AN EVALUATION OF A POINT SNOW MODEL AND A MESOSCALE MODEL
FOR REGIONAL CLIMATE SIMULATIONS
by
Jason Thomas Butke
A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Science in Geography
Fall 2006
Copyright 2006 Jason Thomas Butke All Rights Reserved
UMI Number: 1440623
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AN EVALUATION OF A POINT SNOW MODEL AND A MESOSCALE MODEL
FOR REGIONAL CLIMATE SIMULATIONS
by
Jason Thomas Butke
Approved: ______Brian Hanson, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee
Approved: ______Brian Hanson, Ph.D. Interim Chair of the Department of Geography
Approved: ______Thomas Apple, Ph.D. Dean of the College of Arts and Sciences
Approved: ______Daniel Rich, Ph.D. Provost
ACKNOWLEDGMENTS
I would firstly like to express my gratitude to my thesis advisor, Dr. Brian Hanson, for his expertise, knowledge, and understanding, all of which added considerably to my graduate experience. His brilliance with computers and modeling is second to no one, and his assistance in understanding concepts greatly impacted my perception of numerical modeling. I would also like to thank my committee members Dr. Daniel Leathers and Dr. Andrew Grundstein for their assistance in all aspects of my research project. Finally, I would like to thank Dr. Cort Willmott for his expertise and sincere guidance in more than just academic affairs.
A special thank you goes to Dr. Arthur Samel, without whose motivation and encouragement I may not have considered a graduate career in climatological research. Dr. Samel is the one professor who truly made a difference in my life. It was under his tutelage that I developed a focus and gained confidence. He provided me with direction, technical support, and became more of a mentor and friend, than a professor. It was through his persistence, understanding, and kindness that I completed my undergraduate degree and was encouraged to apply for higher education. I doubt that I will ever be able to convey my appreciation fully, but I owe him my eternal gratitude.
I would also like to thank my mother, Barbara Butke, for putting up with me since childbirth, raising me well, and working so hard to provide for our family, in the absence of my father. Without her hard work and determination, I would not be the person that I am today or come as far as I have.
A thank you goes to the National Center for Atmospheric Research (NCAR) for their computing resources and data that aided in running MM5.
In conclusion, I recognize that this research would not have been possible without the financial assistance of the Department of Geography at the University of Delaware (teaching and research assistantships), and so I express my sincere gratitude. TABLE OF CONTENTS
LIST OF TABLES ...... iv LIST OF FIGURES...... x NOMENCLATURE...... xiii ABSTRACT...... xx
1 LITERATURE REVIEW...... 1
1.1 Introduction...... 1 1.2 Project Objectives ...... 2 1.3 Snow Physics in the Climate System...... 2
1.3.1 Micro-Scale Effects ...... 2 1.3.2 The Forest Canopy and Blowing Snow Effects ...... 6 1.3.3 Ablation and Regional Hydrological Impacts...... 7
1.4 Snow Cover Modeling...... 8
1.4.1 Introduction...... 8 1.4.2 Snow Model Types...... 9 1.4.3 Complex One-Dimensional Snow Models ...... 10 1.4.4 Simple One-Dimensional Snow Models...... 13
1.5 General Circulation Models and Mesoscale Models ...... 14 1.6 Research Objectives ...... 16
2 SNTHERM...... 18
2.1 Introduction...... 18 2.2 Conservation Equations...... 19 2.3 Surface Energy Balance ...... 23
3 MM5...... 26
3.1 Model System Components...... 26 3.2 General Equations...... 29 3.3 Cloud Schemes...... 32 3.4 Precipitation Schemes ...... 33 3.5 Radiation Schemes...... 33 3.6 Surface Schemes ...... 34 3.7 Model Setup...... 35
i 4 MODEL SNOW PHYSICS ...... 38
4.1 NOAH LSM Snow Model Introduction...... 38 4.2 Precipitation Rate...... 40 4.3 Snow Albedo ...... 41 4.4 Thermal Conductivity ...... 42 4.5 New Snow Density...... 47 4.6 Ablation ...... 48 4.7 Surface Energy Budget...... 50
4.7.1 Turbulent Exchange Fluxes...... 51 4.7.2 Snow/Ground Interface Temperature ...... 52 4.7.3 Snow/Ground Interface Heat Flux...... 54
4.8 SNTHERM Snow Compaction, Metamorphosis, and Grain Growth.... 55
5 DATA AND METHODOLOGY ...... 57
5.1 SNTHERM Input Data...... 57 5.2 MM5 Input Data ...... 58 5.3 Observation Data...... 60
5.3.1 Snow Observation Errors...... 60 5.3.2 NCDC Data Errors...... 61
5.4 Model Sensitivity Analysis...... 61 5.5 Model Evaluation Statistics...... 63
6 RESULTS...... 66
6.1 General Model Analysis...... 67 6.2 Heavy Snow Events ...... 70
6.2.1 Anomalous Event ...... 71
6.3 Model Evaluation...... 72 6.4 Snow Physics Evaluation ...... 83
6.4.1 Snow Albedo ...... 84 6.4.2 Turbulent Exchange Fluxes...... 86 6.4.3 Snow Ground Interface...... 88 6.4.4 Subsurface Temperatures...... 99 6.4.5 Snow/Ground Interface Heat Flux...... 115
ii 7 DISCUSSION AND CONCLUSIONS ...... 117
7.1 Discussion...... 117 7.2 Conclusions...... 121
8 BIBLIOGRAPHY...... 125
iii LIST OF TABLES
Table 3.1: List of the 23 sigma levels and corresponding values for this study . . . . 30
Table 4.1: Snow thermal conductivity (W m-1 K-1) values for the NOAH LSM and SNTHERM for varying snow densities (kg m-3). SNTHERM thermal conductivities were calculated assuming the temperature was at 273.15 K and pressure equal to 1013.5 mb...... 46
Table 5.1: The soil and snow physical parameters. βnir is the IR extinction coefficient of the top snow layer, Sr is the irreducible water saturation for snow, qtz is the soil quartz content, z0 is the roughness length, CLE and CH are the wind-less convection coefficients for latent and sensible heats, and RHfo is the fractional humidity relative to steady state...... 58
Table 6.1: Days of the month for each SNTHERM and MM5 model run for each city showing that MM5 was not run across the months and to show the day disconnections that existed. 3-31 means the model was run from day 3 to day 31 during that month...... 66
Table 6.2: Number of days qualifying for each temperature or precipitation categorization for each of the six selected cities The 11th category is all times with 887 days for each city...... 73
Table 6.3: Model evaluation statistics for varying temperature and precipitation situations that both MM5 and SNTHERM met. No snow means no snow falling, no precip means no precipitation falling, snow on ground means all times with snow on the ground, and all times means all days regardless of condition. SNT represents SNTHERM, and OBS represents the observations. The OBS column only applies to the mean, while the MAE, r, and MSEu / MSE are for how SNTHERM compares to MM5. The mean and MAE have units of cm, while r and MSEu / MSE are dimensionless, and given as a percentage of 100 ...... 74
Table 6.4: Total model versus observed evaluation statistics averaged for all cities ...... 76
iv Table 6.5: Average ground temperatures for the NOAH LSM, SNTHERM, and SNTHERM modified as compared to NOAH LSM air temperatures during times with snow or no snow on the ground and times with only snow on
the ground. Tg is the average ground temperature regardless of snow condition, and T is the average ground temperature when snow is on gsnow the ground. Ta is the average air temperature regardless of snow condition, and T is the average air temperature when snow is on the asnow ground. Season 2 is November 2000 through April 2001, and Season 6 is November 2004 through April 2005...... 89
Table 6.6: Number of 3 hour observations qualifying for Bismarck and Scottsbluff for snow seasons two and six with snow or no snow on the ground (all times) and times with only snow on the ground (snow)...... 89
Table 6.7: Average soil temperatures for the NOAH LSM during times with snow or
no snow on the ground and times with only snow on the ground. T0.05 ,
T 0.25 , T0.70 , and T1.50 are the average soil temperatures regardless of snow condition at 0.05, 0.25, 0.70, and 1.50 meters, and T , 0.05snow T , T , and T are the average soil temperatures 0.25snow 0.70snow 1.50snow when snow is on the ground at 0.05, 0.25, 0.70, and 1.50 meters respectively...... 89
Table 6.8: Average soil temperatures for SNTHERM during times with snow or no
snow on the ground and times with only snow on the ground. T0.05 , T 0.25 ,
and T0.70 are the average soil temperatures regardless of snow condition at 0.05, 0.25, and 0.70, and T , T , and T are the 0.05snow 0.25snow 0.70snow average soil temperatures when snow is on the ground at 0.05, 0.25, and 0.70 meters respectively...... 90
Table 6.9: Average soil temperatures for SNTHERM modified during times with snow or no snow on the ground and times with only snow on the ground.
T0.05 , T 0.25 , and T0.70 are the average soil temperatures regardless of snow condition at 0.05, 0.25, and 0.70, and T , T , and 0.05snow 0.25snow T are the average soil temperatures when snow is on the ground at 0.70snow 0.05, 0.25, and 0.70 meters respectively...... 90
Table 6.10: NOAH LSM, SNTHERM, and SNTHERM modified ground heat fluxes (W m-2) and ground heat flux differences for November 6, 2000 through April 1, 2001 for Bismarck, ND...... 114
v Table 7.1: SNTHERM and SNTHERM Modified average snow thermal conductivities (W m-1 K-1) and densities (kg m-3) for November 6th, 2000 though April 1st, 2001 for Bismarck, ND ...... 120
vi LIST OF FIGURES
Figure 3.1: The MM5 system including all pre-processing programs and data input options. Taken from NCAR/Mesoscale and Microscale Meteorology (MMM)...... 26
Figure 3.2: 16 point, two-dimensional parabolic interpolation scheme. Taken from NCAR/MMM ...... 27
Figure 3.3: Cressman-based banana extension objective analysis interpolation scheme in which the arrows indicate the flow direction and the dots are parcels. Taken from NCAR/MMM...... 28
Figure 3.4: Schematic representation of the model vertical structure. The example is for 15 vertical sigma levels. The dashed lines are half-sigma levels, whereas the solid lines are full-sigma levels. K is the sigma level number. Taken from NCAR/MMM ...... 29
Figure 3.5: Illustration of the cumulus process for MM5, in which the arrows represent explicitly modeled processes. Taken from NCAR/MMM . . . .33
Figure 3.6: Free atmosphere radiation processes illustration in which the arrows represent explicitly modeled processes. Taken from NCAR/MMM. . . . 34
Figure 3.7: Surface processes illustration in which the arrows represent explicitly modeled processes. Taken from NCAR/MMM...... 35
Figure 3.8: The physical extent of Domain 1 (D01) and Domain 2 (D02) ...... 36
Figure 3.9: MM5 domain two grid and the six selected cities in the upper Great Plains ...... 37
Figure 4.1: NOAH LSM diagram depicting all modeled or parameterized processes including radiation, turbulent exchanges, and atmospheric forcings. Taken from NCAR/MMM...... 39
Figure 4.2: The MM5 modeling system flow chart with input and output data from the NOAH LSM. Taken from NCAR/MMM...... 39
Figure 4.3: NOAH LSM soil thermal conductivity as a function of volumetric soil moisture for four soil types: sand, silt, loam, and clay. Taken from Chen et al. (2001)...... 43
Figure 4.4: NOAH LSM and SNTHERM snow density (kg m-3) versus snow thermal conductivity (W m-1 K-1)...... 47
vii Figure 5.1: Conceptual diagram showing the flow of input data to the MM5 NOAH LSM coupled model system and subsequent data output flow to SNTHERM...... 59
Figure 5.2: Snow thermal conductivity (a), snow grain size (b), new snow density (c), and porosity and compaction/metamorphosism (d) for Bismarck, North Dakota during January 2004 as compared to SNTHERM during the control run simulation. Snow thermal conductivity has units of W m-1 K-1, snow grain size has units of mm, new snow density has units of kg m-3, and porosity and compactive and metamorphic effects are dimensionless. All variables were held constant during the sensitivity analysis runs while the control run used the model as it would normally be utilized...... 62
Figure 6.1: MM5 average snow depth (m) for domain two for November 2000 (a) and April 2001 (b)...... 67
Figure 6.2: MM5, SNTHERM, and observed snow depth (m) for November 2004 through April 2005 for Bismarck, North Dakota (a) and Scottsbluff, Nebraska (b)...... 68
Figure 6.3: MM5 domain 2 averaged temperature (°C) for November 2002, March 2003 (a), and April 2003 and December 2002, January 2003 and February 2003 (b)...... 69
Figure 6.4: MM5 averaged snow depth (m) for November 2002, March 2003, and April 2003 (a) and December 2002, January 2003 and February 2003 (b)...... 69
Figure 6.5: MM5 domain two snow depth averages (m) for January 24 through January 31, 2004 (a) and February 2 through February 5, 2004 (b)...... 70
Figure 6.6: MM5, SNTHERM, and observed snow depths (m) for November 2003 through April 2004 for Bismarck (a) and Williston (b), North Dakota and Sioux Falls (c) and Huron (d), South Dakota. The red dots demonstrate that February 2004 began much lower than January 2004 ended...... 72
Figure 6.7: MM5, SNTHERM, and observed snow depth from December 1999 through April 2000 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska...... 77
Figure 6.8: MM5, SNTHERM, and observed snow depth from December 2000 through April 2001 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska...... 78
viii Figure 6.9: MM5, SNTHERM, and observed snow depth from December 2001 through April 2002 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska...... 79
Figure 6.10: MM5, SNTHERM, and observed snow depth from December 2002 through April 2003 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska...... 80
Figure 6.11: MM5, SNTHERM, and observed snow depth from December 2003 through April 2004 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska...... 81
Figure 6.12: MM5, SNTHERM, and observed snow depth from December 2004 through April 2005 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska...... 82
Figure 6.13: SNTHERM snow albedo and snow depth for snow season six for Bismarck, North Dakota. X axis ticks are weeks and each label approximates a month. Snow albedos between 0.7 and 0.9 should be considered erroneous as only new snow has an albedo approaching 0.9. 84
Figure 6.14: SNTHERM snow albedo and snow depth for snow season six for Bismarck, North Dakota. X axis ticks are weeks and each label approximates a month. Hour 12 was used as a representative snow albedo because SNTHERM snow albedo varies with the zenith angle leading to erroneously high albedos at low sun angles...... 85
Figure 6.15: NOAH LSM snow albedo and snow depth for snow season six for Bismarck, North Dakota. X axis ticks are days and represent eight 3 hour data points and each label approximates a month...... 86
Figure 6.16: NOAH LSM turbulent fluxes and snow depth for snow season two for Scottsbluff, NE. Each tick represents one week, while each label approximates one month...... 87
Figure 6.17: SNTHERM turbulent fluxes and snow depth for snow season two for Scottsbluff, NE...... 87
Figure 6.18: SNTHERM Modified turbulent fluxes and snow depth for snow season two for Scottsbluff, NE. Each tick represents one week, while each label approximates one month...... 88
ix Figure 6.19: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season two for Bismarck, ND...... 91
Figure 6.20: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season two for Scottsbluff, NE...... 91
Figure 6.21: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season six for Bismarck, ND...... 92
Figure 6.22: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season six for Scottsbluff, NE...... 92
Figure 6.23: NOAH LSM 0.05 meter soil and air temperatures during snow season two for Bismarck, ND...... 93
Figure 6.24: NOAH LSM 0.05 meter soil and air temperatures during snow season two for Scottsbluff, NE...... 94
Figure 6.25: NOAH LSM 0.05 meter soil and air temperatures during snow season six for Bismarck, ND...... 94
Figure 6.26: NOAH LSM 0.05 meter soil and air temperatures during snow season six for Scottsbluff, NE...... 95
Figure 6.27: NOAH LSM snow depth and 0.05 meter soil and air temperature differences during snow season two for Bismarck, ND. Temperature differences are of air temperature subtracted from ground temperature such that positive values indicate a colder ground temperature than air temperature and the opposite is true of negative values...... 95
Figure 6.28: NOAH LSM snow depth and 0.05 meter soil and air temperature differences during snow season two for Scottsbluff, NE. Temperature differences are of air temperature subtracted from ground temperature such that positive values indicate a colder ground temperature than air temperature and the opposite is true of negative values...... 96
Figure 6.29: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season two for Bismarck, ND...... 97
Figure 6.30: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season two for Scottsbluff, NE...... 97
Figure 6.31: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season six for Bismarck, ND...... 98
x Figure 6.32: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season six for Scottsbluff, NE...... 98
Figure 6.33: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Bismarck, ND...... 101
Figure 6.34: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Bismarck, ND...... 102
Figure 6.35: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Bismarck, ND...... 103
Figure 6.36: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Scottsbluff, NE...... 104
Figure 6.37: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Scottsbluff, NE ...... 105
Figure 6.38: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Scottsbluff, NE ...... 106
Figure 6.39: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Bismarck, ND...... 107
Figure 6.40: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Bismarck, ND...... 108
Figure 6.41: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Bismarck, ND...... 109
Figure 6.42: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Scottsbluff, NE...... 110
Figure 6.43: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Scottsbluff, NE...... 111
xi Figure 6.44: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Scottsbluff, NE...... 112
Figure 6.45: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season two for Bismarck, ND. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM ...... 113
Figure 6.46: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season two for Scottsbluff, NE. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM ...... 114
Figure 6.47: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season six for Bismarck, ND. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM ...... 114
Figure 6.48: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season six for Scottsbluff, NE. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM ...... 115
Figure 6.49: NOAH LSM, SNTHERM, and SNTHERM modified ground heat fluxes as compared to snow depth for Bismarck, ND from November 6, 2000 through April 1, 2001. Positive ground heat fluxes are upward from the surface and the opposite is true of negative values...... 116
Figure 7.1: NOAH LSM, SNTHERM, and SNTHERM Modified estimated snow density for snow season two for Bismarck, ND. Snow density estimates are of swe divided by snow depth...... 118
Figure 7.2: SNTHERM and SNTHERM Modified average snow densities as compared to snow depth during snow season two for Bismarck, ND. Average snow density is the bottommost three layers averaged ...... 120
Figure 7.3: SNTHERM and SNTHERM Modified average snow thermal conductivities during snow season two for Bismarck, ND. Average snow thermal conductivity is the bottommost three layers averaged...... 121
xii NOMENCLATURE
All units are in the SI system, with the exception of pressure, which is expressed in mb, and air temperature, which is expressed in ºC.
a Grain growth adjustable variable a1 Empirical constant A Advection A P-intercept b Grain growth adjustable variable B Slope of the regression line
bb0 Old conducted and convected heat plus absorbed solar radiation of the snow layer 2 -1 bvi0 Vapor diffusion constant for ice (663.8 m s ) 2 -1 bvl0 Vapor diffusion constant for liquid water (657.7 m s ) c Specific heat (J kg-1 K-1) -1 5/2 c1 0.003795 kg m c2 0.70 -5 c3 5.95 x 10 mb
c4 1500 K c5 0.0000775 -6 6 -2 c6 1.105 × 10 m kg -3 -1 c7 0.0017 kg m K -8 -3 -3 c8 6.48 × 10 kg K s c9 Empirical constant varying with the bulk density of liquid water and ice c10 Empirical constant varying with the bulk density of liquid water and ice -1 c11 0.08 K 3 c12 0.021 m kg capp Apparent specific heat -1 -1 cair Specific heat of air at constant pressure for dry air (1004.5 J kg K ) ch Surface exchange coefficient for heat and moisture (m s-1) c Specific heat of water vapor at a constant pressure (2106 J kg K-1) p v c Specific heat at constant pressure for liquid water (4218.0 J kg-1 K-1) ph 20 CE Dimensionless bulk turbulent transfer coefficient for latent heat CH Dimensionless Bulk turbulent transfer coefficient for sensible heat -1 -1 csnow Specific heat of the snow medium (J kg K ) d Grain diameter (m) d Index of agreement dbv l,i Change in liquid water or ice saturation vapor density with temperature dT ds Absorbed solar radiation (W m-2) -2 ds0 Old absorbed solar radiation (W m ) dz Change in elemental thickness (m)
xiii dzmedium Combined thickness of Snow and uppermost soil layer (m)
dzsnow Snow layer depth closest to the ground (m)
dzsoil Soil layer depth closest to the surface (m)
dz0 Old snow layer thickness (m) D Diffusion tendency (m2 s-1) 2 -1 DΘ Diffusion of potential temperature (m s ) 2 -1 D0 Effective diffusion coefficient for water vapor in snow (0.0009 m s )
D2 Transmission and reflectance constant 2 -1 De Diffusion coefficient for vapor flow through snow (m s ) Dsnow Snow depth (m) Dsoil Uppermost soil layer depth (m) e Vertical component of Coriolis equal to 2Ωcos λ -1 ecan Canopy water evaporation (kg s ) -2 epot Potential evaporation (W m ) -1 esoil Direct soil evaporation (kg s ) -2 etot Total latent heat flux of both snow and non-snow (W m ) et Amount of direct soil and canopy water evaporation and plant transpiration E Snowpack internal energy (W m-2) -2 -1 Eevap Evaporation (condensation) rate from (to) the snow surface (kg m s ) -2 -1 Esub Sublimation (deposition) rate from (to) the snow surface (kg m s ) EEO Windless exchange coefficient for latent heat
EHO Windless exchange coefficient for sensible heat f Horizontal Coriolis parameter equal to 2Ωsinφ
fage Snow age factor dependent upon grain diameter
fl Fraction of unfrozen liquid water due to capillary and absorbed potential
fgreen Areal fractional coverage of green vegetation
fmin Minimum areal fractional coverage of green vegetation frh Fractional humidity within a medium relative to a saturated state
fvis Approximate breakdown between visible and near infrared radiation
flfall Fraction of liquid water within falling precipitation, varying from 0% at 273.15 K to 40% at 275.15 K -2 Ffreez Freezing rain latent heat flux (W m ) -2 Fsnow Heat flux from the snowpack to the accumulating precipitation (W m ) g Acceleration due to gravity (m s-2) -2 G Soil heat flux (W m ) h Specific enthalpy (J kg-1) -1 hk Specific enthalpy for liquid water and ice (J kg ) -1 hsnow Specific enthalpy for snow with respect to the melting temperature (J kg ) -2 hs0 Old water flux enthalpy adjustment for sensible heat (W m )
xiv -2 Iconv Heat advected by falling rain or snow (W m ) -2 I g Ground heat flux (W m ) -2 I IR Net surface longwave radiation (W m ) ↓ -2 I IR Downwelling longwave radiation, positive upwards (W m ) ↑ -2 I IR Upwelling longwave radiation, positive upwards (W m ) -2 I lat Latent heat flux (W m ) -2 I R Net radiation flux, positive downwards (W m ) -2 I s Net surface shortwave radiation (W m ) ↓ -2 I s Downwelling shortwave radiation, positive upwards (W m ) -2 Is00 Insolation at the top of the atmosphere (W m ) -2 ISen Sensible heat flux (W m ) -2 I top Net surface energy at the snow-air boundary (W m ) J Generalized mass flux for i, l, or v (W m-2) -2 J v Vapor flux term (Frick’s law) (W m ) kmax Saturated permeability K Hydraulic Conductivity of liquid water (m s-1)
Ke Kersten number L Latent heat (J kg-1) -1 Lc Latent heat of condensation (2504500 J kg ) -1 Li Latent heat of fusion (3335000 J kg ) -1 Ls Latent heat of sublimation (2838000 J kg ) -1 Lv Latent heat of vaporization (2260000 J kg ) m Map scale factor, closer to 1.0 causes less distortion mvol Fractional volume of dry soil material MAD Mean absolute deviation MAE Mean absolute error MSE Mean square error MSEs Mean square error systematic MSEu Mean square error unsystematic Melt Snow melt rate (kg m-2) -3 -1 M k Mass rate of melt, sublimation, or evaporation (kg m s ) N Number of observations O Observed variable Ot Observed variable at each time step (t) O Mean observed p Pressure (mb) p(z) Pressure at height z (mb) p* Pressure difference between the top and bottom of the atmosphere (mb) p' Pressure deviation from p0 (mb)
xv pdz Fraction rate of change in snow layer thickness due to compaction dt compaction
pσ Reference state pressure defined for each vertical level (mb) p0 Reference state barometric pressure (1000.0 mb)
ps Surface pressure (mb) ptop Pressure at the top of the atmosphere (100.0 mb) P Input precipitation (m) P Predicted variable ^ P Ordinary Least Squares (OLS) simple linear regression equation Pt Model predicted variable at each time step (t)
Prain Rain precipitation rate
Psnow Snow precipitation rate
Pf Volumetric soil water content -1 -2 Ps Snow load pressure (kg m s )
Pv,air Water vapor pressure at a reference height above the surface (mb) n P vk,sat Saturation vapor pressure with respect to phase k (mb) PE Potential error porosity Fraction volume of voids between ice matrix in snow and between dry soil Q Diabatic warming term r Correlation coefficient r2 Coefficient of determination (correlation squared) rearth Radius of the earth (m) rch Component of the effective snow-ground surface temperature rr Component of the effective snow-ground surface temperature -1 -1 Rw Gas constant for water vapor (461.5 J kg K ) s Liquid water saturation (m3 m-3) s0 Amount of liquid water in the snow volume during the previous time step satl Relative water content of soil 3 -3 se Effective liquid water saturation (m m ) sr Maximum fraction of the snow volume occupied by liquid water during the previous time step 3 -3 ss0 Old effective water saturation (m m ) S Control surface
SO Observed standard deviation
S P Predicted standard deviation ↑ -2 S reflect Reflected shortwave radiation (W m ) t Time (s) T Temperature (K) T1 Amount of heat energy available at the snow surface, having been corrected by latent heat fluxes
xvi T 2 Temperature and thermal diffusivity within the snow and soil mediums
T0 Reference state temperature (K)
Ta Air temperature (K) Tabs Absolute zero (0.0 K)
Tcut Cutoff temperature in new snow density calculation (15.0°C) TD Temperature depression given as Tm – T
Tg / c / s Ground/canopy/snowpack effective skin temperature (K)
Tm Melting temperature (273.15 K)
Tmax Cutoff temperature in new snow density calculation (0.12°C) Tskin NOAH LSM effective skin temperature (K)
Tsnow Snow temperature (K) Tsoil Uppermost soil layer temperature (K)
Tv Virtual temperature (K) u East-west horizontal momentum (kg m s-1) u Unit Vector U Mass flux (kg m-2 s-1)
Ul Liquid water flow through snow -2 Un0 Old net snow layer water flux (W m ) v Velocity (m s-1) v North-south horizontal momentum (kg m s-1) V Control volume thickness (m) w Wind speed (m s-1) w Vertical momentum (kg m s-1) -1 wsstorm Storm average wind speed (m s ) x X-coordinate X Mean X Net heat input into the system during the last time step Xt Model or observation value at each time step (t) y Y-coordinate Y Meltwater change caused by absorbed radiation changes z Incremental volume thickness (m) z Observation height above the snow surface z Zenith angle zo Roughness length (m) Z Amount of compactive change from melt (m)
α Rotation angle of the grid, given as φ – φc α land Land surface albedo α max Maximum deep snow albedo taken from satellite-based snow albedo fields α medium Thermal diffusivity average between the snow and uppermost soil layer (m2 s-1) α snow Snow albedo
xvii αtop Top layer albedo α NIR Near infrared horizontal albedo α vis Visible horizontal albedo
β ∞ Bulk or asymptotic extinction coefficient β nir Near-infrared radiation bulk extinction coefficient β vis Visible radiation bulk extinction coefficient γ Bulk density (kg m-3) -3 γk Partial or bulk density for i, l, or v (kg m ) γ -3 li Combined partial densities of liquid water and ice (kg m ) γ r Ratio of the heat capacities for dry air δkk’ Kronecker delta ε Surface emissivity ε Function dependent upon pore size εair Clear-air, all-wave bulk atmospheric emissivity ' ε air Wachtmann correction for clear-sky emissivity ε snow Snow emissivity (0.90 for NOAH LSM and 0.97 for SNTHERM) η Viscosity coefficient varying with ρ, T, and grain type (kg s-1 m-1) η -1 -1 0 Viscosity coefficient at 273.15 K (3600000 kg s m ) ϑ Potential temperature (K) θ v Water vapor fractional volume Θ Fractional volume (m3 m-3) Θ soil Maximum soil moisture (porosity) κ -1 -1 a Thermal conductivity of air (0.023 W K m ) κ l Hydraulic permeability of liquid water κ -1 -1 i Thermal conductivity of ice (2.30 W K m ) mvol -1 -1 κ min Mineral conductivity (W K m ) κ -1 -1 soil Soil thermal conductivity (W K m ) κ -1 -1 soil_dry Dry soil thermal conductivity (W K m ) κ -1 -1 soil_saturated Saturated soil thermal conductivity (W K m ) κ -1 -1 snow Snow thermal conductivity (W K m ) Κ von Karman constant (0.4) µ -1 -1 l Dynamic viscosity of liquid water (kg m s ) ρ -3 0 Reference-state density (kg m ) -3 ρa Air density (kg m ) ρ -3 snow (new) New snow density (kg m ) ρ -3 snow Snow density (kg m ) ρ -3 snow_max New snow density upper limit (150.0 kg m ) ρ -3 snow_min New snow density lower limit (50.0 kg m )
xviii ρ -3 source Source density (kg m ) ρ -3 v,sat Water vapor density at saturation (kg m ) σ Vertical sigma, terrain-following coordinate . σ Vertical sigma relation σ -8 -1 -2 -4 b Stefan-Boltzmann constant (5.67 × 10 J s m K ) τ 1 Low cloud level atmospheric transmissivity τ 2 Middle cloud level atmospheric transmissivity τ 3 High cloud level atmospheric transmissivity φ Longitude φc Central longitude ψ soil Saturated soil potential (suction) λ Latitude Ω Water component being conserved
Subscripts a Air i Ice j Index k Index for ice, liquid water, or water vapor l Liquid water r Ratio s Snow t Time u East-west wind component v Water vapor v North-south wind component w Vertical wind component
xix ABSTRACT
The ability of atmospheric and climate models to accurately predict snow cover and areal snow distribution is vital for climate simulations. However, due to computational efficiency, general circulation and mesoscale models employ simplified snow physics, limiting their ability to simulate the true nature of the snowpack. A one- dimensional point snow model SNTHERM and Mesoscale Model 5 (MM5) are compared to assess their utility in the evaluation of snow cover. MM5 was run over an upper Great
Plains domain for six consecutive winters, producing one set of snowcover predictions from its simplified snow model. Atmospheric output from MM5 was used to drive
SNTHERM at the locations of six first-order National Weather Service (NWS) stations, providing snowpack estimates from a more detailed snowpack model. Snowpack variables from each model were compared to observations at the same six weather stations. Results indicate that there is general agreement between the models on daily to monthly time scales, although their physics vary considerably. Snow physics comparisons demonstrate that NOAH LSM ground and subsurface temperatures are too cold because of the simplistic one-layer slab representation, causing snow accumulation
(ablation) overestimations (underestimations). A modified version of SNTHERM was able to reasonably reproduce NOAH LSM snow accumulation and ablation rates by using average monthly NOAH LSM 0.05 cm soil temperature as a surrogate for ground temperature and NOAH LSM snow thermal conductivity. Results establish that not for a
400 kg m-3 maximum snow density cutoff, NOAH LSM snow thermal conductivities were too high, leading to a very dense, thermally conductive snowpack, further exacerbating slow ablation rates.
xx Chapter 1: Literature Review
1.1 Introduction
Beginning in fall, as solar zenith angles increase and daylength shortens, the high latitude snow cover shifts equatorward due to passing cyclonic events and less surface radiation, causing colder air temperatures, and increasing North American ephemeral snow cover by 1,000,000 km², equivalent to the combined areas of Montana and Texas.
By late February, as solar zenith angles decrease, surface temperatures increase to above freezing, causing the ephemeral snowpack to melt rapidly northward.
At winter’s peak, snow can cover nearly 50% of the North American continent
(Slater et al. 2001), causing the surface albedo to increase by 30% to 50% (Cohen and
Rind 1991). This increase affects the seasonal global surface radiation balance, intensifying temperature differences between latitudes, and it is these differences that drive global atmospheric circulations (Liston et al. 1999).
Snow cover lowers surface air temperatures and geopotential heights, and it can enhance atmospheric baroclinicity, causing cyclonic system development (Cohen and
Rind 1991). Winter snow accumulation and spring melt also affects regional hydrology.
One region, including the Great Plains, receives 20-25% of its annual precipitation from snow, which is important for agricultural and domestic uses (Stepphuhn 1981). Given the importance of snow, much effort has gone into modeling snow processes.
Models that predict snow cover have become important tools for local, regional, and global climate studies, as well as hydrological planning. These models have been utilized in areas with little observational data, for avalanche prediction, flood assessment,
1 or for modeling the internal snow structure itself. The dominant hydrological period is the timing of accumulation and ablation of the snow cover.
1.2 Project Objectives
This study will utilize modeling to compare snow depth during varied temperature and precipitation regimes. Comparisons will be made between MM5 and a complex point snow model (SNTHERM). Snow depth outputs will be compared to observations in order to determine how simplified snow physics in a three-dimensional mesoscale model compare to a more detailed one-dimensional snow model.
Appropriate model type selection is the most important aspect of a modeling study. By comparing models of varied complexity and scale, it became clear which models would be the most useful for this study. MM5 and SNTHERM were chosen because they are some of the most widely validated, comprehensive, and available mesoscale and point snow models respectively. The initial stage tests the compatibility of MM5 and SNTHERM, because SNTHERM requires specific meteorological data to estimate snowpack parameters. This will answer whether SNTHERM can be driven by
MM5 atmospheric output data.
1.3 Snow Physics in the Climate System 1.3.1 Micro-Scale Effects
When snow falls, it is usually in the classic snowflake form, consisting of six arms and three symmetry lines. This form is responsible for the extremely low bulk density associated with freshly fallen snow, because the surface snowpack consists of up to 97% air. Therefore, as external forces such as wind or contact with the ground are applied, some of the arms break off or shatter, causing the individual snowflakes to metamorphose into rounded forms (Jordan et al. 1991).
2 When snow covers bare ground, the surface albedo increases significantly from a value of between 0.10 and 0.30 to about 0.50 to 0.90. This range depends on solar zenith angle, snow cover fraction (snow patchiness), atmospheric debris, cloudiness, snow grain size and shape, surface roughness, liquid water content, and any snowpack impurities such as dust or pollution (Kuhn 1989, Walland and Simmonds 1997, Yang et al. 1997, and Zhang 2006).
This albedo variation is also highly dependent upon vegetation type, as trees remain above the snow. Therefore, forested area albedos are among the lowest of any naturally occurring land environment when snow cover is present. This is partly due to color and partly due to the multiple scattering of sunlight within the trees. Grasses have a similar effect, but to a much lesser degree than trees, in that they scatter sunlight until the snow depth is great enough to completely obscure the vegetation.
Freshly fallen snow has the highest surface albedo, causing much less incoming shortwave radiation to be absorbed during the day, which results in lower daily air and snow temperatures (Leathers et al. 1998, Walland and Simmonds 1997). The overall albedo warming effect on snow surface temperature is greater during spring than autumn at lower and middle latitudes because of higher solar elevation angles. Conversely, the snow albedo cooling effect is limited during winter months caused by lower solar elevation angles, especially at higher latitudes (Zhang 2006).
Across the infrared portion of the spectrum, snow is a near blackbody. Therefore, snow has a high emissivity, between 0.96 and 0.99, in the wavelengths of outgoing longwave radiation, making snow an effective terrestrial energy radiator. Thus, nights with clear skies and light winds enhance ground infrared radiation losses over a
3 snowpack resulting in very low temperatures. For example, if an equal amount of longwave radiation were released from a snow covered and snow free surface, the snow temperature would be about 4.0 °C colder than the bare soil temperature (Zhang 2006).
This temperature difference has a large influence on both the air and ground thermal regimes.
Additionally, snow has a low thermal conductivity, due to a low density caused by large amounts of air within the snowpack. Therefore, snow acts as a thermal insulator to the covered ground or vegetation. This condition causes the ground temperature to remain nearly isothermal around 0°C (Bartlett et al. 2004 and Strack et al. 2003) and subsequently prevents a positive sensible heat flux from the ground into the lowest atmospheric layer to form (Cohen et al. 1991). Consequently, in spring, as the temperature gradient between the snow cover and atmosphere attempts to increase above the snow temperature, snow begins to melt. This melting causes liquid water to form and evaporate, creating a latent heat sink, which requires energy to be removed from the atmosphere or ground, further impeding atmospheric or soil warming. Meteorological data shows that the snow surface mean winter temperature can be up to 2.0°C lower than the mean winter air temperature (Yershov 1998 taken from Zhang 2006).
Kudryavtsev (1992) observed that a thin snow cover with a high albedo cooled the ground surface. Conversely, as the snow depth increased, the insulating effect of snow increased resulting in a warmer ground surface. This insulating effect reached a maximum around 40 cm of snow depth at which point the insulating effect decreased as snow depth increased caused by the latent heat effect (melt, evaporative, or sublimative
4 cooling). Zhou et al. (2000) observed a 2.8°C to 9.0°C warmer ground than air temperature when snow of 10 to 25 cm depth covered the ground.
Within the snowpack, as snowflakes rub against each other or melt, space between flakes is reduced and individual ice grains will form new bonds and attach to one another, resulting in a stronger, denser snowpack. Conversely, temperature-gradient or constructive metamorphosis can weaken aged snow by grain growth from vapor transport through the pore spaces and densification from water flow (Jordan et al 1991).
The process by which snow changes to ice (firnication) or melt-freeze metamorphosis triggers grain growth by passing melt-freeze cycles and compaction (Loth et al 1993).
Continued snow accumulation on top also generates bond growth, which leads to more efficient grain shapes that pack.
Snow grain size is critical to mass and energy balance equations because it affects snow permeability to liquid water flow. Grain size decreases with depth, leading to decreased permeability with depth. The solar radiation extinction coefficient decreases with depth because light penetration into the snowpack decreases with increasing grain size. Additionally, snow density increases with decreasing grain sizes because smaller grain sizes indicate less air in the snowpack.
Grain diameters range from 0.04 to 0.2 mm for fresh snow and 0.2 to 3.0 mm for aged snow. Within dry snow, grain growth results from the upward moving vapor flux in which the vapor evaporates from the top of snow grains after condensation at the bottom.
Over time, smaller particles are consumed by larger ones due to vapor pressure differences, leading to an upward shift in grain size with time. This accounts for
5 increased snow densities with time, decreasing both snow albedo as well as snow permeability.
Heat exchanges due to rain or snow falling upon a snow-covered surface or the ground heat flux interacting with the bottom snow layer are generally considered negligible by models, but not discounted (Loth et al 1993). Heavy rain or snowfall can transport large amounts of energy to the snow surface, resulting in increased snow densities and snow temperatures. Leathers et al. (1998) used SNTHERM to evaluate the magnitude of the surface energy fluxes to demonstrate that a strong synoptic-scale disturbance can rapidly ablate a snowpack with 7.5 to 15.0 cm of SWE and produce
7.5 cm of rainfall in a three day period. This particular event occurred near
Williamsport, PA and caused 30 fatalities and upwards of $1.5 billion in damages.
1.3.2 The Forest Canopy and Blowing Snow Effects
A forest canopy shades radiation, intercepts precipitation, and reduces wind, affecting accumulation and ablation processes (Marks et al. 1999). Forest canopy interception can store up to 60% of snowfall by midwinter. This produces annual snow cover losses of 30% to 40%, because the canopy is a dry and relatively warm environment, causing much more snow to sublimate than would at the surface, making forested areas difficult to model (Pomeroy et al 1998).
Blowing snow is also common, having its greatest impact in high latitudes due to colder, drier conditions, and little vegetation (Xiao et al. 2000). Within the first 300 meters of fetch, 38% to 85% of annual snowfall is removed by snow transport, a condition that increases with increasing wind speed (Pomeroy 1993). Similarly, annual blowing snow transport and sublimation quantities decrease with increasing surface
6 roughness height and become more noticeable with higher seasonal wind speeds and temperatures. Sublimation requires large amounts of energy, and so the higher the temperature, the more energy available for sublimation (Pomeroy 1993). Wind fields vary locally and instruments have difficulties measuring particle density, shape and size distribution, and relative humidity; all factors that are crucial for estimating sublimation rates (Jingbing et al. 2000).
1.3.3 Ablation and Regional Hydrological Impacts
Spring melt depends mostly upon air temperature, which is elevation dependent, and radiation effects such as slope, aspect, elevation, and shading. Impurity amounts and meltwater evaporation or refreezing within the snowpack also affect melt. Light- absorbing impurities cause lowered snow surface albedos, leading to more energy being absorbed by the snow surface. Similarly, as the snowpack melts, the liquid water evaporates requiring energy to be removed from the environment making less available for further snow melt. However, meltwater also infiltrates the snowpack and refreezes, releasing latent heat that warms the snowpack (Marshall et al 1999).
The melt period occurs in three phases: warming, ripening, and output (Dingman
1994, taken from Williams and Tarboton 1999). During the warming phase, the snowpack reaches 0 ºC caused by the net positive energy input raising snowpack temperatures. During the ripening phase, the snowpack melts isothermally at 0 ºC, and contains meltwater in the pore spaces until the water mass overcomes surface tension.
The meltwater will remain within the snowpack until the retention capacity is exceeded, which is generally 5% of the pore volume, after which runoff will occur. During the
7 output phase, the snowpack also remains isothermal at 0 ºC, but the liquid water is released from the snowpack (Williams and Tarborton 1999).
Meltwater plays a critical role in regional hydrology by recharging groundwater, increasing soil moisture and stream flow runoff, and providing an agricultural fresh-water source (Grundstein 1996). The majority of in-and-out moisture transfer occurs in spring and fall in North America (Marshall et al. 1994), making snowmelt, or out-transfer, paramount for regions that rely on meltwater for annual fresh water supplies. In the western United States, 75% of the water budget comes from snowmelt (Williams et al.
1999). Thus, years with warmer temperatures and more rainfall cause more water losses to runoff and result in a shallower snowpack, which impact the water supplies for cities like Los Angeles and Phoenix.
Additionally, ablation affects hydropower company finances, flooding risk assessment, erosion studies, avalanche forecasting, as well as building snow load standards (Gustafsson et al. 2001; Grundstein et al. 2001). The seasonality of snow cover is significant because early snowpack development reduces, or in severe cases prevents, soil frost development. Therefore, a lessening of soil frost development has a positive impact on biological growth because less frost results in more biological growth
(Gustafsson et al. 2001).
1.4 Snow Cover Modeling 1.4.1 Introduction
Snow models vary in complexity beginning with highly structured, complex one- dimensional snow models, such as SNTHERM (Jordan et al. 1991), Anderson’s (1976) model, CROCUS (Brun et al. 1989), Lynch-Stieglitz (Lynch-Stieglitz 1994), and the
Snow-Atmosphere-Soil Transfer (SAST) model (Sun et al. 1999). These models have
8 advanced, theoretical, and empirical snow physics, utilized for local or regional representations of the snowpack (Cline 1997, Essery et al. 1999, Jin et al. 1999, Marks et al. 1999, Gustafsson et al. 2001, Stieglitz et al. 2001). Simple snow models with limited processes, such as the ABC snow model (Williams et al. 1999), are simple and efficient for a specific purpose.
Mesoscale models and General Circulation Models (GCMs) generally treat snow simply, as a slab, a moisture sink, or composite soil and snow layer, to ensure numerical and computational time efficiency. This distinction is important for mesoscale models since they are generally run for short time periods, during which, the effect of snow is minimal as compared to atmospheric circulations, for example (Stieglitz et al. 2001).
GCMs can be run for centuries, so computational time efficiency is the most important reason for employing simplistic snow physics.
1.4.2 Snow Model Types
Snow models can be categorized by the methods they use to approximate energy exchanges (Anderson 1976). Energy balance models consider snow to be the control volume where the flux sums at both upper and lower level surfaces must balance by the energy rate change in the snowpack (Grundstein 1996). Such models calculate melt based on the radiative, turbulent, and ground heat fluxes as well as advected heat by rainfall,
dE TE = I + I + I + I + I + I − (1.1) IR s lat sen g conv dt
where TE is the total energy available for melt, I IR is the net surface longwave radiation,
I s is the net surface shortwave radiation, I lat is the latent heat flux, I sen is the sensible
9 heat flux, I g is the ground or soil heat flux, I conv is heat advected by rain, E is the snowpack internal energy, and t is time. For such models, the upper and lower surface
flux sums must be balanced by the rate that energy changes within the snowpack.
Simple empirical index models such as Martinec et al.’s (1994) snowmelt runoff
model are practical for runoff quantity expected to appear at a downstream point in a
river (Williams et al. 1999). Several variables are commonly used: air temperature, wind
speed, or insolation. Williams and Tarboton’s (1999) ABC model uses snowmelt
measurements, while others such as Zuzel and Cox (1975) use vapor pressure, net
radiation, and wind speed.
Appropriate model type selection depends on location, accessible data, vegetation
cover, relief, and local or regional climate conditions (Anderson 1976). Energy balance
models perform better in areas susceptible to great seasonal meteorological variability
while index models perform better in areas with little meteorological or climatological
variability. However, local impacts such as relief, slope, and aspect can affect local
variability, making sufficient and available data an important determination.
1.4.3 Complex One-Dimensional Snow Models
SNTHERM is a sophisticated, highly validated, widely used and available point
snow model that has been applied to many different regions and in many different studies
(Jin et al. 1999, Jordan 1991, Jordan et al. 1996, Gustafsson et al. 2001, Cline 1997,
Grundstein et al. 1996, Grundstein et al. 2001, Rowe et al. 1995). Jordan et al. (1991)
developed this one-dimensional energy and mass balance snow model building upon
Anderson’s (1976) snow model. SNTHERM utilizes a variety of micro-processes that all
affect the snowpack energy balance. Surface energy fluxes are calculated for each time
10 step while energy, mass, and momentum are distributed through the snowpack based on the net fluxes of those same variables. New snow density is calculated as a function of temperature, meltwater drains by gravity rather than by the commonly implemented layer holding capacity, and water vapor is allowed to move along the temperature gradient (Jin et al. 1999).
SNTHERM lacks vegetative effect parameterizations and terrain effect algorithms, which cause it to be limited to homogenous vegetation and minimal relief regions. However, vegetative and terrain effects are not widely understood because they vary spatially, temporally, and orographically.
Cline (1997) showed that SNTHERM seemed to represent snowpack internal energy and mass exchange processes correctly, although stated that further model examination was needed during very stable conditions due to large turbulent exchange flux deviations. Jin et al. (1999) demonstrated that SNTHERM more closely represented snowpack processes than the SAST model.
Brun et al. (1989) developed the first sufficiently reliable snow model used for operational avalanche forecasting. Named CROCUS, this model accounts for slope, orientation (aspect), air temperature, wind speed, humidity, cloud cover, and snow albedo. CROCUS, like SNTHERM, has no vegetative parameterizations and limited terrain features. Slope and aspect are used for radiation calculations. The CROCUS model has been widely validated (Brun et al. 1989; Brun et al. 1992; Brun et al. 1997) and shown to accurately model the different phenomena that affect the snow pack.
CROCUS parameterizes a new snow layer for each snowfall, with a maximum of 50 snow layers. This causes problems simulating snow metamorphosism, mainly snow layer
11 settling. However, it is common to have 50 annual snowfall events in mountainous areas, making the model suitable for such terrain. Also, CROCUS is useful for avalanche forecasting where snow layer instability can trigger avalanches.
Lynch-Stieglitz (1994) developed a three-layer energy and mass balance snow model that accounts for snow melting and refreezing, snow density, snow insulating properties, snow albedo, and growth and ablation of the snowpack. Each layer has a volumetric water holding capacity, meaning that generated meltwater will remain in the layer if the liquid water content is less than the holding capacity (Stieglitz et al. 2001).
Meltwater will either flow down to a lower layer and refreeze, remain liquid in that layer, or pass through that layer (Stieglitz et al. 2001).
Stieglitz et al. (2001) coupled the Lynch-Stieglitz model (1994) to the National
Aeronautic and Space Administration’s (NASA) Seasonal to Interannual Prediction
Project (NSIPP) model, a catchment-based LSM, in order to better model soil moisture variability. Furthermore, since the Lynch-Stieglitz (1994) model has vegetative and orographic limitations such as canopy interception and other vegetative interactions, aspect, topography, and wind effects on surface energy fluxes, this coupling accounts for vegetation, with future developments attempting to solve wind and elevation issues.
Sun et al. (1999) developed an energy balance model attempting to simplify
SNTHERM to describe snow cover variations over wide regions. The SAST model retains many of SNTHERM’s processes, including the three snow compaction processes: metamorphosism, weight, and melting-refreezing. However, it simplifies the snow layering to three and changes the treatment of liquid water from gravitational flow to the
12 water-holding capacity concept, very similar to the CROCUS and Lynch-Stieglitz models.
The SAST model is understandably limited since snow grain growth and size changes, wind effects, canopy interception, and other vegetative interactions, as well as heat advection by rainfall, are neglected. Similarly, dry air and vapor components within a snowpack are neglected and 0 ºC liquid water is assumed to have no heat content.
Assuming no heat content simplifies the representation of meltwater and treats the melting and refreezing processes more easily. However, Jin et al. (1999) demonstrated that a model such as the SAST, with at least three snow layers, can closely model snow processes similar to those of a more complicated model like SNTHERM.
1.4.4 Simple One-Dimensional Snow Models
Some snow models are designed for simplicity and efficiency or for specific applications. Williams and Tarboton (1999) developed the ABC energy balance model to simulate basin snowmelt from data generated synthetically by the Utah Energy Balance
(UEB) model. Real-time snowmelt measurements are incorporated by interpolating basin melt and runoff from a Digital Elevation Model (DEM). The model assumes uniform snow albedo as well as no snow albedo changes across the watershed. Similarly, snow temperature, atmospheric and snow emissivities, relative humidity, wind speed, and air density are all assumed spatially homogenous. The effect of wind spatial variability is acknowledged as serious but ignored since it is difficult to quantify. Neither Snow Water
Equivalent (SWE) spatial variability nor snow accumulation can be modeled because observed melt depth over a time step is assumed to be greater than zero, so melt is always occurring. Additionally, grain growth and size changes, metamorphosism, heat advection
13 by rainfall, canopy interception, and other vegetative effects are neglected. The model is simple and specific in design, yet physically based, for estimating a small watershed basin’s snowmelt spatial distribution.
1.5 General Circulation Models and Mesoscale Models
Numerical models are complex computer programs that mathematically attempt to visualize or describe the atmosphere, ocean, or land surface by means of a numerical evaluation of an algorithm utilizing relevant physical laws. Numerical modeling has become an important tool in modern science because there are many applications in which numerical model output may be useful; prediction of the future or past, using real data for events that are already analyzed, or performing experiments that should not be done in the environment, 10x CO2 for example. Additionally, these models allow for separation out of the physics from any simulated result, meaning that why a model simulates a specific variable can be analyzed.
GCMs have existed since the 1950’s and have simulated atmospheric processes to a high quality level (Foster et al. 1996). GCMs attempt to predict climatic changes resulting from slow boundary condition or physical parameter changes. GCMs account for topography, cloud physics, radiation, ocean dynamics, spatial coverage, stability, et cetera. These models can be run for many years independent of data, or long enough to statistically learn about the climate, and they are very sensitive to small surface or radiative changes resulting in stability issues. The boundary condition submodels need a high degree of reliability without new data input. It is also important that these submodels are not overly sensitive to processes that GCMs simulate poorly, such as clouds and precipitation, relative to other fields.
14 Nearly all GCM snow schemes make simplistic parameterizations for ablation and accumulation. GCMs, however, do not include realistic snow accumulation, ablation, metamorphosism, snow crystal shape or grain size, size changes or impurity levels, nor is consideration given to vertical temperature profile within the snowpack, advected heat by rainfall, or meltwater evaporation and refreezing within the snowpack (Brun et al. 1997;
Marshall et al. 1999).
GCM snow scheme performance has been lacking due to reliance on simple snow physics that only account for air temperature, snowcover insulating properties, radiative fluxes, albedo, temporal and spatial variability, and turbulent fluxes (Marshall et al.
1999). Most of these characteristics have great impacts on snow albedo, which affects snow surface radiation budgets and turbulent exchange fluxes that impact snow- atmosphere feedbacks (Marshall et al. 1999). In many instances, GCMs adopt simple snow physics because coupling them to complex snow models dramatically increase computer time and running costs (Marshall et al. 1994).
An alternative approach is to utilize a mesoscale model and focus resolution on a specific region. Mesoscale models differ from GCMs because of sufficiently higher vertical and horizontal resolutions and are therefore run over smaller grid areas whereas
GCMs can be run globally. They also differ because mesoscale models work well when conditions change rapidly in time and space.
MM5 is a highly validated, widely implemented, and available mesoscale model making it an ideal candidate for this study. The Mesoscale Model series was created by
Richard Anthes at PSU in the early 1970’s and was modified at NCAR in the late 1970’s to produce MM0. Since the 1970’s, versions were released every five to ten years as
15 atmospheric understanding and numerical abilities increased (MM1-5). Each new version was designed to broaden its usage. The multiple-nesting capability allowed up to three nested domains to have influence on the focused region and to run from global scale down to cloud scale. Non-hydrostatic dynamics allowed the model to have a high spatial resolution, and additional physics options permitted modelers to utilize varying precipitation physics, cumulus parameterizations, microphysics schemes, planetary boundary layer parameterizations, surface layer parameterizations, and atmospheric radiation schemes.
Although large atmospheric models simulate snow well enough to obtain results that resemble observations, Marshall et al. (1994) and (1999) indicate that more realistic snow modeling is crucial for accurate global climate simulations, especially since snow cover influences mainly the high latitudes where global warming is projected to be dominant.
1.6 Research Objectives
This study compares SNTHERM to the NOAH LSM snow sub-model of MM5.
SNTHERM and other point snow models, including CROCUS or the Lynch-Stieglitz, simulate snow processes in a detailed manner (Brun et al 1997, Foster et al 1996, Liston et al 1999, Marshall et al 1994, Slater et al 1998, Stieglitz et al 2001, and Yang et al
1999). Conversely, large models such as GCMs or mesoscale models do not model snow with as much detail. No study has compared a point snow model to a mesoscale model, making this research unique. I will assess the value of using simplified snow physics in a mesoscale model and whether a more detailed model, such as SNTHERM, would be
16 worth the additional computational complexity if such a model were implemented as the snow cover model in a mesoscale model.
This study will focus on the Northern Great Plains of the United States for three reasons: the Northern Great Plains have extensive areal winter snow cover, relatively homogenous grassland vegetation with minimal slope, aspect, and relief, and the Great
Plains have an array of snow cover monitoring stations.
17 Chapter 2: SNTHERM
2.1 Introduction
SNTHERM’s main objective is surface temperature prediction, but temperature profiles within snow strata and frozen soil, snow accumulation and ablation, freeze-thaw cycles, liquid water and water vapor transport, densification, and metamorphosis are also calculated. Water flow within the soil substrate is discounted and artificially drained when infiltration reaches the snow/ground interface (Jordan 1991).
The modeled system is subdivided into snow and soil layers composed of ice, liquid water, dry solids, and water vapor, each governed by the heat flow and mass balance equations (Jordan 1991). The snowpack and underlying soil are horizontally subdivided into finite control volumes, each solved using an approach by Patankar
(1980), whereby the mass, momentum, and energy conservation equations are solved for each control volume (Jordan 1991). A Crank-Nicolson weighting scheme manages temporal aspects in which equal weights are given to past and current periods. The model time step, for numerical efficiency, varies between user-defined maximum and minimum values to achieve specific accuracy levels. A central difference and upwind scheme are used for numerical approximations of diffusive and convective processes respectively.
The model requires, as input, atmospheric temperature, relative humidity, wind speed, and precipitation. Solar and infrared radiation fluxes or cloud fraction and type are also needed, but the model can estimate radiation data from cloud fraction and type, if data are not available. The model must also be given initial temperature and water content profiles for the snow and soil layers. An internal setup file contains physical
18 properties for snow, sand, and clay, of which the user can customize particular characteristics.
2.2 Conservation Equations
Heat and fluid flow within the snow and soil layers are governed by the mass, momentum, and energy conservation equations. The solution is obtained by subdividing the snow and soil layers into finite control volumes. Within every finite control volume, the time rate of change must equal the sum of the net flow across the boundary plus the internal production rate (Jordan 1991). A conservation equation for the change in density as related to the water mass flux and internal energy production, expressed in integral form is
∂ γ Ω = − ⋅ + ρ k dV J dS source dV ∂ ∫ ∑∫S ∫V t k (2.1) where k is an index for ice (i), liquid (l), or vapor (v), γk is the partial or bulk density denoting the mass of water vapor, liquid water, ice, air, or dry soil per unit volume of each component, Ω is the water component (i,l,v) being conserved, S is the control
ρ surface, dV is the incremental control volume thickness, source is the source density or internal production term and is considered homogenous over ∆V, and J represents the
γ -3 mass fluxes of i, l, or v. For snow, k generally ranges from 50 to 480 kg m , with lower values for fresher snow because of more air within the pore spaces. The overbars indicate temporal averages over the time step (∆t).
The one-dimensional mass balance equations for snow, ice, liquid water, and water vapor is given by
19 ∂ ρ dz = − J (2.2) ∂ ∫ snow ∑∑ k t kS=i,l ,v
and
∂ γ dz = − J + M dz ∂ ∫ k ∑∑ k ∑∑∫ kk ' t kS=i,l ,v kk=≠i,'l,v k (2.3)
ρ where snow is the snow density, dz is the incremental volume thickness, and ∑ S is a
summation over the top and bottom surfaces of the control volume . The variable δkk’ is the Kronecker delta, defined as having a value of 1 when i = j and 0 otherwise, and Mli,
Mvi, and Mvl are the mass rates of melt, sublimation, and evaporation respectively (Jordan
1991). Because the mass of air is less than 1% of the total mass within snow, the snow
ρ γ γ γ density s and the bulk density k of combined liquid water and ice constituents ( i + i) are nearly equal in magnitude (Jordan 1991).
Air is considered to be stagnant and incompressible throughout the pore spaces; therefore, its effect on water flow within the soil matrix is neglected. So, the vapor flux
term ( J v ) is driven solely by diffusion, and if the air is saturated, the vapor flux can be
calculated using Frick’s Law
∂ρ ∂ρ ∂T J = −D v,sat = −D v,sat (2.4) v e ∂z e ∂T ∂z
ρ where v,sat is the water vapor density at saturation, De is the diffusion coefficient for
vapor flow through snow, and T is temperature (Jordan 1991).
Liquid water flow through snow is governed by Richards’ equation. Because
capillary forces within snow are much smaller than those of gravity, they are neglected
and the equation simplifies to include only gravity
20 κ U = − l ρ 2 g (2.5) l µ l l
µ ρ κ where l is the dynamic water viscosity, l is the capillary pressure, and g is gravity. l is the hydraulic permeability, a measure of the ease and rate at which liquid water is transmitted by a medium, such as snow, and is expressed in terms of the effective liquid
saturation ( se ), given by
s − s s = r e 1− s r (2.6) where s is the liquid water saturation and sr is the minimum liquid water level to which a snow cover can be drained, and critical in determining infiltration rates and the
κ equilibrium water content (Jordan 1991). Using se , l can be estimated from a formula by Brooks and Corey (1964)
κ = ε l kmax se (2.7) where kmax is the saturated permeability, computed by Shimizu’s formula (1970), and ε is a function dependent upon pore size (Rowe et al. 1995).
Fluid flow assumes horizontal homogeneity in the snow cover. Ephemeral snow covers undergoing freeze-thaw cycles or that are subject to strong winds, develop ice layers and crusts, complicating the flow pattern (Jordan 1991). During such conditions, water flows through perforations in the crusts, transporting water at a much faster rate than through the horizontal crust itself. SNTHERM does not account for this.
Once fluid flow and adjusted mass balances have been computed, the heat balance equation can be solved. Snowpack heat energy changes in response to energy
21 transferred through mass fluxes, conduction, and radiative exchanges (Grundstein 1996).
The conservation of energy is given as
∂ ∂T ρ h dz = − J h + κ − I (2.8) ∫ snow snow ∑∑k k ∑snow ∑ net ∂t kS=l,v S∂z S
where hsnow is the specific enthalpy of snow with respect to the melting temperature, Tm
(273.15 K), hk are the specific enthalpies of liquid water (l) and water vapor (v)
κ respectively, snow is the thermal conductivity of snow, and I net is the net radiation.
Specific enthalpy, for an isobaric system, is the amount of heat energy required to raise or lower the temperature to Tm from T0 and is written as
Tm h = ∫ c(T)dT + L (2.9) Tabs
-1 -1 -1 where Tabs is absolute zero (0.0 K) and c (J kg K ) and L (J kg ) are the specific and latent heats respectively (Jordan 1991).
Within control volumes where phase changes are occurring, the apparent heat capacity method devised by Albert (1983) is used. Sensible and latent heat changes are combined to create an apparent specific heat (capp)
∂f θ ∂ρ c = c + L l + L v v,sat (2.10) app snow i ∂ v γ ∂ T li T
where csnow is the specific heat of the snow medium, Li and Lv are the latent heats of
θ γ fusion and sublimation, v is the water vapor fractional volume, and li is the combined
partial bulk densities of liquid water and ice. The unfrozen water fraction ( fl ) is given as
γ 1 f = l = l γ 1+ (a T ) 2 li 1 D (2.11)
22 where TD is the temperature depression given as Tm – T and a1 is an empirical constant
(Rowe et al. 1995).
2.3 Surface Energy Balance
The surface energy balance is composed of the sensible and latent heat fluxes, shortwave and longwave radiation, and snow or rainfall heat convection. The net surface
energy budget ( I top ) is expressed by the following equation
↓ ↓ ↑ I = I (1−α ) + I − I + I + I + I top s top IR IR Sen Lat Conv (2.12)
↓ where I top is the net surface energy at the snow/air interface, I s is the downwelling
α ↓ ↑ shortwave radiation, top is the top layer albedo, I IR and I IR are the downwelling and upwelling longwave radiation components, ISen and ILat are the sensible and latent heat fluxes, and IConv is the heat convected by falling rain or snow (Jordan 1991). Contrary to the convention in atmospheric modeling, these surface fluxes are positive downwards.
The magnitude of convective fluxes depends on the surface roughness length, wind speed, atmospheric temperature, and relative humidity (Jordan 1991).
Surface solar absorption depends on surface snow properties such as albedo and grain diameter. Insolation is initially assumed to be diffuse and invariant with respect to direction (isotropic). It is subdivided into near-infrared and visible components with
β β β corresponding bulk extinction coefficients ( nir and vis ). For vis , the asymptotic bulk
extinction coefficient β ∞ is calculated by the function of Bohren and Barkstrom (1974) as
γ c1 k β ≈ β ∞ = (2.13) vis d
where c1 is an adjustable parameter taken from Anderson (1976), set at
23 0.003795 kg-1 m5/2 (Jordan 1991), and d is the grain diameter.
Downwelling solar radiation is estimated using the Shapiro (1987) model, which segments the atmosphere into three levels, corresponding to low, middle, and high cloud heights and is given by
↓ τ τ τ I (z) = 1 2 3 I s D s00 2 (2.14)
τ τ τ where 1 , 2 , and 3 are atmospheric transmissivities at the three different levels, D2 is a transmission and reflectance constant, and Is00 is the insolation at the top of the atmosphere (Jordan 1991).
Soil albedo is set as a constant of 0.40, while the snow albedo is either set as a constant of 0.78, or computed using the Marshall and Warren (1987) or Marks (1988) algorithm. The equation parameterizes the snow spectral albedo into near-infrared and visible components and then estimates albedo changes as a function of grain size and solar zenith angle. Snow cover impurities and snow cover thickness are neglected in the computation of the snow albedo.
The net longwave radiation consists of upwelling thermal radiation from the
Earth’s surface and downwelling emitted radiation from the atmosphere. The emitted upwelling longwave flux at the Earth’s surface follows the Stefan-Boltzmann equation.
The reflected component is proportional to the downwelling flux and the surface albedo.
According to Kirchoff’s law, good absorbers are also good emitters, so the emissivity and reflectance must sum to 1.0, resulting in the following equation for upwelling longwave radiation
↑ = ε σ 4 + − ε ↓ IIR b Ta (1.0 )IIR (2.15)
24 ε σ where is the surface emissivity, and b is the Stefan-Boltzmann constant set as
5.67 × 10-8 W m-2 K-4 (Jordan 1991). Based on comparisons between measured radiation and estimates from the Stefan-Boltzmann law, emissivity for snow is suggested as 0.97
(Jordan 1991).
The downward longwave radiation under clear sky conditions is calculated using the Idso (1981) formula for clear-sky emissivity
c4 ε = σ c + c × P e Ta (2.16) air b 2 3 v,air
-5 -1 in which c2 is a dimensionless constant set to 0.70, c3 is set at 5.95 × 10 mb , c4 is
1500 K, and Pv,air is the water vapor pressure at the gauge height for relative humidity
(Jordan 1991). Equation 2.16 tends to overestimate the emissivity, and is corrected by the Wachtmann correction (Jordan 1991).
ε ' = − + ε − ε 2 air 0.792 3.161 air 1.573 air (2.17)
An additional downwelling longwave radiation component is computed for cloud cover emittance, and no correction is included for sloped surfaces, which can receive additional diffuse radiation from the adjacent terrain, even though less sky is visible (Jordan 1991).
25 Chapter 3: MM5
The following chapter provides a brief description of the MM5 model system components, general equations, and model physics. A more detailed description can be found in Dudhia (1993) and Grell et al. (1994) for MM5 and Chen et al. (2001) for the
NOAH LSM.
3.1 Model System Components
MM5 requires many pre-processing programs (Figure 3.1), but only TERRAIN,
REGRID, RAWINS, INTERPF, and MM5 are needed for this study.
Figure 3.1: The MM5 system including all pre-processing programs and data input options. Taken from NCAR/Mesoscale and Microscale Meteorology (MMM).
TERRAIN configures the mesoscale domains and interpolates latitude and longitude terrain elevation to the mesoscale grid (Figure 3.2). See pages 81-82 of Guo
26 and Chen (1994) for a more detailed description. TERRAIN also calculates constant fields such as latitude and longitude, a map scale factor, and the Coriolis parameter. The map scale factor is ideally as close to one as possible, to limit distortion. TERRAIN requires specific input data including elevation, land use categories, vegetation type, land-water mask, soil categories, vegetation fraction, and deep soil temperature. All data comes from the United States Geological Survey (USGS) global data set, but only the study area grids were used. The data sets are available at 30 second, and 2, 5, 10, 30, and
60 minute resolutions, with 10 and 5 minute resolutions used for Domains 1 and 2 respectively.
Figure 3.2: 16 point, two-dimensional parabolic interpolation scheme. Taken from NCAR/MMM.
REGRID creates the first-guess meteorological fields on the MM5 grid. It reads archived or real-time global or regional meteorological analyses or forecasts and interpolates pressure and surface levels to the horizontal MM5 grid. Typically, reanalysis data are used as the archived standard, while ETA and AVN model analyses or forecasts are used as the real-time standard.
27 RAWINS improves the first-guess gridded analysis from REGRID by incorporating additional observational information and reading radiosonde and surface report observations. RAWINS uses a Cressman-based objective analysis technique, with ellipse and banana extensions, or a multi-quadric analysis. This study uses the Cressman- based banana extension because when RAWINS analyzes wind and relative humidity at pressure levels, the circles from the standard Cressman scheme are elongated in the direction of the flow and curved along the streamlines, resulting in a banana shape. This scheme reduces to the Ellipse scheme under straight flow conditions and the standard
Cressman scheme under low wind conditions (Figure 3.3). See Cressman (1959) for a more detailed description.
Figure 3.3: Cressman-based banana extension objective analysis interpolation scheme in which the arrows indicate the flow direction and the dots are parcels. Taken from NCAR/MMM.
INTERPF calculates surface pressures, vertically interpolates variables to sigma surfaces, and initializes the non-hydrostatic dynamics by linearly interpolating, in the z direction, from hydrostatic sigma levels to non-hydrostatic sigma levels. All vertical interpolations are linear, using pressure or the logarithm of pressure.
28 MM5 is the dynamic model that performs the time integration, implements the dynamics (compressible, non-hydrostatic, terrain following), numerics (temporal finite differencing using second order leapfrog time scheme and second order centered space scheme), and physics (cumulus parameterizations, planetary boundary layer, explicit moisture, microphysics, radiation, and land and water surface schemes).
3.2 General Equations
MM5 is based on a fully compressible atmosphere expressed in the vertical sigma
(σ ) terrain-following coordinate system.
− pσ ptop σ = (3.1) p*
where σ varies from 1.0 at the surface to 0.0 at the top, pσ is the reference-state pressure defined for each vertical level, and p* is the difference between the pressure at the top of the atmosphere (ptop), set at 100 kPa, and the surface (Figure 3.4).
Figure 3.4: Schematic representation of the model vertical structure. The example is for 15 vertical sigma levels. The dashed lines are half-sigma levels, whereas the solid lines are full-sigma levels. K is the sigma level number. Taken from NCAR/MMM.
29 Table 3.1: List of the 23 sigma levels and corresponding values for this study.
σ level σ value 1 0.00 2 0.05 3 0.10 4 0.15 5 0.20 6 0.25 7 0.30 8 0.35 9 0.40 10 0.45 11 0.50 12 0.55 13 0.60 14 0.65 15 0.70 16 0.75 17 0.80 18 0.85 19 0.89 20 0.93 21 0.96 22 0.98 23 0.99 24 1.00
While MM5 can have between 10 and 40 σ levels (Grell et al. 1994), this study uses 23 (0-22), with level 22 (1.0) occurring at the surface and level 0 (0.0) occurring at the top of the atmosphere (Table 3.1). MM5 utilizes a pressure perturbation variable ( p') rather than the full pressure and it is defined as
= + p(x, y, z,t) ps (z) p'(x, y, z,t) (3.2)
where p' is the deviation from a constant, elevation dependent, surface pressure ( ps ).
General governing equations for atmospheric motion represent the most basic physics behind MM5. There are seven prognostic equations that are solved for the horizontal and vertical momentums, pressure, temperature, advection, and divergence.
30 The equations for horizontal and vertical momentum are given by
∂u m ∂p' σ ∂p * ∂p' ∂m ∂m uw + − = −v ⋅∇u + v f + u − v − ewcosα − + D (3.3) ∂ ρ ∂ ∂ ∂σ ∂ ∂ u t a x p * x y x rearth
∂v m ∂p' σ ∂p * ∂p' ∂m ∂m vw + − = −v ⋅∇v − u f + u − v − ewsinα − + D (3.4) ∂ ρ ∂ ∂ ∂σ ∂ ∂ v t a y p * y y x rearth
∂w ρ g ∂p' g p' p T' gR p' u 2+v2 − 0 + = −v⋅∇w+ g 0 − d + e(ucosα − vsinα) + +D (3.5) ∂ ρ ∂σ γ w t a p * r p pT0 c p p rearth where m is the map scale factor, u and v are the east-west and north-south components
∧ ∧ ∧ and w is the vertical component respectively, v is velocity defined as v = u i+ v j+wk ,
f = 2Ωsinλ and e = 2Ωcosλ are for the horizontal and vertical Coriolis parameters
λ γ where is latitude, r is the ratio of the heat capacities for dry air, rearth is the radius of the earth, α is the rotation angle of the grid, given as φ - φc, where φ is longitude and φc is the central longitude, and D is the diffusion tendency.
The pressure equation is given by
∂p ' γ p − ρ gw + γ p∇ ⋅v = −v ⋅∇p ' + r (3.6) ∂ 0 r t Ta
The thermodynamic equation for temperature is given by
∂T 1 ∂p' Q T = −v ⋅∇T + + v ⋅∇p'−ρ gw + + 0 D (3.7) ∂ ρ ∂ 0 Θ Θ t cair t cair 0
where DΘ is diffusion of potential temperature, T0 is a reference state temperature, and
-1 -1 cair is the specific heat of air at constant pressure (1004.5 J kg K ). The term in the parentheses is the adiabatic warming term and the Q term is the diabatic warming term.
31 The advection terms can be expanded as
∂A ∂A . ∂A v ⋅∇A ≡ mu + mv + σ ∂ ∂ ∂σ x y (3.8)
where
. ρ g σ ∂p * σ ∂p * σ = − 0 w − u − v (3.9) p * p * ∂x p * ∂y
The divergence term can be expanded as
∂ u mσ ∂p * ∂u ∂ v mσ ∂p * ∂v ρ g ∂w ∇ ⋅v = m2 − + m2 − − 0 ∂ ∂ ∂σ ∂ ∂ ∂σ ∂σ x m p * x y m p * y p * (3.10)
3.3 Cloud Schemes
MM5 utilizes cumulus schemes to represent sub-grid scale vertical fluxes, convective rainfall-producing column moisture, temperature tendencies, and surface convective rainfall. There are eight varying cumulus parameterization schemes including none, Anthes-Kuo, Grell, Arakawa-Schubert, Fritsch-Chappell, Kain-Fritsch, Betts-
Miller, and Kain-Fritsch 2. This study utilizes the Kain-Fritsch 2 scheme because its sophisticated cloud-mixing scheme accounts for both shallow and deep convection, making it better able to resolve convective precipitation (Figure 3.5). See Grell et al.
(1991), Grell (1993), Dudhia (1993), or Kain (2002) for a more complete cloud scheme description.
32 Figure 3.5: Illustration of the cumulus process for MM5, in which the arrows represent explicitly modeled processes. Taken from NCAR/MMM.
3.4 Precipitation Schemes
To resolve precipitation processes, microphysics (explicit moisture) schemes provide tendencies of temperature, all moist variables, and surface non-convective rainfall. Additionally, cloud information is passed to and used by the radiation schemes.
Eight different microphysics schemes including dry, stable precipitation, warm rain
(Hsie), simple ice (Dudhia), mixed-phase (Reisner 1), Goddard microphysics, Reisner 2
(graupel), and Schultz are available. This study utilizes the Schultz scheme because it has the same processes as the simple ice scheme and also accounts for cloud ice and snow, supercooled water, and it has gradual snow melt as it falls.
3.5 Radiation Schemes
Radiation schemes represent radiative effects, both in the atmosphere and at the surface. MM5 has five radiation schemes including none, simple cooling, cloud
33 radiation, CCM2 (Community Climate Model 2) radiation, and RRTM (Rapid Radiative
Transfer Model) longwave radiation. The latter three have cloud effects on insolation and downwelling longwave radiation. This study utilizes the RRTM scheme because it provides atmospheric radiative effects due to modeled clouds and uses a sophisticated look-up table scheme for longwave radiation (Figure 3.6). Additionally, the treatment of planetary boundary layer physics uses the Hong and Pan (1996) scheme.
Figure 3.6: Free atmosphere radiation processes illustration in which the arrows represent explicitly modeled processes. Taken from NCAR/MMM.
3.6 Surface Schemes
Surface schemes represent land and water surface effects, provide latent and sensible heat fluxes, sub-soil temperature and moisture profiles, as well as snow cover tendencies and surface moisture availability. Figure 3.7 illustrates the surface processes, and shows the simplistic slab treatment of snow.
34 Figure 3.7: Surface processes illustration in which the arrows represent explicitly modeled processes. Taken from NCAR/MMM.
3.7 Model Setup
MM5 was run over the upper Great Plains using two nested domains (Figure 3.8).
The outer domain (hereafter D1) was run at a 75 km resolution with central latitude of
44.8°N and central longitude of 100.0°W. The grid was 35 points in the east-west direction and 30 points in the north-south direction. The inner domain (hereafter D2) was run at a 25 km resolution and the grid was 28 points in the east-west direction and 40 points in the north-south direction. While it is important to have D2 influenced by D1, only the D2 output data was used in this study, to improve the resolution. The D2 output data represents a grid box average value. Because point observations are being compared to a 25 km by 25 km average grid box value, there will be some sub-grid scale variability that will not be resolved.
35 Figure 3.8: The physical extent of Domain 1 (D01) and Domain 2 (D02).
The model was run from December 1999 until April 2005, skipping May through
October, since there is little or no snow during those months. Six grid cells (Figure 3.9) were chosen to compare to the first-order NWS station observations at Bismarck, and
Williston in North Dakota; Sioux Falls, and Huron in South Dakota; Scottsbluff and
North Platte in Nebraska, respectively.
36 Figure 3.9: MM5 domain two grid and the six selected cities in the upper Great Plains.
37 Chapter 4: Model Snow Physics
The following chapter provides a detailed comparison of the snow physics of the
MM5 coupled NOAH LSM model system and SNTHERM. For more detailed information about specific processes consult Chen et al. (2001) for the NOAH LSM and
Jordan (1991) for SNTHERM.
4.1 NOAH LSM Snow Model Introduction
MM5 utilizes a simplistic one-layer snow model that simulates accumulation, sublimation, ablation, and heat exchanges at the snow-atmosphere and snow-soil interfaces. Metamorphosis and grain growth over time are not considered. This simplistic approach results from having a very detailed and computationally expensive atmospheric model, meaning that some processes must be simplified for numerical efficiency. However, because atmospheric models are run with short time scales, surface conditions do not change much, making it difficult for atmospheric models to accurately simulate surface conditions, such as snowcover changes.
This study uses MM5 coupled to an interactive LSM called the NOAH LSM. The
NOAH (National Centers for Environmental Prediction (NCEP), Oregon State
University, Air Force, and Hydrologic Research Lab) LSM gives four-layer soil temperature, moisture and water, surface runoff, underground runoff, canopy moisture, water-equivalent snow depth, snow depth, ground heat flux, and surface albedo (Figure
4.1). The NOAH LSM requires additional inputs of soil texture, mean annual surface temperature, seasonal vegetation fraction, and initial soil temperature and moisture
(Figure 4.2).
38 Figure 4.1: NOAH LSM diagram depicting all modeled or parameterized processes including radiation, turbulent exchanges, and atmospheric forcings. Taken from NCAR/MMM.
Figure 4.2: The MM5 modeling system flow chart with input and output data from the NOAH LSM. Taken from NCAR/MMM.
39 Similar to the MM5 snow model, the NOAH LSM accounts for accumulation, sublimation, ablation, and heat exchanges at the snow-atmosphere and snow-soil interfaces. Metamorphosis and grain growth over time are also not considered.
However, a variable thermal conductivity, snow density, and snow albedo are calculated, leading to a better representation of the snowpack than the MM5 uncoupled model system (Chen et al. 2001).
4.2 Precipitation Rate
Because MM5, as well as the NOAH LSM, treat snow as a slab, each snow event adds to the pre-existing snowpack, modifying one uniform snow layer. This leads to a less accurate representation at the snow-ground and snow-atmosphere interfaces.
Accumulation for both the NOAH LSM and SNTHERM are simply the precipitation rate multiplied by the time step.
The NOAH LSM and SNTHERM precipitation rates are calculated from the input precipitation of rain or snow. For SNTHERM, the input precipitation is corrected for wind effects, surface roughness length, and gauge height. The undercatch correction for snow is given by
1.0 P = P * exp(0.0055 − 0.133* ws ) storm (4.1) and for rain as
1.0 P = P * (4.2) − 1.0 0.02* wsstorm where P is the input precipitation in m, the constants -0.133 and -0.02 have units of
-1 -1 s m , and wsstorm is the storm average wind speed during a precipitation event in m s .
This leads to the calculation of the snow and rain precipitation rates given as
40 (1.0 − fl ) P = P * fall (4.3) snow 3600.0 and
fl P = P * fall (4.4) rain 3600.0
where flfall is the fraction of liquid water within falling precipitation, varying from 0% at
273.15 K to 40% at 275.15 K.
4.3 Snow Albedo
The NOAH LSM snow albedo is calculated by
α = α + − − α − α snow land (1.0 ( fgreen f min )) * fsnow *( max land ) (4.5)
where fgreen is the areal fractional coverage of green vegetation, fmin is the minimum
α areal fractional coverage of green vegetation, max and is the maximum deep snow albedo taken from the satellite-based maximum snow albedo fields provided by Robinson
(1985).
SNTHERM uses a variable albedo algorithm for snow cover that is either set at
0.78 or computed using the Marshall and Warren (1987) or Marks (1988) algorithms.
This study uses the Marshall and Warren (1987) algorithm. The equation parameterizes the snow spectral albedo into near-infrared and visible components and then estimates albedo changes as a function of grain diameter and solar zenith angle given by
α = α + − α snow f vis * vis (1.0 f vis )* NIR (4.6)
where fvis represents the approximate breakdown between visible and near infrared
α α radiation and vis and NIR are the visible horizontal albedo and near infrared albedo approximated by
41 α = − + [ − − ] vis 0.95(1.0 0.2 f age ) 0.4 cos z 1.0 0.95(1.0 0.2 f age ) (4.7) and
α = − + [ − − ] NIR 0.65(1.0 0.5 f age ) 0.4 cos z 1.0 0.65(1.0 0.5 f age ) (4.8)
where fage is the snow age factor, dependent upon grain diameter, and z is the solar zenith angle.
4.4 Thermal Conductivity
Thermal conductivity is a function of snow age and snow density, with typical values ranging from 0.08 W m-1 K-1 for fresh snow to 0.42 W m-1 K-1 for old snow. The
NOAH LSM values range from 0.05 to 4.04 W m-1 K-1 for newer and older, denser snow respectively (Table 4.1 and Figure 4.4). Smaller snow thermal conductivity values cause warmer ground temperatures, because air is a poor conductor, and underestimations of snow accumulation rates, because a warmer ground surface melts a portion of the falling snow. However, because the higher snow densities have thermal conductivity values more than that of ice (2.29 W m-1 K-1), caused by an exponential equation, this causes more rapid conductive cooling of the ground and subsurface.
The NOAH LSM snow thermal conductivity is calculated as
ρ κ = 0.03815*10.(0.00225 * snow ) snow (4.9) where the constant 0.03815 has units of W m-1 K-1, the constant 0.00225 has units of
-3 -3 -3 m kg , and ρsnow ranges between 50 kg m for fresh snow to 400 kg m for older snow.
Additionally, the NOAH LSM soil thermal conductivity is calculated as a function of the volumetric soil water content, given by
[− + ] ≤ 420 exp (2.7 Pf ) , Pf 5.1 κ = (4.10) soil > < 0.1744, Pf 5.1 0,
42 and
b Θ P = log ψ soil (4.11) f soil Θ
Θ ψ where soil and soil are maximum soil moisture (porosity) and saturated soil potential
(suction) respectively, both depending on soil texture. This formulation was found to overestimate (underestimate) during wet (dry) periods and therefore a cap of
1.9 W m-1 K-1 was set. This cap prevented unrealistic calculations of the surface heat fluxes, which are very sensitive to soil thermal conductivity (Chen et al. 2001) (Figure
4.3).
Figure 4.3: NOAH LSM soil thermal conductivity as a function of volumetric soil moisture for four soil types: sand, silt, loam, and clay. Taken from Chen et al. (2001).
SNTHERM calculates effective snow thermal conductivity, including vapor diffusion, from a base equation before checking the volume fraction of liquid water levels and adjusting the snow thermal conductivity. Effective snow thermal conductivity accounts for heat flow enhancements from ice layers within the snowpack, which can
43 impact snow thermal conductivity values because ice has a much higher thermal conductivity than liquid water or vapor. Therefore, SNTHERM’s effective snow thermal conductivity combines the two components, air and ice, that compose most of the snowpack.
6 2 p T dbvl ,i κ = κ + [](c * ρ + c * ρ )*(κ − κ ) +L * D * 0 * a * (4.12) snow a 5 snow 6 snow i a s 0 p T dT m a where
L c −1.0 dbv L T R l = bv *exp− c * a w (4.13) l 0 2 dT Ta Rw Ta and
L c −1.0 dbv L T R i = − c a w bvi0 *exp * dT T R T 2 a w a (4.14)
κ -1 -1 a is the thermal conductivity of air, set as a constant of 0.023 W m K , c5 is a constant
-5 3 -1 -6 6 -2 κ set at 7.75 × 10 m kg , c6 is a constant set at 1.105 × 10 m kg , i is the thermal
-1 -1 conductivity of ice, set as a constant of 2.29 W m K , Ls is the latent heat of sublimation, set as a constant of 2.838 ×106 J kg-1, if the volume fraction of liquid water is greater than 2%, or the latent heat of vaporization, set as a constant of 2.26 ×106 J kg-1, if the volume fraction of liquid water is less than 2%. D0 is the effective diffusion coefficient for water vapor in snow at 1000 mb and 273.15 K, set as a constant of
-5 2 -1 dbvl,i 9.0 × 10 m s , and p0 is a reference barometric pressure set as 1000.0 mb. is the dTa change in liquid water or ice saturation vapor density per degree K (kg m-3 K-1). Vapor
44 density is really an absolute humidity in that it represents the ratio of the mass of water vapor to the density of the water vapor. This measure is not conservative with respect to adiabatic processes of compression or expansion, and is therefore not commonly used by
dbv atmospheric scientists. The liquid water calculation l is used when the volume dT
dbv fraction of liquid water is greater than 2%, while the ice calculation i is used in all dT
dbv other instances. However, these values ( l,i ) are very, very small and are therefore dTa considered negligible. bvl0 is the vapor diffusion constant for liquid water equaling
2 -1 6 -1 657.7 m s , Lc is the latent heat of condensation set as 2.5045 ×10 J kg , Rw is the gas
-1 -1 constant for water vapor set as 461.5 J kg K , and bvi0 is the vapor diffusion constant for ice equaling 663.8 m2 s-1. The first terms in brackets represent a density flow, liquid or frozen, while the last term is the diffusion of heat based on temperature, pressure, and vapor pressure through that snow layer.
SNTHERM calculates soil thermal conductivity as a combination of dry and saturated soils multiplied by the dimensionless Kersten number given by
κ = κ + − κ soil Ke * soil_saturated (1.0 Ke ) * soil_dry (4.15) where
+ > 0.7 *log(satl ) 1.0 if course soil and Ta 273 = + > K e log(satl ) 1.0 if fine soil and Ta 273 (4.16) < satl if Ta 273 and
mvol (1.0−mvol) κ min *0.57 if T > 273 κ = a soil_saturated (4.17) κ mvol ( fl*porosity) porosity < min *0.249 * 2.29 if Ta 273
45 and
0.113 if clay κ = soil_dry (4.18) 0.184 if sand
where satl is the relative total water content of soil given as the volume fraction of liquid
mvol water plus the volume fraction of ice divided by porosity, κ min is the mineral conductivity raised to the fractional volume of dry soil material (mvol), fl is the fraction of unfrozen liquid water due to both capillary and absorbed potential, porosity is the fraction volume of voids between ice matrix in snow and between dry soil in general.
SNTHERM uses sand as the soil type and the subsequent soil thermal conductivities range from 1.0 W m-1 K-1 to 2.0 W m-1 K-1 depending on the soil water content.
Table 4.1: Snow thermal conductivity (W m-1 K-1) values for the NOAH LSM and SNTHERM for varying snow densities (kg m-3). SNTHERM thermal conductivities were calculated assuming the temperature was at 273.15 K and pressure equal to 1013.5 mb.
NOAH LSM SNTHERM ρsnow κsnow ρsnow κsnow 50.0 0.049 50.0 0.038 100.0 0.064 100.0 0.066 150.0 0.083 150.0 0.111 200.0 0.108 200.0 0.158 250.0 0.139 250.0 0.223 400.0 0.303 400.0 0.494 600.0 0.854 600.0 0.971 800.0 2.407 800.0 1.688 900.0 4.041 900.0 2.122
46 Figure 4.4: NOAH LSM and SNTHERM snow density (ρsnow) (kg m-3) versus snow thermal conductivity (W m-1 K-1).
1000.0 4.500
900.0 4.000
ρsnow 800.0 NOAH LSM κsnow 3.500 SNTHERM κsnow
700.0 )
3.000 -1 K -1 600.0 ) -3 2.500
500.0
2.000 Density (kg m (kg Density 400.0
1.500 Thermal Conductivity m (W 300.0
1.000 200.0
0.500 100.0
0.0 0.000 123456789
4.5 New Snow Density
Both the NOAH LSM and SNTHERM calculate new snow density based solely upon temperature and an equation derived by La Chapelle (1961) called the Alta function. The Alta function new snow density is set at a constant value of 50.0 kg m-3 if the temperature is below -15 ºC, calculated for temperatures between -15 ºC and 0 ºC, and set at a constant value of 150.0 kg m-3 if the temperature is above 0.12ºC. This function accurately represents new snow density because freshly fallen snow has a variable density depending on the meteorological conditions at the time of the snowfall, namely temperature. The Alta function is given by
47 ρ > snow_max Ta Tmax ρ = ρ + + 1.5 − < < snow (new) snow_min c7 *(Ta Tcut ) Tcut Ta Tmax (4.19) ρ T < −T snow_min a cut
ρ -3 ρ where snow (new) is the new snow density (kg m ), snow_max represents the empirical
-3 ρ new snow density upper limit set at 150.0 kg m , snow_min represents the empirical new
-3 snow density lower limit set at 50.0 kg m , c7 is an empirical constant set at
-3 -1 0.0017 kg m K , Ta is the air temperature (°C), Tcut is the cutoff temperature set at
15.0°C, and Tmax is another cutoff temperature set at 0.12°C.
4.6 Ablation
Ablation occurs when the snow or air temperature is above the melting temperature. The NOAH LSM ablation rate is a function of a variety of fluxes including net radiation, soil, sensible heat, total evaporation, new snow accumulation to snow surface, freezing rain, and temperature; all representative of the phase change heat. This rate does not account for any meltwater infiltration, because the snowpack is treated as a one-layer slab, leading to either further melt or refreezing; having the potential to add or remove large amounts of heat. Also, metamorphic effects are ignored. Ablation (kg m-2) is given by
= []↓ − − − σ ε 4 − − −ϑ − dt Melt I IR Fsnow Ffreez b * snow *Tskin G (rch *(Ts )) etot * (4.20) Li
where Fsnow is the heat flux from the snowpack to the newly accumulating precipitation,
ε Ffreez is the freezing rain latent heat flux, snow is the snow emissivity set at 0.90, G is the
soil heat flux, negative if downward from the surface, Tskin is the effective skin temperature which depends on the effective snow-ground surface temperature being
48 ϑ above or below freezing, is potential temperature, Li is the latent heat of fusion of ice,
5 set as a constant of 3.335 × 10 J kg-1, and etot is the total latent heat flux of both snow and non-snow given by
= + etot Esub * Ls Eevap * Lv (4.21)
-2 -1 where Esub is the sublimation (deposition) rate from (to) the snow surface (kg m s )
-2 -1 and Eevap is the evaporation (condensation) rate from (to) the snow surface (kg m s ). rch is given by
= ρ rch ch * a * cair (4.22) where ch is a surface exchange coefficient for heat and moisture (m s-1), but really a
ρ conductance since it has been multiplied by wind speed, and a is the air density.
SNTHERM’s ablation rate is a function of internal energy changes, absorbed radiation, meltwater infiltration from neighboring snow layers, and snow layer thickness changes caused by compaction. This more empirical equation leads to a better representative meltrate, because compactive and meltwater infiltration can add or remove large amounts of heat, thereby greatly impacting snowpack stratigraphy, and therefore ablation. Ablation, with no temperature change in each snow layer, is calculated by
Melt = X + Y − Z (4.23)
Term X represents the net heat input into the system during the last time step and is given by
= + X 2.0* (bb0 U n0 * hs0 ) (4.24)
49 where bb0 is the old conducted and convected heat plus absorbed solar radiation of the
snow layer, U n0 is the old net snow layer water flux , and hs0 is the old water flux enthalpy adjustment for sensible heat. The term old applies to the past time step’s value.
Term Y represents the meltwater change resulting from absorbed radiation changes and is given by
ds − ds 0.09 *((1− s ) + s + s ) Y = 0 * r 0 r (4.25) 2.0 Li
where ds is the absorbed solar radiation, ds0 is the old absorbed solar radiation, 0.09 is a dimensionless constant and represents the specific gravity ratio difference between liquid
-3 -3 water (1.0 kg m ) and ice (0.91 kg m ), s0 is the amount of liquid water in the snow
volume during the previous time step, and sr is the maximum fraction of the snow volume occupied by liquid water during the previous time step, set as a dimensionless constant of 0.07.
Term Z represents the amount of compactive change from melt and is given by
= − + + pdz Z 1000.0* ((1 sr ) s0 sr ) * dz0 * (4.26) dt compaction
pdz where dz0 is the old snow layer thickness and is the fraction rate of dt compaction change in snow layer thickness due to compaction.
4.7 Surface Energy Budget
The surface energy budget is the driving force behind snow accumulation and ablation events. Therefore, how the NOAH LSM and SNTHERM partition the surface energy budget into the turbulent exchange fluxes of sensible and latent heat, and how
50 much insolation is reflected by the albedo are critical to properly simulating the snowpack. The NOAH LSM and SNTHERM partition the turbulent exchange fluxes similarly, but it is the small differences in parameterizations that lead to large differences in output.
4.7.1 Turbulent Exchange Fluxes
The NOAH LSM sensible and latent turbulent heat fluxes are given by
chc p I = − air s (4.27) sen × ϑ − (rTv ) ( Tg / c / s ) and
= + I lat Esub et * Lv (4.28)
where Tv is the virtual temperature, Tg / c / s is the ground/canopy/snowpack effective skin temperature, and et is the amount of direct soil and canopy water evaporation as well as plant transpiration. These fluxes are defined as positive upwards.
The SNTHERM sensible and latent turbulent heat fluxes are given by
I = (E + ρ c C w)(T − T n ) sen HO a air H a (4.29) and
L = + i − n I lat (EEO CE w)(Pv,air f rh P vk,sat ) (4.30) RwTa
where EHO is the windless exchange coefficient for sensible heat that maintains some sensible heat flux even during times of low wind speeds and stable conditions, CH is the dimensionless bulk turbulent transfer coefficient for sensible heat, w is the wind speed,
EEO is the windless exchange coefficient for latent heat, CE is the dimensionless bulk turbulent transfer coefficient for latent heat, frh is the fractional humidity within the
51 n medium relative to a saturated state, and P vk,sat is the saturation water vapor pressure with respect to phase k (Jordan 1991). Unlike the NOAH LSM, these fluxes are defined as positive downwards.
Bulk transfer coefficients are defined by the surface roughness length and the measurement reference heights for wind speed, temperature, and relative humidity.
Under atmospheric neutrality (average daily stability condition), the bulk transfer coefficients for the latent and sensible heat fluxes are considered equal and given by
2 = = K CE CH 2 z ln z 0 (4.31) where Κ is the von Karman constant set to 0.4. This log wind speed profile in which wind speeds increase with the logarithmic of the height above the ground, governs the velocity profile adjacent to a boundary in a turbulent boundary layer. The variable zo is the roughness length and z is the observation height above the snow surface (Jordan
1991).
4.7.2 Snow/Ground Interface Temperature
The snow/ground interface temperature has undo influence over the oldest part of the snowpack, which will carry upwards in the form of water vapor transport, or downwards in the form of meltwater. The NOAH LSM effective skin temperature at the snow/ground interface is simulated based on heat fluxes between the snowpack, soil, and on net radiation given by
T + T1+ T 2 T = a (4.32) skin α 1.0 + medium dzmedium rr rch
52 where
↓ I − F − F − ε σ T 4 e sfc snow freez snow b a + ϑ − T − tot a rch rch T1 = (4.33) rr and
α T T 2 = medium soil (4.34) dzmedium rr rch where
c * P ph 20 rain 4 if raining ε *T *c rch rr = sfc a 8 +1.0 + (4.35) p × ch c * P pi snow if snowing rch
↓ α where I sfc is the radiation forcing at the surface, medium is the thermal diffusivity
2 -1 average between the snow and uppermost soil layer (m s ), dzmedium is the combined
ε thickness of those two layers, sfc is the surface emissivity, c8 is a constant set at 6.48 ×
10-8 kg K-3 s-3, and c is the specific heat at constant pressure for liquid water equaling ph 20
4218.0 J kg-1 K-1. T1 is the amount of heat energy available at the snow surface, having been corrected by latent heat fluxes, while T2 accounts for temperature and thermal diffusivity within the snow and soil mediums. Subsequently, when the snowpack is melting, sublimating, or evaporating, T1 will be negative, while T2 is always positive.
SNTHERM calculates this temperature as an average temperature gradient along the snow/soil interface for when snow is on the ground or simply the top soil layer temperature when no snow cover is present calculated by
53 T dz + T dz soil snow snow soil snow = + Tsg (dzsoil dzsnow ) (4.36) Tsoil no snow
where Tsoil and Tsnow are the soil and snow temperatures respectively, dzsnow is the snow
layer depth closest to the ground, and dzsoil is the soil layer depth closest to the surface.
4.7.3 Snow/Ground Interface Heat Flux
The snow/ground interface heat flux is calculated in a similar way for both models as the average thermal diffusivity or conductivity gradient existing between the snow and soil surfaces multiplied by the temperature difference across the same interface.
Therefore, a positive ground heat flux arises when the ground temperature is warmer than the snow or air temperature, leading to conductive cooling of the ground and the opposite is true of negative ground heat fluxes.
The NOAH LSM ground heat flux is given by
α (T − T ) G = medium a soil (4.37) dzmedium
α 2 -1 where medium is the average thermal diffusivity (m s ) of the snow and soil mediums.
However, for SNTHERM, the ground heat flux is only calculated when there is snow on the ground, making it a heat flux across the snow/soil surface, not through the entire soil and snow medium or soil medium when there is no snowpack present. The calculation is given by
κ κ G = snow soil × (T − T ) (4.38) κ + κ snow soil ( snow dzsoil soil dzsnow )
κ where soil is the soil thermal conductivity. This makes comparisons between the two heat fluxes only applicable when snow is on the ground.
54 4.8 SNTHERM Snow Compaction, Metamorphosis, and Grain Growth
For compaction and metamorphosis, the compaction rate is recalculated for every new time step, continuously when the snow has a high density, during new snowfalls, as well as for 72 hours after a snowfall. The snow cover deformation rate accounts for metamorphosism, compaction caused by overburden, and snow structural losses during melt caused by destructive metamorphosism. The algorithms for metamorphosism and overburden follow the approach of Anderson (1976). For new snow, with densities less than 150 kg m-3, destructive metamorphosism caused by settling is important. Anderson
(1976) developed an empirical formula for compaction at this stage, given by
∂∆ 1 z − −0.04()T −T = −2.778×10 6 × c × c × exp m (4.39) ∆ ∂ 9 10 z t metamorphosism where c9 and c10 are empirical values that vary with the bulk densities of liquid water, and ice such that
c = c = 1 if γ = 0 and γ ≤ 150 kg m -3 9 10 l i c = exp[−0.046(γ −150.0)] if γ > 150 kg m -3 (4.40) 9 i i c = 2 if γ = 0 10 l
After the snow cover has completed the initial settling stage, densification proceeds at a much slower rate and is largely influenced by the overburden or snow load
(Jordan 1991). The compaction, or deformation, due to overburden is calculated from a linear snow load pressure function given by
∂∆ P 1 z = − s ∆z ∂t η overburden (4.41)
-1 -2 η where Ps is the snow load pressure (kg m s ) and is a viscosity coefficient varying with density, temperature, and grain type (kg s-1 m-1) (Jordan 1991). The viscosity
55 ρ coefficient increases exponentially as Ps and s come into hydrostatic equilibrium and is given by
− ρ η = η c11 (Tm T ) c12 s 0 e e (4.42)
η η where 0 is the viscosity coefficient at Tm. Anderson (1976) suggested 0 be set at
6 -1 -1 -1 3 3.60 x 10 kg s m , c11 at 0.08 K , and c12 at 0.021 m kg respectively.
In addition to compaction effects, grain growth due to vapor movement
(constructive metamorphosism) and densification from liquid water flow are considered
(Jordan 1991). Grain growth is calculated based upon an equation used for growth prediction by sintering (a method for making objects from powder by heating the material below its melting point until particles adhere to each other) in metals and ceramics and is given by
∂d − d = ae (b / T ) ∂t (4.43) where d is the mean grain diameter and a and b are adjustable variables (Jordan 1991).
Grain size affects the permeability of snow to liquid water or air fluid flow and the extinction coefficient for solar radiation (Jordan 1991). Stephenson (1967) proposed grain diameters of 0.04 to 0.2 mm for new snow, 0.2 to 0.6 mm for older snow, and 2.0 to
3.0 mm for older snow near the melting point.
56 Chapter 5: Data and Methodology
5.1 SNTHERM Input Data
SNTHERM requires a variety of meteorological input data including temperature, relative humidity, wind speed used for sensible and latent heat turbulent exchanges, water equivalent precipitation, precipitation type, precipitation diameter, and storm averaged wind speed (wind speed average over time periods with precipitation) used for a precipitation undercatch correction. Additionally, either insolation, reflected solar radiation, and downwelling longwave radiation, or low cloud cover fraction, low cloud cover type, mid cloud cover fraction, mid cloud cover type, high cloud cover fraction, and high cloud cover type are required. If the cloud fraction and cloud type information are given as input, SNTHERM will estimate radiation, but not vice versa
(Figure 5.1).
↑ Reflected shortwave radiation ( S reflect ) was estimated using the empirical formula given by
↑ = α × ↓ S reflect land I s (5.1)
Precipitation type was set for rain when T > Tm and set for snow when
T < Tm. Precipitation diameter was set at 0.001 m for rain and 0.01 m for snow respectively. The model utilizes seven different cloud types corresponding to the three different atmospheric levels. Low clouds are between the surface and
2000 m, assumed to be stratiform, and include cumulus, stratus, and stratocumulus.
Middle clouds are between 2000 m and 6000 m and assumed to be altostratus or altocumulus. High clouds are between 6000 m and 13000 m; classified as cirrus with a fraction below 50% and cirrostratus with greater than 50% fraction.
57 In addition to the various meteorological input data, other parameters must be specified or determined. Soil and snow physical characteristics were determined from previous work by Jordan (1991) (Table 5.1). A constant albedo of 0.2 was set for bare soil, selected to account for grass and fallow crops and to provide a middle value between dark and light soils (Grundstein 1996). Instrument heights were needed for turbulent energy exchange computations, where temperature, relative humidity, and wind speed were set at 2.0 m.
Table 5.1: The soil and snow physical parameters. βnir is the IR extinction coefficient of the top snow layer, Sr is the irreducible water saturation for snow, qtz is the soil quartz content, z0 is the roughness length, CLE and CH are the wind- less convection coefficients for latent and sensible heats, and RHfo is the fractional humidity relative to steady state.
Parameter Snow Soil
βnir 400.0 — Sr 0.04 — qtz — 0.40 z0 0.001 0.001 CLE 0.0 1.0 CH 1.0 1.0 RHfo 1.0 1.0
Additionally, in order to satisfy SNTHERM data requirements, the three hour
MM5 outputted data were run through an Akima cubic spline interpolator in order to resolve the three-hour data into one-hour data. See Akima (1970) for a more detailed description.
5.2 MM5 Input Data
MM5 requires initial, lateral, and lower boundary conditions from temperature, wind, and relative humidity. Geopotential heights are taken at the 1000, 850, 700, 500,
400, 300, 250, 150, and 100 mb pressure levels respectively. One can also specify polar
58 stereographic, Mercator, or Lambert Conformal map projections dependent upon the modeled region size and location. The land-use type data include albedo, moisture availability, emissivity, roughness length, and thermal inertia.
Many input data options are available, including the NCEP Global Analyses Final
Analysis (FNL), NCEP Automated Data Processing (ADP), European Center for
Medium-Range Weather Forecasts (ECMWF) TOGA analyses, National Center for
Atmospheric Research (NCAR)/NCEP Reanalysis project (NNRP), ECMWF Reanalysis
Analyses (ERA), and GCIP NCEP ETA model output (AWIP). This study used the
NCEP ADP observation and NNRP data.
The NCEP ADP observation data include surface, ship, and upper air observations over a 2.5 × 2.5 degree resolution (T62) grid. The surface observations include SYNOP, METAR, AWOS, and ASOS, while the marine data include moving ship, fixed ship, Maritime Mobile Access and Retrieval System (MARS) (moving and fixed), and moored and drifting buoys. The surface and ship data contain pressure, temperature, dewpoint depression, wind direction, and wind speed, at six hour intervals.
The upper air data are a global synoptic set, at six hour intervals, and include land and ship launched radiosondes and pibals. The data are available at up to 20 mandatory pressure levels from 1000 mb to 1 mb, plus a few significant levels, and contain pressure, temperature, geopotential height, dewpoint depression, wind direction, and wind speed information.
The NNRP data include global reanalyses of over 80 variables, at six hour intervals, in several different coordinate systems (17 pressure level stack on 2.5 × 2.5 degree grids, 28 sigma level stack on 192 × 94 Gaussian grids, or 11 isentropic level
59 stack on 2.5 × 2.5 degree grids), used to calculate the initial, lateral, and lower boundary conditions from temperature, wind speed, relative humidity, and geopotential heights.
The coordinate system chosen was the Gaussian grid with 28 σ level stack.
Implementing the NOAH LSM, as well as the various physics options that were discussed in sections 3.4 through 3.8, required specific and/or additional data requirements including soil texture, mean annual surface temperature, seasonal vegetation fraction, and initial soil temperature and moisture data, making this input data combination necessary (Figure 5.1).
Figure 5.1: Conceptual diagram showing the flow of input data to the MM5 NOAH LSM coupled model system and subsequent data output flow to SNTHERM.
Upper Air Data (NNRP)
NOAH LSM Data SNTHERM Requirements Data Requirements (NNRP)
MM5
Surface, Initial, Lateral, Ship, and and Lower Buoy data Boundary (NCEP Conditions ADP) (NNRP)
5.3 Observation Data 5.3.1 Snow Observation Errors
Data quality can be one of the most important factors for any climatological study. Without good quality data, it would be impossible to develop reasonable models and statistically compare results to directly sampled data. Furthermore, without good
60 quality control (QC) procedures in place, snow observations could contain recording errors, such as decimal place errors, and other apparent errors including increases or decreases in snow depth or SWE without precipitation or melt conditions present
(Schmidlin et al. 1995, Schmidlin 1990).
5.3.2 NCDC Data Errors
In this study, the National Climatic Data Center (NCDC) local climatological data were used for the six cities. There were two errors entered into the data records, which were missed by QC procedures, during November 2003 in Williston, North Dakota, and during March 2001 in Sioux Falls, South Dakota. Correcting for the errors did not cause any substantive statistical change in model performance, with the observation mean and correlation increasing or decreasing slightly in both cases.
5.4 Model Sensitivity Analysis
Sensitivity analysis is the process of varying model input parameters over a reasonable range of uncertainty in values, and observing the relative change in model accuracy. The purpose being to demonstrate the sensitivity of the model simulations to uncertainties in model input data values.
Several sensitivity studies were conducted to determine the responsiveness of
SNTHERM to specific variables in an attempt to determine to what components are
SNTHERM most sensitive. Snow thermal conductivity, snow grain size, new snow density, porosity, and no compaction or metamorphosism were selected and analyzed to determine what effect each variable had on snow depth. Bismarck, North Dakota was randomly chosen as the test site and January 2004 as the month because it had model predicted snow on the ground for both MM5 and SNTHERM during the entire month.
61 Qualitative graphical analysis demonstrates that snow thermal conductivity, new snow density, and compactive and metamorphic effects have a significant impact on snow depth. Conversely, snow grain size and porosity have little to no impact on snow depth (Figure 5.2). These results demonstrate that inaccurate representations of snow thermal conductivity, new snow density, or compactive and metamorphic effects will lead to less accurate simulations of the modeled snowpack.
Figure 5.2: Snow thermal conductivity (a), snow grain size (b), new snow density (c), and porosity and compaction/metamorphosism (d) for Bismarck, North Dakota during January 2004 as compared to SNTHERM during the control run simulation. Snow thermal conductivity has units of W m-1 K-1, snow grain size has units of mm, new snow density has units of kg m-3, and porosity and compactive and metamorphic effects are dimensionless. All variables were held constant during the sensitivity analysis runs while the control run used the model as it would normally be utilized.
0.5 0.45 SNTHERM 0.45 SNTHERM K=0.05 0.4 grain size=0.05 0.4 K=0.10 grain size=0.2 0.35 K=0.15 grain size=0.5 0.35 K=0.20 0.3 grain size=1.0 0.3 K=0.25 grain size=3.0 K=0.30 0.25 grain size=5.0 0.25 K=NOAH 0.2 0.2 Snow Depth (m) Depth Snow 0.15 Snow Depth (m) 0.15
0.1 0.1
0.05 0.05
0 0 1 3 5 7 9 11131517192123252729 1 3 5 7 9 11131517192123252729 Day Day a b
0.45 0.6 SNTHERM 0.4 ρ=50.0 0.5 SNTHERM ρ=100.0 0.35 no_compaction/metamorphosis ρ=150.0 porosity=0.5 0.3 ρ=200.0 0.4 ρ=250.0 porosity=1.0 0.25 ρ=400.0 0.3 0.2 Snow Depth (m) 0.15 Depth (m) Snow 0.2
0.1 0.1 0.05
0 0 1357911131517192123252729 1 3 5 7 9 11131517192123252729 Day Day c d
62 It is important to note that no definitive conclusions can be drawn from this analysis because the synergistic effect of one variable to another is impossible to quantify, so snow grain size and porosity may be as or more important to properly simulate than snow thermal conductivity, for example.
Additionally, all clouds and no clouds were implemented in SNTHERM to determine how clouds affect snow depth. Specifying the cloud fraction and cloud types had little effect on snow depth. Using radiation data led to a better simulation of snow depth as compared to the observations.
5.5 Model Evaluation Statistics
A quantitative assessment of model performance, or the degree to which the model output matches reliable observations, is useful to provide an evaluation of the model’s predictive ability. Comparisons should be made between model-predicted (P) and observed (O) values using a suite of statistics to determine differences, accuracy, and precision. Selection and application of performance statistics is important, since some statistics are more appropriate than others.
Correlation (r) and its square, the coefficient of determination (r2), are commonly used to demonstrate model efficacy, although they may not be the most appropriate measures (Willmott 1984). With r and r2, it is possible to have very high values, approaching 1.0, when P and O have little in common. It also is possible that P and O are similar when r or r2 is small, approaching 0.0.
This analysis will utilize both univariate and bivariate statistics including the mean, mean absolute deviation (MAD), mean absolute error (MAE), index of agreement
63 (d), and also the systematic (MSEs) and unsystematic (MSEu) portions of the mean square error (MSE). The mean is the average of all values over the period of record. It is
N = 1 X ∑ X t (5.2) N t=1 where Xt is a model or observation value at each time step (t). The mean absolute deviation (MAD) is the mean of the absolute deviations of a dataset about its mean. It is
N = 1 − MAD∑ X t X . (5.3) N t=1
The MAE represents the difference between the predicted and observed variable and is given by
N = 1 − MAE ∑ Ot Pt N t=1 (5.4) where Ot is an observed value and Pt is a corresponding model-predicted value at each interval.
The index of agreement (d) was developed by Willmott (1981) to represent the relative degree to which P approaches O. It attempts to overcome the insensitivity of correlation-based measures to the observed and predicted means and variances. The index varies from 0.0 to 1.0, with higher values indicating better agreement between the model predictions and observations. Willmott (1984) indicated that d represented the ratio of the mean square error (MSE) over a measure of potential error (PE), all subtracted from unity (1.0). The index was written as
N − 2 ∑ (Ot Pt ) = − t=1 d 1.0 N (5.5) ()− + − 2 ∑ Pt O Ot O t=1
64 Willmott and others have come to believe that the index of agreement (d) is a better measure when it is based on the absolute values of the errors rather than on squared errors (Willmott and Matsuura, 2005). The modified index is
N − ∑ Pt Ot = − t=1 d 1.0 N ()− + − ∑ Pt O Ot O t=1 (5.6) and it is the version used here.
The systematic MSE (MSEs) and unsystematic MSE (MSEu) can be good statistical measures of systematic model-prediction error and the unsystematic component of error. It is generally easier to correct for systematic error than unsystematic error.
MSEs and MSEu are given by
N ^ 2 = 1 − MSE s ∑ Pt Ot N t=1 (5.7) and
N ^ 2 = 1 − MSE u ∑ Pt Pt N t=1 (5.8)
^ where P is the Ordinary Least Square (OLS) simple linear regression equation between
P and O. The linear-regression equation is
^ P = A + B × O i i (5.9)
S where A = P − B *O and B = r × P . The P-intercept is A, B is the slope of the regression SO
line, S P is the predicted standard deviation, and SO is the observed standard deviation respectively.
65 Chapter 6: Results
Model analysis begins in December 1999 and runs through April 2005, skipping the months of May through October, as little to no snow accumulates in the Great Plains during those months. Because the MM5 NOAH LSM coupled model system was not run across the months, in other words, not for multiple months per run, SNTHERM had to be initialized with the previous month’s snowpack characteristics, if snow were on the ground during the last day of the previous month. This led to no disconnections between months. Also, the first day of each MM5 model run was discarded for spin-up, as with each SNTHERM model run, causing comparable model simulations to observations to begin on the third day of each month (Table 6.1). Snow depth was the only field compared to the observations as some of the daily SWE data were missing from the
NCDC local climatological data. It is important to note that snow depth is not a perfect surrogate for SWE.
Table 6.1: Days of the month for each SNTHERM and MM5 model run for each city showing that MM5 was not run across the months and to show the day disconnections that existed. 3-31 means the model was run from day 3 to day 31 during that month.
Bismarck Williston Sioux Falls Huron Scottsbluff North Platte SNT MM5 SNT MM5 SNT MM5 SNT MM5 SNT MM5 SNT MM5
January 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 February 3-28 2-28 3-28 2-28 3-28 2-28 3-28 2-28 3-28 2-28 3-28 2-28 March 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 April 3-30 2-30 3-30 2-30 3-30 2-30 3-30 2-30 3-30 2-30 3-30 2-30 November 3-30 2-30 3-30 2-30 3-30 2-30 3-30 2-30 3-30 2-30 3-30 2-30 December 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 3-31 2-31 2001 January 3-28 2-28 3-28 2-28 3-28 2-28 3-28 2-28 3-28 2-28 3-28 2-28 February 3-22 2-22 3-22 2-22 3-22 2-22 3-22 2-22 3-22 2-22 3-22 2-22 April 3-26 2-26 3-26 2-26 3-26 2-26 3-26 2-26 3-26 2-26 3-26 2-26 2002 December 3-27 2-27 3-27 2-27 3-27 2-27 3-27 2-27 3-27 2-27 3-27 2-27 2005 February 3-19 2-19 3-19 2-19 3-19 2-19 3-19 2-19 3-19 2-19 3-19 2-19
66 6.1 General Model Analysis
November is the month that the snowfall season generally begins, while by April, most snow has melted (Figure 6.1). By the end of November, because of lessening solar radiation, temperatures decrease with increasing latitude. This causes the Great Plains to have a distinctive spatial snowpack pattern in place, which increases with increasing latitude (Figure 6.2). Additionally, by April, in non mountainous areas, this distinctive spatial snowpack pattern decreases with decreasing latitude, caused by increased solar radiation (Figure 6.2). Conditions at 6 am were selected to represent each day, approximating the time at which the snow depth observations were taken.
Figure 6.1: MM5 average snow depth (m) for domain two for November 2000 (a) and April 2001 (b).
(a) (b)
67 Figure 6.2: MM5, SNTHERM, and observed snow depth (m) for November 2004 through April 2005 for Bismarck, North Dakota (a) and Scottsbluff, Nebraska (b).
(a) (b)
The region can be split into two temporal groups based on temperature, snowfall, and snow duration on the ground with November, March, and April representing months with warmer temperatures, less snowfall, and therefore less snow on the ground than
December, January, and February, which represent the opposite (colder temperatures, more snowfall, more snow on the ground) (Figures 6.3 and 6.4). This conclusion was reached by graphical comparison of monthly snow depths between the six cities making it evident that these groupings were appropriate.
68 Figure 6.3: MM5 averaged temperature (K) for November 2002, March 2003 (a), and April 2003 and December 2002, January 2003 and February 2003 (b).
(a) (b)
Figure 6.4: MM5 averaged snow depth (m) for November 2002, March 2003, and April 2003 (a) and December 2002, January 2003 and February 2003 (b).
(a) (b)
69 6.2 Heavy Snow Events
Heavy snow events are an important model resolution issue because lower resolution model runs have a difficult time resolving heavy and/or anomalous snowfall events. Domain two of MM5 was not able to simulate one heavy snowfall event. The event occurred at Sioux Falls, South Dakota from February 3 though 5, 2004, during which 0.30 m of snow fell.
The Sioux Falls, South Dakota event was a snowfall that MM5 resolved well, but to a lesser degree than the observations, and had it located too far to the south, over southeastern Nebraska, rather than southeastern South Dakota (Figure 6.5). Regionally,
Bismarck and Williston were unaffected, while Huron, North Platte, and Scottsbluff received between 0.05 and 0.10 m (Figure 6.6).
Figure 6.5: MM5 domain two snow depth averages (m) for January 24 through January 31, 2004 (a) and February 2 through February 5, 2004 (b).
(a) (b)
70 6.2.1 Anomalous Event
An anomalous event occurred at Williston, Bismarck, Huron, and Sioux Falls from January 24, 2004, to February 2, 2004, in which MM5 resolved a heavy snow event well but reinitiated its snow depth to a much lesser value beginning the next month
(February). There is no explanation for this other than MM5 began the next month with much less snowfall than with the previous month ended. MM5 is driven by reanalysis data and subsequently knows how much snow is on the ground to begin a month. This ability has been demonstrated during many months (November 2002 and 2003 for example), making this event, for Bismarck and Huron (Figure 6.6 a and d), make sense because both cities’ simulated snow depths did not match the observations. However, for
Williston and Sioux Falls (Figure 6.6 b and c), this ability was not exercised, making this event unexplainable. This did not affect SNTHERM’s performance, as MM5 snow depth is not a required input field.
71 Figure 6.6: MM5, SNTHERM, and observed snow depths (m) for November 2003 through April 2004 for Bismarck (a) and Williston (b), North Dakota and Sioux Falls (c) and Huron (d), South Dakota. The red dots demonstrate that February 2004 began much lower than January 2004 ended.
(a) (b)
(c) (d)
6.3 Model Evaluation
Model evaluation is a way to assess, during differing scenarios, how well a model simulates snow depth. Various temperature and precipitation categories were created to test MM5 and SNTHERM, leading to eleven different classifications.
Six temperature regimes were selected: very cold, cold, around freezing, warm, below freezing, and above freezing, during which no precipitation fell. Very cold were days below -15 ºC, cold were from -15 ºC to -2 ºC, around freezing were from -2 ºC to
72 2 ºC, and warm were days above 2 ºC. Additionally, three precipitation categories were selected, including high intensity, multiday, and high intensity and multiday. During high intensity precipitation events, more than 0.15 m of snow fell, while multiday were multiple days where any amount of snow accumulated, and high intensity and multiday were high intensity events that occurred over more than a 24 hour period. Also, all times when snow was on the ground and all times regardless of condition were the last two scenarios (Table 6.2).
Table 6.2: Number of days qualifying for each temperature or precipitation categorization for each of the six selected cities. The 11th category is all times with 887 days for each city.
Very cold Cold Around freezing Warm Below Above High Multi High intensity Snow on no snow no snow no precip no precip freezing freezing intensity day and multiday ground
Bismarck 59 215 85 98 663 234 15 150 14 493 Williston 51 181 113 157 646 241 23 203 22 541 Sioux Falls 41 222 103 191 620 267 22 129 21 386 Huron 35 204 111 193 595 292 31 139 28 410 Scottsbluff 4 140 158 271 520 367 14 45 7 226 North Platte 3 145 151 290 527 360 22 59 17 183
There are more very cold and cold days with no snow falling in the north and more around freezing and warm days with no precipitation falling in the south (Table
6.2). Also, there are more multiday snowfall events and snow persists on the ground for more days in the north. These are expected conclusions because temperature decreases with increasing latitude and so snow will fall more often and remain on the ground for longer periods of time in the north than the south.
73 Table 6.3: Model evaluation statistics for varying temperature and precipitation categories that both MM5 and SNTHERM met. No snow means no snow falling, no precip means no precipitation falling, snow on ground means all times with snow on the ground, and all times means all days regardless of condition. SNT represents SNTHERM, and OBS represents the observations. The OBS column only applies to the mean, while the MAE, r, and MSEu / MSE are for how SNTHERM compares to MM5. The mean and MAE have units of cm, while r and MSEu / MSE are dimensionless, and given as a percentage of 100.
Bismarck Williston Sioux Falls Huron Scottsbluff North Platte SNT MM5 OBS SNT MM5 OBS SNT MM5 OBS SNT MM5 OBS SNT MM5 OBS SNT MM5 OBS MEAN Very cold-no snow 9.4 17.8 7.1 14.7 18.8 16.8 6.9 10.2 5.5 6.8 13.0 4.9 11.8 15.8 8.3 11.0 14.5 9.4 Cold-no snow 4.7 11.0 3.8 5.1 10.7 7.9 3.3 6.2 4.6 2.7 6.7 6.6 3.1 6.1 1.6 2.8 5.6 1.8 Around freezing 1.2 4.4 1.5 3.2 6.4 5.7 1.0 3.4 1.2 0.8 3.1 1.8 0.7 2.4 0.7 0.8 2.4 0.7 Warm-no precip 0.2 1.3 0.2 0.1 1.3 1.2 0.1 0.5 0.2 0.1 0.6 0.4 0.1 0.7 0.3 0.2 0.6 0.1 Below freezing 5.9 11.0 4.7 8.2 11.6 10.6 4.8 8.0 5.9 5.3 9.7 9.1 2.5 5.1 1.8 2.2 4.5 1.3 Above freezing 0.5 1.9 0.4 0.8 2.4 2.2 0.3 1.0 0.4 0.3 1.2 1.0 0.2 1.0 0.6 0.2 0.7 0.2 High intensity 16.1 19.6 10.8 18.3 15.2 19.1 12.4 15.2 11.8 14.0 17.4 18.9 16.1 17.5 8.4 11.3 13.0 5.7 Multiday 8.6 13.7 5.8 8.5 12.4 10.3 7.7 11.4 9.6 8.2 12.8 14.3 6.4 10.8 6.0 5.6 8.5 2.8 High intensity/Multiday 6.2 19.6 11.6 17.5 14.7 18.5 11.8 14.7 12.3 14.0 17.4 20.5 16.2 19.1 8.6 9.7 13.0 4.8 Snow on ground 8.6 14.9 6.7 10.1 13.8 12.8 7.9 12.3 9.1 7.8 13.4 13.3 6.0 10.1 3.9 6.0 9.7 3.0 All times 4.6 8.8 3.7 6.2 9.1 8.3 3.4 5.9 4.3 3.6 6.9 6.4 1.5 3.4 1.2 1.3 2.7 0.8 MAE Very cold-no snow 3.6 10.9 8.4 5.9 9.2 7.5 4.6 5.4 3.3 3.1 8.1 6.2 7.2 7.5 4.8 3.6 6.5 3.5 Cold-no snow 2.3 6.6 5.7 5.0 5.3 6.3 3.4 4.4 2.9 5.6 6.8 4.3 2.6 5.0 3.2 2.2 4.5 3.1 Around freezing 1.0 3.3 3.3 3.5 3.4 4.3 1.3 2.9 2.4 2.0 3.5 2.5 0.9 2.3 1.8 0.7 1.9 1.7 Warm-no precip 0.2 1.2 1.1 1.2 1.1 1.2 0.2 0.5 0.5 0.5 0.7 0.5 0.3 0.7 0.6 0.2 0.5 0.4 Below freezing 2.9 6.8 5.7 4.9 6.5 6.5 3.9 5.3 3.5 7.1 8.8 4.8 2.3 4.2 2.8 1.7 3.6 2.6 Above freezing 0.4 1.6 1.5 1.8 1.7 1.8 0.5 1.0 0.8 1.0 1.5 1.0 0.6 1.0 0.9 0.2 0.7 0.6 High intensity 6.9 11.5 6.5 6.4 15.3 11.6 6.1 9.1 4.3 11.1 12.2 5.0 10.2 11.5 4.3 7.3 8.6 3.9 Multiday 4.1 8.1 5.3 5.1 6.8 6.2 5.6 7.3 4.3 11.2 12.1 5.4 4.5 7.0 5.0 3.4 6.0 3.6 High intensity/Multiday 6.4 10.9 6.6 6.6 15.7 11.7 5.2 8.4 4.5 11.3 12.0 5.0 8.4 10.7 5.3 6.3 9.2 3.6 Snow on ground 3.8 8.6 7.1 5.7 7.4 7.5 5.9 7.6 4.8 10.5 12.4 6.3 5.1 7.9 4.6 3.9 7.0 4.6 All times 2.3 5.5 4.6 4.1 5.2 5.2 2.9 4.0 2.7 5.1 6.4 3.6 1.5 2.9 2.0 1.1 2.2 1.6 r Very cold-no snow 87.1 88.5 92.3 82.3 61.7 62.6 50.1 46.2 91.2 82.0 83.1 92.0 56.9 73.9 94.9 99.7 99.9 100.0 Cold-no snow 75.1 78.5 82.1 69.3 68.1 70.8 56.5 51.3 90.0 41.6 31.1 80.2 54.3 47.6 90.8 64.2 56.3 89.2 Around freezing 72.5 78.5 81.0 74.2 75.5 69.1 42.8 36.6 75.3 30.6 27.9 75.3 35.8 31.3 74.3 60.6 67.4 79.6 Warm-no precip 69.7 55.8 72.2 49.1 69.7 53.8 66.9 27.9 50.1 30.6 26.8 44.7 41.5 47.2 53.2 56.2 53.7 63.3 Below freezing 80.4 75.5 78.9 83.9 58.4 58.4 65.4 59.5 90.0 48.5 46.6 88.0 49.2 43.8 85.8 61.6 54.2 82.6 Above freezing 76.6 67.9 77.2 59.2 74.1 70.3 40.7 31.4 62.1 33.6 31.2 73.0 33.1 48.0 55.8 38.1 57.7 69.7 High intensity 77.7 69.3 91.5 88.3 20.8 39.8 45.2 25.1 77.2 63.7 63.3 87.1 27.2 40.9 86.7 37.7 30.9 80.9 Multiday 67.5 65.4 85.8 76.4 39.1 51.2 61.3 50.8 85.5 22.6 27.0 82.1 53.1 40.6 75.5 65.7 53.9 81.9 High intensity/Multiday 83.0 75.8 91.6 88.1 17.6 35.9 60.4 33.8 75.0 65.9 66.3 87.4 64.4 87.5 89.1 42.6 34.6 96.3 Snow on ground 73.8 68.0 70.1 81.0 50.0 48.7 53.8 46.5 86.3 37.7 35.6 84.4 27.7 21.7 80.5 54.9 41.6 72.5 All times 83.1 78.7 81.8 84.4 65.6 64.9 68.7 63.4 90.5 52.1 50.5 89.3 49.1 47.2 84.9 61.9 53.8 82.3 MSEu / MSE Very cold-no snow 69.0 19.2 61.5 43.8 81.1 66.2 81.3 31.8 82.3 45.1 0.8 0.2 Cold-no snow 91.6 36.2 36.3 55.3 43.3 69.8 6.2 20.6 85.8 67.4 85.2 73.7 Around freezing 81.1 54.2 46.8 69.7 64.4 77.9 6.8 24.5 76.1 82.5 83.2 80.5 Warm-no precip 09.5 92.7 1.5 65.2 22.9 91.9 10.9 43.3 18.6 88.6 98.8 85.0 Below freezing 91.7 46.5 63.3 44.8 49.3 73.3 13.1 30.5 85.5 76.1 92.4 77.7 Above freezing 99.7 69.5 24.2 73.6 23.6 76.5 5.8 25.9 31.5 83.1 79.9 89.7 High intensity 63.4 59 6 69.6 23.6 67.7 59.9 16.6 25.2 29.7 47.5 55.2 43.8 Multiday 73.0 33.1 55.6 34.3 38.2 46.6 10.9 19.4 81.9 63.8 64.7 53.2 High intensity/Multiday 59.7 55.3 66.6 22.6 70.1 65.8 15.7 24.2 39.7 21.4 60.1 47.2 Snow on ground 84.7 37.7 61.7 32.9 40.7 56.9 10.1 22.7 62.1 52.1 60.1 50.2 All times 93.4 51.0 61.9 55.1 50.9 79.2 14.1 34.9 85.3 84.3 92.7 84.6
In winter, temperatures decrease with increasing latitude and elevation,
consequently, snowfall is greater in the Northern Great Plains because of more days with
74 temperatures below freezing, allowing for a higher likelihood of snow than rain (Figures
6.7 through 6.12). Additionally, the snow remains on the ground for longer durations in the north because temperature and ablation are related such that less days above freezing leads to less melting and vice versa (Table 6.3; r values for Bismarck and Williston,
North Dakota during very cold and cold periods with no snow falling).
Consequently, SNTHERM and MM5 better simulate snow in the Northern Great
Plains due to the less ephemeral nature of the snowpack, leading to less melt periods.
Conversely, more solar radiation and warmer temperatures cause less snowfall and less snow to remain on the ground in the Southern Great Plains, causing more ablation periods, leading to poorer model performance (Table 6.3; r values for Sioux Falls, Huron,
Scottsbluff, and North Platte for very cold and cold periods with no snow falling).
High intensity and multiday snow events are better resolved in the Northern Great
Plains, as colder temperatures cause less of a convective precipitation component, which can increase precipitation rates as well as cause more mixed precipitation (sleet and freezing rain) (Table 6.3; r values for Williston and Bismarck, North Dakota).
Table 6.3 shows that model performance is critically dependent upon cold temperatures and temperatures that do not regularly increase above freezing, causing ablation periods. Correlation analysis shows a definitive decrease in r from very cold to warm scenarios in nearly every city and for both models. Furthermore, in every case,
MM5 to SNTHERM correlations (labeled OBS on Table 6.3) decrease from very cold to warm scenarios. This demonstrates that model agreement to observations as well as to one another decreases with increasing temperatures. So, MM5 and SNTHERM better simulate snow in areas that remain well below freezing for long time periods.
75 Unsystematic model error generally decreases from very cold to warm scenarios as well as from northern cities to southern (Table 6.3). This demonstrates that model output that does not match the observations is still in general agreement and not random.
Generally, a high systematic error is better than a high unsystematic error because systematic errors are usually easily correctable, while high unsystematic errors are not.
Total model evaluation averaged for all cities regardless of condition demonstrates that SNTHERM better compares to the observations than MM5, both in variability as well as in magnitude (Table 6.4 correlation and d values). Additionally,
SNTHERM has a slightly higher unsystematic error, as was the case with most of the temperature and precipitation scenarios, than MM5.
Table 6.4: Total model versus observed evaluation statistics averaged for all cities MM5 Correlation: 0.598 SNTHERM Correlation: 0.661 MM5 to SNTHERM Correlation: 0.820 MM5 Index of Agreement (d): 0.564 SNTHERM Index of Agreement (d): 0.691 MM5 to SNTHERM Index of Agreement (d): 0.718 MM5 MSEs / MSE: 0.352 MM5 MSEu / MSE: 0.648 SNTHERM MSEs / MSE: 0.332 SNTHERM MSEu / MSE: 0.668
76 Figure 6.7: MM5, SNTHERM, and observed snow depth from December 1999 through April 2000 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska.
(a) (b)
(c) (d)
(e) (f)
77 Figure 6.8: MM5, SNTHERM, and observed snow depth from November 2000 through April 2001 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska.
(a) (b)
(c) (d)
(e) (f)
78 Figure 6.9: MM5, SNTHERM, and observed snow depth from November 2001 through April 2002 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska.
(a) (b)
(c) (d)
(e) (f)
79 Figure 6.10: MM5, SNTHERM, and observed snow depth from November 2002 through April 2003 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska.
(a) (b)
(c) (d)
(e) (f)
80 Figure 6.11: MM5, SNTHERM, and observed snow depth from November 2003 through April 2004 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska.
(a) (b)
(c) (d)
(e) (f)
81 Figure 6.12: MM5, SNTHERM, and observed snow depth from November 2004 through April 2005 for Bismarck (a) and Williston (b), North Dakota, Sioux Falls (c) and Huron (d), South Dakota, and Scottsbluff (e) and North Platte (f), Nebraska.
(a) (b)
(c) (d)
(e) (f)
82 6.4 Snow Physics Evaluation
Snow physics differences are the purpose of this study because MM5 (hereafter
NOAH LSM) and SNTHERM have different snow physics, causing different snow accumulation and ablation rates. Variables such as new snow density and air and ground temperatures impact snow accumulation rates, while snow albedo, snow density, sensible, latent, and ground heat fluxes, thermal conductivity, metamorphosis and compaction, and the snow/ground interface temperature impact snow ablation rates. Without careful analysis of the variables available for comparison, no definitive conclusions can be ascribed to the differences between SNTHERM and the NOAH LSM.
Bismarck, North Dakota and Scottsbluff, Nebraska were chosen for analysis to represent a northern and southern city within the study area. Additionally, November
2000 through April 2001 (hereafter snow season two) and November 2004 through April
2005 (hereafter snow season six) were chosen as representative seasons for analysis.
Snow season two was chosen because it was a cold season with snow on the ground for long durations with many partial ablation periods for both cities (Figure 6.8) while snow season six was chosen because it was a warmer season with several ablation periods immediately following snow events (Figure 6.12).
A modified version of SNTHERM was created attempting to replicate the NOAH
LSM snow accumulation and ablation rates. The version (hereafter SNTHERM modified) utilizes NOAH LSM average monthly 0.05 meter subsurface temperatures as well as the NOAH LSM snow thermal conductivity equation. The 0.05 meter subsurface temperature was used as a surrogate for ground temperature because the NOAH LSM ground temperature was the snow temperature when snow was on the ground. This
83 occurs because the NOAH LSM considers the snowpack as a one-layer slab, causing
MM5 to consider the top of the snowpack to be the ground.
6.4.1 Snow Albedo
SNTHERM used MM5 radiation data as input, causing the SNTHERM snow albedo minimum to approximately equal the snow albedo of the NOAH LSM. The snow albedo of SNTHERM fluctuated from between 0.64 and 0.90, caused by the diurnal change in solar zenith angle. Cline (1997) recommended only using SNTHERM snow albedo during solar zenith angles greater than 0.50, to reduce errant values caused by low sun angles (Figures 6.13 and 6.14).
Figure 6:13: SNTHERM snow albedo and snow depth for snow season six for Bismarck, North Dakota. Snow albedos between 0.7 and 0.9 should be considered erroneous as only new snow has an albedo approaching 0.9. X axis ticks are weeks and each label approximates a month.
1.00 0.16 SNTHERM Albedo
0.90 SNTHERM Snow Depth 0.14
0.80 0.12 0.70
0.10 0.60
0.50 0.08 Albedo
0.40 0.06 (m) Depth Snow
0.30 0.04 0.20
0.02 0.10
0.00 0.00 1 225 449 673 897 1121
84 Figure 6.14: SNTHERM snow albedo and snow depth for snow season six for Bismarck, North Dakota. Hour 12 was used as a representative snow albedo because SNTHERM snow albedo varies with the zenith angle leading to erroneously high albedos at low sun angles. X axis ticks are weeks and each label approximates a month.
1.00 0.16
SNTHERM Albedo 0.90 SNTHERM Snow Depth 0.14
0.80
0.12
0.70
0.10 0.60
0.50 0.08 Albedo Snow Depth (m) Depth Snow 0.40 0.06
0.30
0.04
0.20
0.02 0.10
0.00 0.00 1 29 57 85 113 141
The NOAH LSM snow albedo was nearly constant at 0.64, caused by using a maximum deep snow albedo derived from satellites 20 years ago. It is impossible to determine which maximum deep snow albedo was chosen, with reported values ranging from 0.47 to 0.79 over North America, with a mean for all latitudinal bands of 0.56
(Robinson et al. 1985) Also, the lack of temporal resolution in the satellite-based annual cycle of vegetative greenness, which is a significant factor in determining snow albedo, may lead to snow albedo underestimations (Figure 6.15).
85 Figure 6.15: NOAH LSM snow albedo and snow depth for snow season six for Bismarck, North Dakota. X axis ticks are weeks and each label approximates a month.
0.80 0.25
NOAH LSM Albedo 0.70 NOAH LSM Snow Depth
0.20 0.60
0.50 0.15
0.40 Albedo
0.10 (m)Snow Depth 0.30
0.20 0.05
0.10
0.00 0.00 1 225 449 673 897 1121
6.4.2 Turbulent Exchange Fluxes
To accurately simulate snow pack energy gains or losses, turbulent exchange fluxes such as the sensible and latent heat fluxes must be partitioned properly. The turbulent fluxes are displayed so that positive fluxes represent heat losses to the snow cover and negative fluxes indicate heat gains to the environment (air or ground). The
SNTHERM and SNTHERM modified sensible heat fluxes, during times with snow on the ground, were of similar magnitude as compared to the NOAH LSM, caused by the temperature gradient from the ground or snow surface to the atmosphere.
Figures 6.16 through 6.18 show NOAH LSM, SNTHERM, and SNTHERM modified three hourly sensible and latent heat fluxes compared to snow depth for snow season two in Scottsbluff, NE. Sensible heat fluxes are consistently negative, cooling the air and warming the surface (snow or ground), during ablation periods and positive, warming the air and cooling the surface, during accumulation periods. Latent heat fluxes
86 are consistently positive when snow is on the ground, indicating evaporative, sublimational, or melt cooling of the surface, and the opposite is true of negative values caused by condensational, depositional, or freeze warming.
Figure 6.16: NOAH LSM turbulent fluxes and snow depth for snow season two for Scottsbluff, NE. X axis ticks are weeks and each label approximates a month.
200.0 0.30
NOAH LSM Latent Heat NOAH LSM Sensible Heat NOAH LSM Snow Depth 150.0 0.25
100.0 0.20 ) -2
50.0 0.15 Snow Depth (m) Snow Depth Heat Flux m Heat (W
0.0 0.10 1 225 449 673 897 1121
-50.0 0.05
-100.0 0.00
Figure 6.17: SNTHERM turbulent fluxes and snow depth for snow season two for Scottsbluff, NE.
200.0 0.30
SNTHERM Latent Heat 150.0 SNTHERM Sensible Heat 0.25 SNTHERM Snow Depth
100.0 0.20 ) -2
50.0 0.15 Snow Depth (m) Depth Snow Heat Flux (W m (W Flux Heat
0.0 0.10 1 225 449 673 897 1121
-50.0 0.05
-100.0 0.00
87 Figure 6.18: SNTHERM Modified turbulent fluxes and snow depth for snow season two for Scottsbluff, NE.
200.0 0.30 SNTHERM Modified Latent Heat SNTHERM Modified Sensible Heat 150.0 SNTHERM Modified Snow Depth 0.25
100.0
0.20 50.0
0.0 0.15 1 225 449 673 897 1121 Snow Depth (m) Snow Depth Heat Flux (W m-2) (W Flux Heat -50.0 0.10
-100.0
0.05 -150.0
-200.0 0.00
6.4.3 Snow-Ground Interface
The snow-ground interface never changes in height and is therefore a fixed position to make comparisons between models. Because the NOAH LSM ground and snow temperatures were the same, the 0.05 meter soil temperature was used as a surrogate for ground temperature. Tables 6.5 through 6.9 compare average soil temperatures at three different levels between the NOAH LSM, SNTHERM, and
SNTHERM modified.
88 Table 6.5: Average ground temperatures for the NOAH LSM, SNTHERM, and SNTHERM modified as compared to NOAH LSM air temperatures during times with snow or no snow on the ground and times with only snow on
the ground. Tg is the average ground temperature regardless of snow condition, and T is the average ground temperature when snow is on gsnow the ground. Ta is the average air temperature regardless of snow condition, and T is the average air temperature when snow is on the asnow ground. Season 2 is November 2000 through April 2001, and Season 6 is November 2004 through April 2005.
NOAH LSM SNTHERM SNTHERM MODIFIED NOAH LSM City and Season T T T T T T T T g gsnow g gsnow g gsnow a asnow Bismarck Season 2 268.5 267.5 271.5 270.9 263.3 260.8 265.0 263.2 Scottsbluff Season 2 270.6 270.3 273.2 271.6 269.9 267.7 270.6 268.7 Bismarck Season 6 271.2 268.2 272.3 265.5 269.5 266.2 270.5 267.5 Scottsbluff Season 6 275.4 271.9 275.5 272.0 273.9 269.4 274.7 270.8
Table 6.6: Number of 3 hour observations qualifying for Bismarck and Scottsbluff for snow seasons two and six with snow or no snow on the ground (all times) and times with only snow on the ground (snow).
City and Season NOAH LSM SNTHERM SNTHERM MODIFIED all times snow all times snow all times snow Bismarck Season 2 1198 1085 1198 940 1198 1013 Scottsbluff Season 2 1223 954 1223 658 1223 958 Bismarck Season 6 1270 984 1270 495 1270 887 Scottsbluff Season 6 1269 535 1269 204 1269 586
Table 6.7: Average soil temperatures for the NOAH LSM during times with snow or
no snow on the ground and times with only snow on the ground. T0.05 ,
T 0.25 , T0.70 , and T1.50 are the average soil temperatures regardless of snow condition at 0.05, 0.25, 0.70, and 1.50 meters, and T , 0.05snow T , T , and T are the average soil temperatures 0.25snow 0.70snow 1.50snow when snow is on the ground at 0.05, 0.25, 0.70, and 1.50 meters respectively.
NOAH LSM City and Season T T T T T T T T 0.05 0.05snow 0.25 0.25snow 0.70 0.70snow 1.50 1.50snow Bismarck Season 2 268.5 267.5 271.3 270.6 273.2 272.8 275.5 275.3 Scottsbluff Season 2 270.6 270.3 272.0 272.6 273.8 274.1 276.7 276.0 Bismarck Season 6 271.2 268.2 273.0 270.7 274.6 273.2 276.1 275.4 Scottsbluff Season 6 275.4 271.9 276.3 273.7 277.4 275.8 278.7 278.0
89 Table 6.8: Average soil temperatures for SNTHERM during times with snow or no
snow on the ground and times with only snow on the ground. T0.05 , T 0.25 ,
and T0.70 are the average soil temperatures regardless of snow condition at 0.05, 0.25, and 0.70, and T , T , and T are the 0.05snow 0.25snow 0.70snow average soil temperatures when snow is on the ground at 0.05, 0.25, and 0.70 meters respectively.
SNTHERM City and Season T T T T T T 0.05 0.05snow 0.25 0.25snow 0.70 0.70snow Bismarck Season 2 272.6 271.1 273.7 272.5 279.4 278.7 Scottsbluff Season 2 274.0 272.5 275.6 274.2 281.1 280.1 Bismarck Season 6 273.8 271.1 275.2 272.5 280.9 278.7 Scottsbluff Season 6 276.1 273.3 277.6 275.1 282.7 281.6
Table 6.9: Average soil temperatures for SNTHERM modified during times with snow or no snow on the ground and times with only snow on the ground.
T0.05 , T 0.25 , and T0.70 are the average soil temperatures regardless of snow condition at 0.05, 0.25, and 0.70, and T , T , and 0.05snow 0.25snow T are the average soil temperatures when snow is on the ground at 0.70snow 0.05, 0.25, and 0.70 meters respectively.
SNTHERM Modified City and Season T0.05 T0.05 T 0.25 T0.25 T0.70 T0.70 snow snow snow Bismarck Season 2 264.9 262.7 266.5 264.5 272.2 270.5 Scottsbluff Season 2 270.2 267.9 271.6 269.5 277.4 275.9 Bismarck Season 6 269.6 265.6 270.7 267.1 276.0 273.3 Scottsbluff Season 6 274.5 270.2 276.1 272.2 281.8 279.3
A clear result is that the NOAH LSM snow-ground interface temperature
(hereafter ground temperature) is much lower when snow is on the ground than compared to SNTHERM (Table 6.5). This is also true at the 0.25 and 0.70 meter soil layer temperatures (Tables 6.7 through 6.9). This causes an overestimation of snow accumulation and underestimation of snow ablation. SNTHERM modified was able to replicate this result when snow was on the ground. Figures 6.19 through 6.22 demonstrate the large 0.05 meter soil temperature differences between the NOAH LSM and SNTHERM of up to 20°C when snow is on the ground.
90 Figure 6.19: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season two for Bismarck, ND. X axis ticks are weeks and each label approximates a month.
295.0
SNTHERM Ground Temperature 290.0 NOAH LSM Soil Temperature 0.05m SNTHERM Modified Ground Temperature 285.0
280.0
275.0
270.0 Temperature (K) Temperature
265.0
260.0
255.0 1 225 449 673 897 1121
Figure 6.20: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season two for Scottsbluff, NE.
300.0
295.0 SNTHERM Ground Temperature NOAH LSM Soil Temperature 0.05m 290.0 SNTHERM Modified Ground Temperature
285.0
280.0
275.0 Temperature (K) Temperature
270.0
265.0
260.0 1 225 449 673 897 1121
91 Figure 6.21: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season six for Bismarck, ND.
300.0
SNTHERM Ground Temperature 295.0 SNTHERM Modified Ground Temperature 290.0 NOAH LSM Soil Temperature 0.05m
285.0
280.0
275.0
270.0 Temperature (K) Temperature 265.0
260.0
255.0
250.0 1 225 449 673 897 1121
Figure 6.22: NOAH LSM, SNTHERM, and SNTHERM Modified ground temperatures for snow season six for Scottsbluff, NE.
300.0
295.0 SNTHERM Ground Temperature SNTHERM Modified Ground Temperature 290.0 NOAH LSM Soil Temperature 0.05m
285.0
280.0
275.0 Temperature (K)
270.0
265.0
260.0 1 225 449 673 897 1121
92 Comparisons between the ground and air temperatures are also indicative of how snow accumulates and how it melts. When snow is on the ground, if ground temperatures remain colder than air temperatures, snow accumulation will be higher than if the ground temperature were warmer. Similarly, if ground temperatures remain colder than air temperatures during ablation periods, the snow will persist on the ground for a longer time than if ground temperatures were warmer. Figures 6.23 through 6.26 demonstrate a comparison between air and ground temperatures while Figures 6.27 and
6.28 compares that temperature difference with snow depth, where positive values indicate that the ground temperature is colder than the air and the opposite is true of negative values. Figures 6.27 and 6.28 demonstrate that colder ground than air temperatures exist during times when snow is on the ground resulting in slower ablation rates and higher accumulation rates, caused by less surface melt.
Figure 6.23: NOAH LSM 0.05 meter soil and air temperatures during snow season two for Bismarck, ND. X axis ticks are weeks and each label approximates a month.
290.0
285.0 NOAH LSM Air Temperature NOAH LSM Soil Temperature 0.05m 280.0
275.0
270.0
265.0
260.0 Temperature (K)
255.0
250.0
245.0
240.0 1 225 449 673 897 1121
93 Figure 6.24: NOAH LSM 0.05 meter soil and air temperatures during snow season two for Scottsbluff, NE.
300.0
295.0 NOAH LSM Air Temperature 290.0 NOAH LSM Soil Temperature 0.05m
285.0
280.0
275.0
270.0 Temperature (K) Temperature
265.0
260.0
255.0
250.0 1 225 449 673 897 1121
Figure 6.25: NOAH LSM 0.05 meter soil and air temperatures during snow season six for Bismarck, ND.
300.0
NOAH LSM Air Temperature NOAH LSM Soil Temperature 0.05m 290.0
280.0
270.0 Temperature (K) Temperature 260.0
250.0
240.0 1 225 449 673 897 1121
94 Figure 6.26: NOAH LSM 0.05 meter soil and air temperatures during snow season six for Scottsbluff, NE.
300.0
295.0 NOAH LSM Air Temperature NOAH LSM Soil Temperature 0.05m 290.0
285.0
280.0
275.0
270.0 Temperature (K) Temperature
265.0
260.0
255.0
250.0 1 225 449 673 897 1121
Figure 6.27: NOAH LSM snow depth and 0.05 meter soil and air temperature differences during snow season two for Bismarck, ND. Temperature differences are of air temperature subtracted from ground temperature such that positive values indicate a colder ground temperature than air temperature and the opposite is true of negative values.
0.35 15.0 NOAH LSM Snow Depth NOAH LSM Temperature Difference 0.30 10.0
0.25 5.0
0.20 0.0
0.15 -5.0 Snow Depth (m) Snow Depth Temperature Difference (K) Difference Temperature
0.10 -10.0
0.05 -15.0
*NOAH LSM Air Temperature is 3.0 K colder than the NOAH LSM 0.05 meter soil temperature 0.00 -20.0 1 225 449 673 897 1121
95 Figure 6.28: NOAH LSM snow depth and 0.05 meter soil and air temperature differences during snow season two for Scottsbluff, NE. Temperature differences are of air temperature subtracted from ground temperature such that positive values indicate a colder ground temperature than air temperature and the opposite is true of negative values.
0.35 10.00 NOAH LSM Snow Depth NOAH LSM Temperature Difference
0.30 5.00
0.25
0.00
0.20
-5.00
0.15 Snow Depth (m) Depth Snow
-10.00 Temperature Difference (K)
0.10
-15.00 0.05
*NOAH LSM Air Temperature is 1.2 K colder than the NOAH LSM ground temperature 0.00 -20.00 1 225 449 673 897 1121
Comparisons between snow depths demonstrate the differences between snow accumulation and ablation rates as well as the dependence on ground temperature.
Figures 6.29 through 6.32 show that the modified version of SNTHERM was able to replicate to a reasonable degree, NOAH LSM snow accumulation and ablation rates as well as overall snow depth. This result indicates that snow accumulation and ablation rates are highly sensitive to ground temperatures, and that the MM5 NOAH LSM coupled model system overestimates snow accumulation and underestimates snow ablation because of colder ground temperatures.
96 Figure 6.29: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season two for Bismarck, ND. X axis ticks are weeks and each label approximates a month.
0.40
0.35 NOAH LSM Snow Depth SNTHERM Snow Depth SNTHERM Modified Snow Depth 0.30
0.25
0.20
Snow Depth (m) 0.15
0.10
0.05
0.00 1 225 449 673 897 1121
Figure 6.30: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season two for Scottsbluff, NE.
0.30 NOAH LSM Snow Depth SNTHERM Snow Depth SNTHERM Modified Snow Depth 0.25
0.20
0.15
Snow Depth (m) 0.10
0.05
0.00 1 225 449 673 897 1121
97 Figure 6.31: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season six for Bismarck, ND.
0.25
NOAH LSM Snow Depth SNTHERM Snow Depth SNTHERM Modified Snow Depth 0.20
0.15
0.10 Snow Depth (m)
0.05
0.00 1 225 449 673 897 1121
Figure 6.32: NOAH LSM, SNTHERM, and SNTHERM Modified snow depths during snow season six for Scottsbluff, NE.
0.35
0.30 NOAH LSM Snow Depth SNTHERM Snow Depth SNTHERM Modified Snow Depth 0.25
0.20
0.15 Snow Depth (m) Depth Snow 0.10
0.05
0.00 1 225 449 673 897 1121
98 6.4.4 Subsurface Temperatures
Subsurface temperature gradients impact the ground heat flux and subsequently the ground temperature making subsurface soil temperature estimations critical to modeling the snow-ground interface. Soil temperatures at the 0.05, 0.25, and 0.70 meter levels were compared to assess what impact the NOAH LSM’s colder ground temperatures had on the underlying soil layers as well as the ground heat flux.
Soil temperature comparisons at the 0.05, 0.25, and 0.70 meter depths generally show that ground temperatures are colder than subsurface temperatures and that subsurface temperatures warm with depth (Figures 6.33 through 6.44). Because observed subsurface temperatures warm and fluctuate less with depth (Bartlett et al. 2004 and
Strack et al. 2003), these results make sense. Figures 6.33, 6.36, 6.39, and 6.42 make it clear that the much colder NOAH LSM 0.05 meter ground temperatures bias the subsurface temperatures such that they are much colder than the SNTHERM subsurface temperatures.
A more interesting result is that the SNTHERM modified subsurface temperatures are very similar to the NOAH LSM subsurface temperatures when snow is on the ground, especially at the deeper levels (0.25 and 0.70 meters) (Figures 6.35, 6.38, 6.41, and 6.44).
This result makes sense for the NOAH LSM because very cold 0.05 meter soil temperatures will conductively cool the underlying soil. So, the SNTHERM modified version was able to reproduce the NOAH LSM snow accumulation and ablation rates as well as snow depth and subsurface temperatures to a reasonable degree. This result can definitely attribute the snow accumulation (ablation) overestimation (underestimation) to cold surface and subsurface temperatures.
99 It is important to note that because NOAH LSM average monthly 0.05 meter soil temperatures were prescribed in the modified version of SNTHERM, the associated output can not be considered a definitive result. Nonetheless, the results do give credence to the fact that the NOAH LSM subsurface temperatures should be colder than they are considering the very cold modeled 0.05 meter soil temperatures.
100 Figure 6.33: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Bismarck, ND.
101 Figure 6.34: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Bismarck, ND.
102 Figure 6.35: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Bismarck, ND.
103 Figure 6.36: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Scottsbluff, NE.
104 Figure 6.37: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Scottsbluff, NE.
105 Figure 6.38: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season two for Scottsbluff, NE.
106 Figure 6.39: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Bismarck, ND.
107 Figure 6.40: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Bismarck, ND.
108 Figure 6.41: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Bismarck, ND.
109 Figure 6.42: NOAH LSM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Scottsbluff, NE.
110 Figure 6.43: SNTHERM snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Scottsbluff, NE.
111 Figure 6.44: SNTHERM Modified snow temperature (a), 2 meter air temperature (b), and snow depth (c) as compared to soil temperatures (d) during snow season six for Scottsbluff, NE.
112 SNTHERM and SNTHERM modified difference maps demonstrate that both versions of the models are warmer than the NOAH LSM. The SNTHERM modified differences are less and the near-surface variability is also decreased caused by the prescribed average monthly 0.05 meter soil temperatures from the NOAH LSM. This result is important because it shows that the NOAH LSM subsurface temperatures should be warmer than they are, according to the SNTHERM modified results. Because both models soil components are simplistic in design, it is only possible to infer which model better simulates subsurface thermal regimes, with SNTHERM better matching Great
Plains field observations. Additionally, inflated soil thermal conductivities are not causing anomalous subsurface cooling because of a 1.9 W m-1 K-1 cap (Figure 4.3)
Figure 6.45: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season two for Bismarck, ND. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM.
(a) (b)
113 Figure 6.46: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season two for Scottsbluff, NE. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM.
(a) (b)
Figure 6.47: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season six for Bismarck, ND. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM.
(a) (b)
114 Figure 6.48: SNTHERM (a) and SNTHERM Modified (b) soil temperature difference maps for snow season six for Scottsbluff, NE. Difference is SNTHERM and SNTHERM Modified minus the NOAH LSM.
(a) (b)
6.4.5 Snow/Ground Interface Heat Flux
The snow/ground interface heat flux (hereafter ground heat flux) can be an important component of the surface energy balance, especially over snow-covered surfaces. When snow covers the ground, a positive ground heat flux (using the NOAH
LSM and SNTHERM convention) means that heat is conductively transported upwards because the subsurface is warmer than the surface. The opposite is true if the surface is warmer than the subsurface. Therefore, accurate subsurface simulations lead to a better representative ground heat flux magnitude and direction.
There are no significant differences between the NOAH LSM and SNTHERM ground heat fluxes, despite the fact that the ground and subsurface temperatures are very different. However, because the degree to which they differ is similar, it makes sense that the associated ground heat flux magnitudes and directions are similar. The most
115 interesting result is that the SNTHERM modified ground heat flux averages out to be negative during the time that snow is on the ground (Figure 6.49 and Table 6.10). This happened because the snow temperature at the bottommost snow layer was nearly isothermal at 273K while the ground temperature was colder, leading to a negative ground heat flux. This did not happen with the NOAH LSM because of colder ground than 0.05 meter soil temperatures leading to a positive ground heat flux.
Figure 6.49: NOAH LSM, SNTHERM, and SNTHERM modified ground heat fluxes as compared to snow depth for Bismarck, ND from November 6, 2000 through April 1, 2001. Positive ground heat fluxes are upward from the surface and the opposite is true of negative values.
100.0 NOAH LSM Ground Heat Flux 80.0 SNTHERM Ground Heat Flux SNTHERM Modified Ground Heat Flux 60.0
40.0 ) -2 20.0
0.0 1 225 449 673 897 -20.0 Heat Flux (W Flux m Heat -40.0
-60.0
-80.0
-100.0
Table 6.10: NOAH LSM, SNTHERM, and SNTHERM modified ground heat fluxes (W m-2) and ground heat flux differences for November 6, 2000 through April 1, 2001 for Bismarck, ND.
↑ ↑ ↑ G NOAH G SNT G SNT_MOD NOAH − SNT NOAH − SNT_MOD SNT − SNT_MOD +13.2 +15.6 -6.6 -2.4 +19.8 +22.2
116 Chapter 7: Discussion and Conclusions
7.1 Discussion
Land surface modeling plays a pivotal role in understanding the interaction at the air/ground interface. This modeling study offers insight into how simplified snow physics in a mesoscale model compare to complex snow physics in a one-dimensional snow model. However, because there are no observations for much of the model output, it was only possible to compare output between the models, without being able to compare the results to something measured or observed.
SNTHERM required reflected shortwave radiation as input, which was calculated using the MM5 land surface albedo from equation 5.1. This equation results in higher albedos for a snow covered surface and the opposite is true of a snow-free surface.
Because SNTHERM ground temperatures were nearly isothermal at 273 K, when snow was on the ground, ablation rates were faster leading to more snow-free days. Thus, there were many instances when less surface radiation would reach SNTHERM caused by using MM5 albedo when MM5 simulated a snow covered surface. While a lower surface radiation forcing would result in colder ground temperatures, this did not seem evident with SNTHERM. Because MM5 snow accumulation (ablation) rates were so overestimated (underestimated), there were no instances when SNTHERM had snow on the ground and MM5 did not. This would have resulted in SNTHERM very rapidly melting off the snowpack because of prescribed land surface albedos for a snow-free, rather than a snow covered surface.
The modeling results showed considerable differences between snow thermal conductivities, ground and subsurface temperatures, as well as snow accumulation and
117 ablation rates. The snow thermal conductivity algorithm in the NOAH LSM significantly overestimates denser snowpacks, such that they are greater than that of ice (Table 4.1).
This would cause much colder ground temperatures because higher thermal conductivities allow for more rapid conductive cooling of the ground surface. This occurs because less air is in the snowpack causing a colder snow temperature. However, the NOAH LSM has a snow density maximum set at 400 kg m-3, making snow thermal conductivity an unlikely reason for the cold ground temperatures (Figure 7.1).
Figure 7.1: NOAH LSM, SNTHERM, and SNTHERM Modified estimated snow density for snow season two for Bismarck, ND. Snow density estimates are of swe divided by snow depth.
700.0
600.0 NOAH LSM Density SNTHERM Density SNTHERM Modified Density
) 500.0 -3
400.0
300.0
Density Estimate (kg m 200.0
100.0
0.0 1 225 449 673 897 1121
Soil thermal conductivities are similar between models with values generally ranging between 0.5 and 2.0 W m-1 K-1, depending on soil moisture. However, the
NOAH LSM near-surface temperatures show a definitive diurnal propagation of cold or
118 warm air downward. If the soil thermal conductivities were inflated then this propagation would make sense. Therefore, it is the simplistic one layer slab treatment of the snowpack where snow temperature is uniform throughout the snowpack that causes the rapid conductive cooling of the subsurface and not a coupling between inflated snow and soil thermal conductivities.
Ground and subsurface temperatures were much colder in the NOAH LSM than
SNTHERM, leading to overestimations of snow accumulation and underestimations of snow ablation rates. Ground temperature measurements show that surface temperatures should remain nearly isothermal around 273.0 K when snow is on the ground and that subsurface temperatures should warm with depth. Schmidt et al (2001) demonstrated that the differences between 1 cm ground temperatures and air temperatures from December to February in Fargo, ND can be as much as 20°C because of the insulating properties of snow.
The SNTHERM modified version demonstrated that snow densities at the bottommost snow layers averaged above 500 kg m-3 and at times exceeded 800 kg m-3
(Table 7.1 and Figure 7.2) with snow thermal conductivity values that averaged nearly
1.0 W m-1 K-1 and at times exceeded 3.0 W m-1 K-1 (Table 7.1 and Figure 7.3).
According to equation 4.9, the NOAH LSM overestimates snow thermal conductivity at higher densities because of the exponential calculation.
The SNTHERM modified version demonstrates that using this exponential thermal conductivity equation along with the average monthly 0.05 meter soil temperatures leads to a very dense and thermally conductive snowpack. This very dense and thermally conductive snowpack allows for more rapid propagation of cold air
119 temperatures, leading to unrealistic simulations of subsurface temperatures (Figures 6.33,
6.36, 6.39, and 6.42).
Figure 7.2: SNTHERM and SNTHERM Modified average snow densities as compared to snow depth during snow season two for Bismarck, ND. Average snow density is the bottommost three layers averaged.
0.40 900.0 SNTHERM Modified Snow Depth SNTHERM Snow Depth 800.0 0.35 SNTHERM Modified Snow Density SNTHERM Snow Density 700.0 0.30
600.0 0.25 ) -3 500.0
0.20
400.0 Density (kg m Snow Depth (m) Depth Snow 0.15 300.0
0.10 200.0
0.05 100.0
0.00 0.0 1 225 449 673 897 1121
Table 7.1: SNTHERM and SNTHERM Modified average snow thermal conductivities (W m-1 K-1) and densities (kg m-3) for November 6th, 2000 though April 1st, 2001 for Bismarck, ND.
Snow Thermal Conductivity Snow Density SNTHERM SNTHERM Modified SNTHERM SNTHERM Modified 0.191 0.966 154.0 504.0
120 Figure 7.3: SNTHERM and SNTHERM Modified average snow thermal conductivities during snow season two for Bismarck, ND. Average snow thermal conductivity is the bottommost three layers averaged.
7.2 Conclusions
This project used a physically based, one-dimensional point snow model
(SNTHERM) and a mesoscale model (MM5) coupled to an LSM (NOAH LSM) to compare snow depth output to observations across the Northern Great Plains. MM5 was run from December through April of the 1999/2000 through 2004/2005 season using a
25-km resolution inner domain. Meteorological output from MM5, such as temperature, wind speed, and precipitation, was used to drive the SNTHERM model for six pre- selected cities (Bismarck, Williston, Huron, Sioux Falls, North Platte, and Scottsbluff).
The closest MM5 domain 2 grid was chosen as representative of each city.
Before beginning with any analysis, some model sensitivity testing was necessary because SNTHERM required either cloud cover or radiation information. Cloud cover
121 and cloud type had little effect on snow depth, and therefore radiation information was given as input to SNTHERM.
New snow density, snow grain size, snow thermal conductivity, porosity, and snow compactive and metamorphic effects were also tested to determine SNTHERM’s sensitivity to changes in these variables. Snow grain size and porosity had little effect on snow depth, while new snow density, snow thermal conductivity, and snow compactive and metamorphic effects were all very sensitive to changes in any of these variables.
Time-series graphs were produced for each snow season in order to compare
SNTHERM and MM5 snow depth output to the observations. Invariably, SNTHERM better models snow depth owed to more credibly simulating the snow-ground interface temperature. There were, of course, several seasons that MM5 outperformed
SNTHERM, but overall, SNTHERM modeled snow depth at a higher quality level. This assessment was confirmed by various model evaluation statistics averaged for all cities
(Table 6.4).
Time-series comparisons of MM5 and SNTHERM with the observations are generally favorable. They show similar accumulation and ablation events, and capture many of the heavier snow events. However, in a few cases, the observations show a large snowfall event that MM5 did not simulate well. This problem could be explained by comparing point observations to an average grid box value (25-km by 25-km), in which sub-grid scale variability can not be resolved, or that MM5 simulated the location of the heavy event incorrectly owed to too large of a grid resolution.
Snow physics differences were compared between SNTHERM and MM5 because large-scale mesoscale models or GCMs simplify snow physics for computational and
122 numerical efficiency. Consistently, even with a more sophisticated LSM coupled to
MM5, the snow physics were less complex, as compared to SNTHERM. This led to
MM5 snow accumulation overestimations and snow ablation underestimations. The problem stems from ground and subsurface temperatures that are too cold caused by simulating the snowpack as a one layer slab. This consistently causes overestimations in snow accumulation and underestimations in ablation, both much less in agreement with the observations than SNTHERM accumulation and ablation rates.
SNTHERM attempts to treat the snow layers as they would naturally occur, where each new snowfall does not add to the preexisting snowpack, rather creates its own snow layer with the characteristics (humidity, temperature, et cetera) of the event during which the snow fell. SNTHERM also has more complex snow thermal conductivity, density, ablation, and accumulation calculations and accounts for snow metamorphosism whether from compaction, overburden, or freeze-thaw cycles. Additionally, SNTHERM simulates ground and subsurface temperatures much more in agreement with what others have observed in the field. All of these differences lead to different energy budget and melt calculations at the snow-atmosphere and snow-ground interfaces, with SNTHERM better simulating the snowpack.
SNTHERM with only two modifications was able to reasonably reproduce the
NOAH LSM snow depth output and reasonably simulate subsurface temperatures.
Therefore, SNTHERM modified results make it appropriate to conclude that the NOAH
LSM simplistic slab representation would lead to a snowpack that is too dense and thermally conductive which would cause a ground and subsurface that is too cold. All of which cause snow depth overestimations and snow ablation underestimations, much less
123 in agreement with the observations than SNTHERM unmodified. However, because the
NOAH LSM uses a maximum snow density cutoff of 400 kg m-3, it is the simplistic one layer slab treatment of the snowpack, not the overestimations in snow thermal conductivity and snow density that cause the much colder ground and subsurface temperatures.
Future work could involve adding or coupling SNTHERM to a mesoscale model such as MM5 or the new Weather Research and Forecasting (WRF) model. The argument for not including complex snow models in large atmospheric models has always been computational load. However, with recent advances, this is no longer an issue. SNTHERM does not have terrain or vegetative effect parameterizations, making a coupling ideal for areas with little relief and homogeneous vegetation. However, if
SNTHERM were coupled to an LSM, such as the NOAH LSM, then SNTHERM could calculate the snowpack information while the LSM handled all the vegetative and terrain effect calculations. This should lead to a better representation of the snow-atmosphere and snow-ground interfaces, which should lead to better simulations of the boundary layer.
Model analysis makes it clear that such a coupling could be quite advantageous considering the simplistic treatment of the snowpack leading to unrealistically cold ground temperatures and overestimations (underestimations) in snow accumulation
(ablation) rates. The latter two rates are fundamental for accurate snow modeling because both affect all surficial processes.
124 Chapter 8: Bibliography
Akima, H., 1970: A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures. Journal of the Association of Computing Machinery, 17, 589- 602.
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