southeast of El Nido, where both the USGS (period 2008 to 2010; Sneed and

Brandt, 2015) and the NASA JPL (period 2015 to 2017) studies identified the subsidence from InSAR images. The reason for Cryosat-2 altimeter data missed this detection may be due to the area and magnitude of deformation is too small to be detectable.

Furthermore, we use cubic spatial interpolation, which might smooth the subsidence signal around El Nido region.

Time series comparison between Cryosat-2 and Jason-2 height anomalies is displayed in

Figure 4-14. Figure 4-14 shows the large variance in Cryosat-2 time series, due to uncertainty of surface interpolation method. We also compare subsidence rate between

GPS, Crsyoat-2, and JPL InSAR estimates at GPS sites location. The RMSE between

GPS and Cryosat-2 is ± 12.3 cm/yr, which is relatively higher than RMSE between GPS and InSAR, ± 3.6 cm/yr. Though we used five months altimetry data to fit the surface, there is still a large spatial gap exists (see Figure 4-8), which may cause errors in the interpolation process. Further studies are including more CryoSat-2 data to diminish the

101 spatial data gaps or using more robust spatial interpolation method (e.g. Kriging), for improving CryoSat-2 2D land subsidence estimates. For retracker comparison, the performance of Threshold (Figure 4-9) and Modified Threshold (Figure 4-10) is similar.

Figure 4-9. Comparison among Cryosat-2 (grid), Jason-2 (circles), and GPS (Triangles).

Cryosat-2 and Jason-2 all used the Threshold 10% retracker to process altimetry data, and

the subsidence rate is computed using data from 2010 to 2015. 102

Figure 4-10. Comparison among Cryosat-2 (grid), Jason-2 (circles), and GPS (Triangles).

Cryosat-2 and Jason-2 all used the Modified Threshold 10% retracker to process

altimetry data, and the subsidence rate is computed using data from 2010 to 2015.

103

Figure 4-11. Comparison among JPL InSAR (background image), Jason-2 (circles), and

GPS (Triangles). In figure, we use Jason-2 and Jason-3 Modified Threshold 10% results.

The subsidence rate of GPS and altimetry is derived in period from March 2015 to May

2017.

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Figure 4-12. The subsidence rate along latitude. JPL InSAR (black line) and Cryosat-2

Modified Threshold (red line) results are interpolated using Jason-2 and Jason-3 ground

tracks. For Jason mission, we compute subsidence rate in the period of 2015 to 2017

(green line) and period of 2010-2015 (blue line), to compare with InSAR and Cryosat-2

rates.

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Figure 4-13. (A) The cumulative groundwater level drop during October 2011 to October

2015 (Credit: Ojha et al., 2019), (B) The Cryosat-2 Modified Threshold 10% derived

subsidence rate during December 2010 to September 2015. The black polygons are

California Bulletin 118 Groundwater Basins. 106

Figure 4-14. Time series comparison between Cryosat-2 (gray) and Jason-2 (blue).

Table 4-2. The subsidence rate comparison between GPS, Crsyoat-2 (left), and JPL

InSAR (right) estimates at GPS sites locations.

Subsidence Rate (cm/yr) Subsidence Rate (cm/yr) December 2010 – September 2015 April 2015 – April 2017 GPS GPS GPS Cryosat-2 Diff. GPS InSAR Diff. Station Station P544 -0.305 NA NA P544 -0.675 -4.064 -3.388 P303 -3.413 -3.718 -0.305 P303 -3.511 -4.070 -0.559 P304 -2.607 -12.363 -9.756 P304 -3.637 -2.388 1.249 P300 0.125 NA NA P300 -0.336 -5.385 -5.049 CRCN -15.333 -27.728 -12.395 CRCN -21.752 -29.428 -7.676 LEMA -9.785 -12.109 -2.324 LEMA -16.408 -23.500 -7.091 P565 -4.626 NA NA P565 -4.510 -4.506 0.004 P566 -1.019 -1.080 -0.061 P566 -1.906 -4.171 -2.264 P307 -3.072 19.407 22.479 P307 -4.655 -2.473 2.182 Mean of Differences -0.394 Mean of Differences -2.510 RMSE 12.318 RMSE 3.557 107

4.4.2 Performance of Envisat, Jason-2, and Jason-3: validated by GPS observed trends

The profiles of land subsidence rate derived from Envisat (2002 ~ 2010), Jason-2 and

Jason-3 (2008 ~ 2019) along latitude are compared with trends observed by GPS data in

Figure 4-15 ~ Figure 4-17. The corresponding vertical deformation rate are listed in

Table 4-3. The figures reveal that vertical deformation rates obtained from altimetry data agree well with GPS trends. The major subsiding bowl is identified in Envisat Track 684

(Figure 4-16) and Jason Track 43 (Figure 4-17), the largest altimetry-derived subsidence rate near city of Corcoran (latitude is around 36.2°) is about -22 cm/yr.

The time series of the two closest GPS stations near Corcoran, CRCN and LEMA, are compared with nearest altimetry points, the results are shown in Figure 4-18 and Figure

4-19. The RMSE between GPS and altimetry-derived time series are ± 0.176 at CRCN and ± 0.431 m at LEMA, and correlation coefficient are all higher than 90%. The surface subsidence rate at the CRCN GPS site is -14.7 cm/yr, where our altimetry-derived trend is -16 cm/yr, indicating good agreement. However, the land subsidence rate at the GPS

LEMA is -10.4 cm/yr, where our altimetry-derived is -22 cm/yr. The discrepancy may be due to the distance between LEMA and nearest altimetry point is 16.5 km, and the rate around this region vary greatly (see Figure 4-13) due to Corcoran has severe land subsidence during the persistent drought in California from 2012 to 2017. The other reason may be that altimetry measurements still have unaccounted error sources as well as data noise, including radar signal scatters by vegetation and rough terrains. Figure 4-

18 and Figure 4-19 also show that the land surface height significantly decreased about 1

108 m between year 2012 and 2017, and noticeably uplifted if the total precipitation is larger than 50 mm (gray lines in figures).

Figure 4-20 clearly shows that Jason-2 and Jason-3 derived land surface time series can observe seasonal signals, which are highly correlated with heavy precipitations during the rainy seasons, October (solid line in Figure 4-20) through April (dashed line in Figure 4-

20), when aquifer recharges and uplift of the land surfaces. During the first quarter of

2017, parts of California were hit by a series of floods, and the flood signal is also sensed by Jason-2 and Jason-3 altimeter land deformation time series (blue rectangle in Figure 4-

20). The altimeter-derived deformation time series clearly illustrated the evolution of the flood in the 2017 California winter flood from its genesis to its retreat. This result illustrates the potential applications of the altimeter time series to measure the deformation of the land, which is caused by rapid recharging and run-off of flood water, for disaster response and management in California. Same flood and seasonal signals can be found in GPS detrended time series (green line in Figure 4-20). However, the amplitude of GPS seasonal signal is much smaller than altimetry derived. The reason may be GPS and altimetry measure the different signals. It needs to analyze the monument and location of GPS site, and also the porous response of soil. Further research can be conducted for this problem.

In Table 4-3, the performance of two retrackers, the Threshold 10% and the Modified

Threshold 10% retracker, is similar. The RMSE between altimetry and GPS derived subsidence rate is about ± 5 cm/yr, which is close to InSAR RMSE results (± 3.5 cm/yr).

It is interesting to note that sometime unretracked results even have better performance.

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The altimetry-derived time series of surface height in Figure 4-18 rise 0.3 m around year

2014 with an unknown reason. Similar situation was found in Lee et al. (2008a, 2008b), that retracking and surface gradient correction may increase noise in the raw altimeter data. In addition, big variances are found in subsidence rate profile at south part of the altimeter Track 153, 226, and 611, due to surface gradient dramatically changes degrading the accuracy of altimetry derived heights.

Table 4-3. Land subsidence rate comparison between GPS and the closest altimetry

points (within 25 km). Thre10/ModThre10/Unret represent Threshold 10%/Modified

Threshold 10%/ unretracked results. Gray filled table is the most accurate method

compared with GPS.

Land Subsidence Rate (cm/yr) Time Span 2002 - 2010 2010-2019 P300 P304 P307 P544 P565 P566 CRCN LEMA GPS Station 0.108 -1.106 -1.817 -0.563 -1.336 -1.136 -14.719 -10.376 Envisat Thre10 -5.203 -5.104 2.278 Track ModThre10 2.449 -7.013 3.267 N/A 153 Unret -25.065 -3.791 5.116 Envisat Thre10 0.197 -1.458 -4.048 Track ModThre10 1.671 -4.731 -3.870 N/A 226 Unret -10.989 6.607 1.004 Envisat Thre10 -10.581 -3.238 Track ModThre10 N/A 9.876 -3.451 N/A 611 Unret 7.845 4.541 Envisat Thre10 -5.828 Track ModThre10 N/A -3.905 N/A 684 Unret -1.327 Jason Thre10 -16.504 -22.776 Track ModThre10 N/A -16.397 -21.091 043 Unret -16.913 -24.107

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Figure 4-15. The profile of land subsidence rate along latitude. Blue/red/black line is

Envisat Track 153 (top) and 226 (bottom) Threshold 10% / Modified Threshold 10% /

Unretracked results, gray dots are GPS subsidence rate.

111

Figure 4-16. The profile of land subsidence rate along latitude. Blue/red/black line is

Envisat Track 611 (top) and 684 (bottom) Threshold 10% / Modified Threshold 10% /

Unretracked results, gray dots are GPS subsidence rate.

112

Figure 4-17. The profile of land subsidence rate along latitude. Blue/red/black line is

Jason-2 and Jason-3 Track 43 Threshold 10% / Modified Threshold 10% / Unretracked

results, gray dots are GPS subsidence rate

Figure 4-18. Time series comparison of surface height anomaly between the CRCN GPS

station (green line), and the closest altimetry (Jason-2 and Jason-3) point (blue and red

lines). Gray line is the total monthly precipitation larger than 50 mm, from the Global

Summary of the Month (GSOM) data. 113

Figure 4-19. Time series comparison of surface height anomaly between LEMA GPS

station (green line), and the closest altimetry (Jason-2 and Jason-3) point (blue and red

lines). Gray line is the total monthly precipitation larger than 50 mm, from the Global

Summary of the Month (GSOM) data.

Figure 4-20. The detrended time series of Jason-2, Jason-3 (blue line), and CRCN GPS site (green line). The solid black line is the start of rainy season (Oct.), and dashed line is

the end of rainy season (Apr.). Blue rectangle is the period of 2017 California flood.

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4.4.3 Combination of Envisat, Jason-2, and Jason-3 (May 2002 ~ Oct 2019)

We combine the Envisat, Jason-2, and Jason-3 results at crossover point (CP in Figure 4-

1), to derive long-term deformation time series (Figure 4-21). The systematic bias between each altimetry mission is computed by mean of differences during overlapped period. The bias then be added to the time series using Envisat altimeter height as a reference. The derived time series is compared with Sub-waveform retracker results from Hwang et al. (2016) and the closest GPS station, CRCN. For all of the time series, they show good agreement for land subsidence rate, -20 ~ -25 cm/yr, during the

California drought in 2012 to 2017. Although the retracking results do not improve pretty much when compared with GPS, the Enivsat unretracked height contain large error in year 2010, and can be corrected using retrackers. It is noted that the Jason-2 time series of Hwang’s results contain large variance, the reason may be that temporal smoothing was not applied or the poor performance of the terrain gradient correction.

Hwang et al. (2016) utilized least-squares 2nd order surface fitting (or called collinear method in Su et al, 2015) to correct the terrain gradient. In this study, we apply accurate and high ground sampling USGS 3D Elevation Program (3DEP) DEM, which can minimize the error of terrain gradient corrections.

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Figure 4-21. The time series of surface height obtained from (A) Sub-waveform retracker

(Hwang et al., 2016), (B) Threshold 10%, (C) Modified Threshold 10%, (D) unretracked

results, and (E) GPS. Red rectangles are drought period in California. In (A) ~ (D),

black line is Envisat, red line is Jason-2, and blue line is Jason-3 results. 116

4.5 Error Sources of Land Subsidence Rate Derivation

Although our results have good agreements compared with GPS, InSAR and groundwater well data, there are some error sources needs to be noted in our study.

1. Spatial interpolation error for Crsyoat-2 data. In our process, we use Triangulation-

based cubic interpolation method, which can reduce the interpolation artifacts but

smooth the subsidence signal. In addition, although we utilize five months altimetry

data to construct the DEM, there is still a data gap exist that leads the interpolation

error.

2. Terrain gradient error for Envisat, Jason-2 and Jason-3 data. In this study, we apply

USGS 3DEP DEM and linear equation [Eq. (4-2)], to do the terrain gradient

correction. The vertical accuracy of 3DEP DEM is 3.04 m (95 % confidence level;

Gesch et al., 2014), and the uncertainty of datum transformation (from NAVD88 to

WGS84) is about 8 cm (USDC, NOAA, and NOS, 2019).

3. Retracking error for all satellite altimetry missions. As previous results and study

show, the retracking algorithm might cause the noise in raw data (Lee et al., 2008).

Filtering criteria is needed to be developed for removing the bad quality data after

retracking process.

4. Finally, the uncertainties of the estimated subsidence trend depend on the geology,

weather, terrain gradient, vegetation or land cover types, and more importantly, the

data span of the vertical land motion.

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4.6 Conclusion

In this study, we map land subsidence rate in San Joaquin Valley using Cryosat-2 mission during period December 2010 to September 2015. This is the first-time using altimetry data to generate 2D land subsidence map. The results show altimetry derived 2D deformation map agrees well with GPS, Jason-2, and NASA JPL InSAR. The largest subsidence bowl is identified near city of Corcoran (California, US) in Cryosat-2 results, same evidence was discovered in JPL InSAR data. The excessive groundwater pumping during drought period causes subsidence rate reaches to -30 ~ -35 cm/yr in this severely sinking region. It should be noted that Cryosat-2 data did not detect the second large subsidence bowl at the southeast of El Nido, and the time series of Cryosat-2 has large variance. The main reason may be the uncertainty of surface interpolation method, future studies and more CrySat-2 data are needed to improve the accuracy of CrySat-2 deformation time series.

The conventional altimetry missions, Envisat, Jason-2 and Jason-3, are processed using methods similar to prior studies (Kuo et al., 2015), with the exception of our choice of slightly different retrackers, gradient correction methods, and data editing techniques.

The RMSE between GPS and altimetry-derived time series are ± 0.176 m at the CRCN

GPS station, and ± 0.431 m at LEMA GPS station, with the correlation coefficients all higher than 90%. In addition, the Jason-2 and Jason-3 derived time series can detect the seasonal signal during rainy season (October through April) and 2017 California flood signal. It proves the potential applications of the altimeter time series for disaster response and management in California. The performance of Threshold and Modified

118

Threshold is similar for all satellite missions, sometimes retracking and surface gradient correction may even increase noise in the raw data. Moreover, we find that the short- scale change of the surface gradient dramatically decreases the accuracy of the altimetry retrieved land deformation time series.

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Chapter 5: Conclusions and Future Work

Satellite altimetry, a sensor capable of measuring global geocentric surface height and its changes, was initially designed for observing global ocean surface topography since the launch of the most accurate satellite radar altimeter mission, TOPEX/POSEIDON, in

1992. Since then, numerous innovative methodologies have been developed to enable interdisciplinary scientific applications over non-ocean surface, including coastal oceans, hydrologic bodies, wetlands, glaciers, ice sheets, sea ice, and solid Earth. In this study, two non-ocean nadir altimetry applications have been explored and examined: lake ice thickness retrieval in the Laurentian Great Lakes, north America (Chapter 3), and land subsidence detection in the San Joaquin Valley, California, USA (Chapter 4).

In Chapter 3, we use Cryosat-2 LRM and ICESat-2 ATL13 data products to derive lake ice thickness using the ice freeboard method, which has been proven and widely used for sea ice thickness retrieval in polar region but has not yet applied for lake ice thickness. In our processing, we utilize altimetry and radar waveform retracker to optimally derive ice freeboard height, which is obtained by differencing the height between snow/ice surface

(or air/snow surface for ICESat-2) and water height. With knowledge of snow depth and ice/snow/water density, we then can compute the ice thickness based on hydrostatic equilibrium assumption in Great Lakes during winter 2011 to winter 2019. Because this 120 method is first time used in lake region, we test and change some criteria and parameters in order to be suitable for lake application. 1) To identify altimetry data is observed over water or ice surface, we examine seven waveform characteristics with GLERL ice cover data, and find out PP (pulse peakiness) and OCOG width can effectively assort Cryosat-2 data. The classified result is validated by PlanetScope satellite image data and show good agreement, demonstrating the classification method is robust in lake region. 2) We test and define the filtering criteria using leading edge width (LEW), bin of maximum power (MaxP), and OCOG width, to remove the low quality Cryosat-2 data. The criteria are appropriate and proved for Cryosat-2 data all over entire Great Lakes. 3) To evaluate altimetry derived water level height, we use in-situ water level gauge data to validate.

The correlations coefficient between altimetry derived and in-situ water surface height are all larger than 90%, and RMSE are all smaller than ± 0.1 m. 4) In our study, the snow depth and snow density data are downloaded from SNODAS (Snow Data Assimilation

System) model output. To confirm the accuracy of SNODAS snow depth data, we compare it with GHCN-D (Global Historical Climatology Network Daily) in-situ snow depth data and HRRR (High-Resolution Rapid Refresh) model output, the results show good agreement. For Cryosat-2 derived ice thickness, the results show good agreement with in-situ data in winter 2014, the difference between Cryosat-2 derived ice thickness and in-situ data reaches 0.2 m. The Cryosat-2 solution is further compared with in-situ ice cover and air temperature data, the correlation coefficients are all larger than 70%, implying that estimated interannual variability of our estimated ice thickness is valid.

Through the linear regression, we discover the Cryosat-2 Threshold 40% ice thickness

121 and ice cover data (ice duration and annual maximum ice cover) have strong linear relationship. The R2 of fitting results are all 0.65, and the p-value of 0.000 is within 95% confident level. The one-year long ICESat-2 dataset is used, for the first time, to get the ice thickness in Great Lakes region. Comparison between Cryosat-2 and ICESat-2 derived ice depth, the Cryosat-2 estimation is much higher than ICESat-2. To confirm which result is correct, we compare both altimetry derived ice thickness with USCG

(United States Coast Guard) estimated values. However, both altimetry derived ice thickness values are all higher than USCG estimation. The reason is USCG estimated ice thickness is mostly from thermal growth and did not account for ridging causing theses in-situ estimates are lower than the actual values. In addition, we do not consider the problem of penetration in snow layer, that Cryosat-2 signal might be scattered in snow layer or ICESat-2 signal might penetrate to snow layer. It's difficult to conclude which sensor (Cryosat-2 or ICESat-2) is correct or whether altimetry can derive the correct ice thickness in Great Lakes, since we only have one winter in-situ data and there are many uncertainty in our process. More in-situ data are needed in future work. For possible future study, exploring the range correction for the traveling range of radar and laser pulse in snow layer. In our analysis, we discover the error of ice freeboard (or total freeboard) measurement has large influence for ice thickness estimation. Therefore, the penetration problem and changes of light speed in snow layer are imperative research tasks for lake ice thickness retrieval. The other future work is generating the snow data map using air temperature over lake. In our process, we interpolate Snow Data

Assimilation System (SNODAS) snow data using data over land, because there is no

122

SNODAS data over lake surface. However, the conditions on land are completely different than that over lake ice. We could use the air temperature data over lake surface and temperature index model (Bormann et al., 2014) to construct the snow map.

In Chapter 4, we use Cryosat-2 LRM data product with spatial interpolation to map the

0.3° x 0.3° 2D land subsidence rate, for the first time, at San Joaquin Valley, CA, during period 2010 to 2015. The methods of Kuo et al. (2015) are implemented to process pulse-limited radar altimetry data, including Envisat, Jason-2 and Jason-3, to compare with Cryosat-2 solution. Though several techniques have been developed and applied in

California, including GPS, InSAR, extensometers, and leveling survey. But the spatial or temporal resolution of GPS, extensometers, and leveling survey is sparse, and processed

InSAR product is not available between 2010 to 2015. The results show the Cryosat-2 derived 2D deformation map agrees well with GPS, Jason-2 altimetry and NASA JPL

InSAR derived velocities. The largest subsidence bowl is identified near city of Corcoran in Cryosat-2 results, the maximum subsidence rate reaches to -30 ~ -35 cm/yr in this sinking region due to excessive anthropogenic groundwater pumping. Same evidence was found in the GPS, NASA JPL InSAR results, and in-situ groundwater well data. It is anticipated that the new observation from this study can be used to provide additional constraints or information for other sensors (e.g., GPS, InSAR or leveling survey). The results of Envisat, Jason-2 and Jason-3 are compared with GPS velocity data, with good agreements. The RMSE between GPS and altimetry-derived time series are ± 17.6 cm at

GPS CRCN station and ± 43.1 cm at the LEMA GPS station, the correlation coefficients

123 are all higher than 90%. Furthermore, the Jason-2 and Jason-3 derived time series can detect the seasonal signal during rainy season (October through April) and 2017

California flood signal. For future possible work, improving the current spatial interpolation method. In our experiment, Triangulation-based cubic interpolation method is utilized in our data processing. However, Cryosta-2 does not detect the second large subsidence bowl at the southeast of El Nido and the time series of Cryosat-2 has large variance, likely due to the deficiency of the surface interpolation method. The other possible future work is applying this method to other subsidence regions, e.g., North

Carolina or Louisiana, and other parts of the world where have severe land subsidence issue.

124

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Appendix A: Time Series of Waveform Characteristic w.r.t Ice Cover

134

Figure A-1. Time series of PPL with respect to four groups in each Lake. Group 1 (blue)

and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and

Group 3 (red) represent the altimetry over Lake ice region

135

Figure A-2. Time series of PPR with respect to four groups in each Lake. Group 1 (blue)

and Group 4 (black) represent the altimetry data over water area, Group 2 (gray) and

Group 3 (red) represent the altimetry over Lake ice region

136

Figure A-3. Time series of gate of max power (MaxP) with respect to four groups in each

lake. Group 1 (blue) and Group 4 (black) represent the altimetry data over water area,

Group 2 (gray) and Group 3 (red) represent the altimetry over Lake ice region 137

Figure A-4. Time series of max power value with respect to four groups in each Lake.

Group 1 (blue) and Group 4 (black) represent the altimetry data over water area, Group 2

(gray) and Group 3 (red) represent the altimetry over ice region

138

Figure A-5. Time series of LEW with respect to four groups in each Lake. Group 1

(blue) and Group 4 (black) represent the altimetry data over water area, Group 2 (gray)

and Group 3 (red) represent the altimetry over ice region

139