ieee transactions on geoscience and remote sensing 1...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

Observing System Simulation of Snow MicrowaveEmissions over Data Sparse Regions—

Part II: Multilayer PhysicsDo Hyuk Kang and Ana P. Barros, Senior Member, IEEE

Abstract—A multilayer formulation of snow hydrological pro-cesses implemented in an existing snow hydrology-emission model(MLSHM-ML) was applied in observing system simulation mode(OSS) to two very different climatic and physiographic regions(Valdai, Russia and Colorado, USA) for both wet and dry snowregimes, and over multiple years. The results were evaluatedagainst ground-based observations of snowpack physical prop-erties and microwave radiometric observations from scanningmultichannel microwave radiometer (SMMR), special sensor mi-crowave/imager (SSM/I), and advanced microwave scanning ra-diometer-EOS (AMSR-E) observations at 18–19-, 22–23-, and36–37-GHz vertical and horizontal polarizations (V-pol and H-pol,respectively). Whereas snow water equivalent (SWE) results aresimilar to the results obtained with single-layer physics when thesnow is dry, the multilayer physics have a better skill at capturingthe overall temporal evolution of bulk density, snow temperature,and snow depth during the accumulation season, and at the onsetand throughout the melting season. However, snow density profilesoverestimate density at the bottom of the snowpack, consistentwith the lack of an explicit representation of depth hoar in therearrangement of mass and grain size distribution in the snow-pack. Regarding the radiometric behavior, the multilayer SMMROSS for Valdai shows improved results for nighttime simulations(descending SMMR paths, 11 P.M. LST) and H-pol (∼3–5 Kdecrease in error statistics), particularly at 37 GHz. For daytimesimulations (ascending SMMR paths, 11 A.M. LST), there aremodest improvements at 18 (∼1 K) and 37 GHz (∼2–3 K) forH-pol, and generally loss of skill for V-pol at all frequencies. Sys-tematic improvements at nighttime but not during daytime suggestthat surface heterogeneities, including subgrid scale variability oftransient melting, play an important role on surface emissivity.This is the case for cold land process experiment in Colorado,where spatial variability in fractional forest cover, geology, andcomplex topography explains the modest differences between thesingle and multilayer SSM/I OSS for H-pol, whereas significantgains (∼ 4–8 K decrease in error statistics) were attained for V-polat 37 GHz only. For AMSR-E, the multilayer OSS looses skill forH-pol, and only bias and mean absolute error improve for V-polat all frequencies. These somewhat mixed results suggest thatrepresentation of snow stratigraphy alone is not sufficient to im-prove the OSS ability to describe the nonlinear interactions amonghydrologic and electromagnetic processes. Chief among these arethe temporal evolution of snow correlation length with depth and

Manuscript received November 30, 2010; revised May 28, 2011 and August19, 2011; accepted September 11, 2011. This work was supported in part by aNASA Earth System Science Fellowship with the first author, and NASA GrantNNX07AK40G and NOAA Grant NA080AR4310701 with the second author.

The authors are with the Pratt School of Engineering, Duke University,Durham, NC 27708 USA (e-mail: [email protected]).

Color version of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2011.2169074

the representation of subgrid scale variability constrained by thespatial resolution and inherent uncertainty of the meteorologicalforcing. Nevertheless, the multilayer OSS improved performanceat 37 GHz is an important finding toward reducing ambiguity inthe sensitivity of 37-GHz H-pol brightness temperature to SWE inretrieval models.

Index Terms—Electromagnetic propagation in absorbing me-dia, multi-layer, nonhomogeneous media, snow hydrology.

I. INTRODUCTION

KANG and Barros [1] presented a framework for moni-toring snow water equivalent (SWE) and snowpack ra-

diometric properties including microwave emissions that wasdeveloped by combining a snow hydrology model [24] witha microwave emission model [2], [3]. The idea is to rely onthe radiometry of snow surfaces interpreted in the light of thesnow physics to track the temporal evolution of snowpack mi-crophysical and hydrologic properties, and consequently elim-inate ambiguity in the interpretation of satellite observations.Generally, the ultimate goal is to map ice sheets, glaciers,and snowpack properties including snow-covered area, snowdepth, snow wetness, and SWE particularly in regions of remoteaccess, or inhospitable climate and terrain where ground-basedmeasurements are not feasible and aircraft-based measurementsare impractical. In addition to the role of snow cover extent andcomposition on albedo, and thus in the surface energy budgetof the planet [5], snowpacks store precipitation temporarilyduring the cold season for release during the warm season, andtherefore snow accumulation plays also a critical role in thewater budgets and freshwater resources of vast regions of theworld, such as the western U.S. [6].

Satellite-based remote sensing of snow originally relied onphysically based empirical relationships between the differencein emission behavior at 37 GHz (V or H polarizations, the mostsensitive frequency to changes in snow microstructure), andthe emission behavior at a lower frequency (18 or 19 GHz),and snowpack properties namely snow depth and SWE onthe other [7], [8]. Relevant sensors in this context in-clude passive microwave radiometers such as scanning mul-tichannel microwave radiometer (SMMR) [9], special sensormicrowave/imager (SSM/I) [10], and advanced microwavescanning radiometer-EOS (AMSR-E) [11], respectively, onboard of Nimbus-7 [12], defense meteorological satellite pro-gram [13], and AQUA [14] satellites. Prompted by the necessityto estimate snowpack properties at locations around the worldwith different terrain, soils, vegetation cover, air pollution, and

0196-2892/$26.00 © 2011 IEEE

2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

overall climate, it became clear early that empirical modelsrequiring place-based calibration based on local observationscould not be used for reliable operational retrievals. Instead,dynamical calibration approaches relying on a mix of satelliteand ground-based ancillary data were developed to produceglobal estimates of snow cover and snow depth [36]. To addressthis challenge, alternative approaches were developed based onphysically based models that simulate the microwave emissionof the snowpack as a function of its physical and electromag-netic properties. Specifically, multilayer snow hydrology mod-els such as SNTHERM [20], CROCUS [21], and SNOWPACK[22] have been coupled successfully to microwave emissionmodel for multilayered Snowpacks (MEMLS) [2]–[4], [23].

Part 1 [1] describes the MLSHM, a hydrology-emissionmodel that resulted from coupling an existing hydrology model,the LSHM [24], to MEMLS both using single and multi-layer physics. The single-layer adaptation of MLSHM yieldedconsistently good performance statistics for observing systemsimulation (OSS) simulations of SMMR (six years simulation),SSM/I (1 year simulation), and AMSR-E (1 year simulation)with absolute bias during dry snow periods that does not exceed4.5 K. Overall, error statistics presented by [1] throughoutthe snow season from accumulation through melt yield betteror similar skill to previous emission modeling studies (e.g.,[16]). Yet, the forward simulations of snowpack emissivitywere significantly better for the vertical polarization than forhorizontal polarization at all frequencies and for all sensorswith differences in error statistics greater than 10 K. Forinstance, the bias at 37 GHz decreases from 19.25 K forH-pol to 4.53 K for V-pol in the Valdai case. Furthermore,an evaluation of the snowpack physical properties indicatedthat melting was taking place faster than observed, and densityand snow depth tended to be, respectively, lower and higherduring the late accumulation and ripening phases than thosefrom snowpit observations during the cold land process fieldexperiment (CLPX, [31]). Although some of these disparitiesmay be the result of spatial scale discrepancies between modelresolution and nominal sensor footprints, as well as subgridscale variability associated with land use and land cover (e.g.,fractional vegetation cover, [38]) and terrain complexity, it ishypothesized that a multilayer formulation of snow hydrologythat can capture snowpack stratigraphy should have a positiveimpact on the representation of vertical gradients of tempera-ture, compaction rates, and thus density. Better representationof snow density profiles should lead to more accurate estimatesof snowpack radiometric properties (permittivity, absorption,and scattering coefficients) taking full advantage of the mul-tilayer formulation of MEMLS.

In this paper, the multilayer implementation of the snowhydrology model [1], [2] coupled to MEMLS (MLSHM-ML)is applied in fully prognostic OSS mode to the two case studiesdescribed by [1]: first, a multiyear simulation in Valdai, Russiato be compared against SMMR observations; and second, anextended cold season simulation (October–May) in 2002–2003encompassing accumulation, ripening, and melting phases dur-ing CLPX to be compared against SSM/I and AMSR-E bright-ness temperatures. In both cases, a suite of ground-basedobservations including SWE, snow density, and snow depth

Fig. 1. Schematic view of the multilayer snowpack containing snow tempera-ture Ts, snow water equivalent (SWE) hswe, snow depth hsn, snow density ρs,and volumetric liquid water content (LWC) lw for each snow layer.

are available, which permit evaluation of the evolution of thesnowpack physics concurrently.

Section II provides a short overview of key elements of themultilayer implementation of the coupled hydrology-emissionmodel (MLSHM-ML). A more detailed model description canbe found in [1]. Data used to force the coupled MLSHM-ML and to evaluate the model simulations are described inSection III. Section IV presents analysis of the results anddiscussion for Valdai, whereas the CLPX case study is pre-sented in Section V. Synthesis and conclusion are presented inSection VI.

II. MODEL DESCRIPTION

The basic structure of the coupled snow hydrology-emissionmodel is the same as described in [1], except that the focus hereis on the implementation of the multilayer coupled hydrology-emission model (MLSHM-ML). The snow layering algorithmtreats the mass and energy balance and snow compaction equa-tions on a layer-by-layer basis using first-order finite-differenceapproximations to describe vertical gradients. The number oflayers is adaptive during the simulation depending on layerdepth and volumetric liquid water content (LWC). The sameatmospheric correction scheme described by [1] is applied hereto the brightness temperatures as needed.

A. Multilayer Snowpack Hydrology

The multilayer snow hydrology model is already describedin the companion paper (Part 1, [1]). In the snow layering algo-rithm, the layers are divided and compacted as the snow depthincreases with precipitation, or decreases due to snowmelt. Inaddition, liquid water percolation between the snow layers andbetween the bottom snow layer and the upper soil layer isexplicitly resolved. A schematic view of the stacked snowpackis shown in Fig. 1. Each snow layer is characterized by statevariables such as layer thickness hsn, snow temperature Ts,SWE hswe, and volumetric LWC lw both expressed as a waterdepth [volume per unit area], and bulk density ρs. Snow layersbegin to accumulate from the bottom (layer 1, Fig. 1) up to thetop of the snowpack (layer n, Fig. 1). The mass flow exchangebetween layers below the top layer is governed by liquid waterflow when melting occurs and during rain-on-snow events.

KANG AND BARROS: OBSERVING SYSTEM SIMULATION OF SNOW MICROWAVE EMISSIONS II 3

Upon reaching the ground, snowflake morphology and snowgrain size evolve fast initially, and then slower in time due tothermodynamic processes associated with vapor transport (dif-fusion and deposition) in the snowpack. This leads to roundingand coarsening of snow grain size distributions over time. In theMLSHM, the evolution of the size distribution is parameterizedas a function of snow density following [32] and [34]. Depthhoar formation processes which become increasingly importantwith time and manifest themselves by a decrease of snowdensity in the lower (that is, deeper) layers of aged snowpacksand increase (by deposition) at mid-depths are not accountedfor explicitly [45]. The mass balance equation of each layer isexpressed by

dhjswe

dt=

1

ρw

(P jsn + xP j

r

)− Φj

sn j = 1 to n. (1)

Where ρw [kg/m3] is the density of water, Psn [kg/(sec m2)] isprecipitation in the form of snow, and xPr [kg/(sec m2)] is theaccumulated precipitation from rain-on-snow events. P j

sn andxP j

r are zero when j is not equal to n, and Φnsn [m/s] is the

snowmelt flux toward the lower layer

Φjsn = ρw

dhjsm

dtj = 1 to n (2)

where hjsm [m] is the depth of liquid water from snowmelt or

rainfall in layer j. This is obtained from the energy balanceequation. The maximum retention capacity of liquid water ineach layer is 5%. Above this value, the liquid water is releasedto the lower layer below. Also, it is noted that intermittentmelting is only triggered in the top layer due to diurnal solarforcing. Integrating from the bottom to the top of the n layersof thickness hj

sn(hjsn = (ρw/ρsn)h

jswe), volumetric LWC lwj,

ice water content iwj , and snow density ρjs [kg/m3], snowpackintegral properties such as total snow depth hsd (m), SWE [m],and snowpack volumetric LWC LWC [m] can be calculated.

When the snow depth at layer j, hjsn is less than a specified

minimum criterion, h∗sn (0.14 m in CLPX and 0.12 m in Valdai

based on the local climatology of annual snowfall), all relatedmass terms such as hj

sn and hjswe are combined, whereas T j

s

and the layer density ρjs are depth averaged using as weightsthe snow layer thickness at the previous and current time stepssimilar to [20]

Ts comb =hmsn · Tm

s + hm−1sn · Tm−1

s

hksn + hk−1

sn

(3)

hsncomb =hmsn + hm−1

sn (4)

ρs comb =hmsn · ρms + hm−1

sn · ρm−1s

hmsn + hm−1

sn

. (5)

B. Microwave Emission Model of LayeredSnowpacks (MEMLS)

While the bulk layer approach only considers simulation ofsingle-layer emissions, the multilayer model has n horizontallayers, which therefore enables taking advantage of the detailedvolume scattering calculations in MEMLS (see [1]–[3]).

Considering layer j (j = 1, n) in the multilayered snowpack,the outgoing radiation from the snowpack to the layer above

Fig. 2. Schematic view of the incoming and outgoing microwave propagationvariables of snow layers in MEMLS. Variables defined in the text.

and the layer beneath can be expressed as follows (Fig. 2):

Aj = rjBj + tjCj + ejTj (6)Dj = tjBj + rjCj + ejTj . (7)

With incoming radiation defined as follows:

Bj = sj−1Aj + (1− sj−1)Dj−1 (8)Cj =(1− sj)Aj+1 + sjDj . (9)

In the MEMLS multilayer formulation, the brightness tem-perature, Tb of each layer is Bj+1 [Bj+1 = sjAj+1 + (1−sj)Dj ], Aj+1 is the downwelling brightness temperature and sjis the reflectivity at the interface of adjacent layers, and betweenthe snow surface and the atmosphere at the top of the snowpack.

Equations (8) and (9) form a system of coupled linear equa-tions for the brightness temperatures Aj and Dj

Aj = rj[sj−1

Aj + (1− sj−1)Dj−1

]+ tj [(1− sj)Aj+1 + sjDj ] + ejTj (10)

Dj = tj[sj−1

Aj + (1− sj−1)Dj−1

]+ rj [(1− sj)Aj+1 + sjDj ] + ejTj . (11)

In matrix formation, the equations above can be rewritten

A =M1 ·A+M2 ·D + E (12)D =M3 ·A+M4 ·D + E. (13)

Where A and D account for the brightness temperatures of nlayers, M1 to M4 are n by n matrices containing r, t, and e, andE and F are the n vectors with brightness temperatures at theboundaries including Tsky and Tsoil. Using linear algebra, thefinal solution is

D = (I −M5)−1 ·

[M3 · (I −M1)

−1 · E + F]

(14)

where

M5 = M3 ·[(I −M1)

−1 ·M2

]+M4. (15)

After determining Dn, the outgoing brightness temperaturefrom the snow surface is given by B2 which is Tb

Tb = B2 = snTsky + (1− sn)Dn. (16)

The internal reflectivity, transmissivity, and emissivity, r,t, and e, respectively, are determined by absorption, γa andscattering, γb coefficients within the snowpack [1]. The layer


TABLE ILOCALLY ESTIMATED PARAMETERS βf AND Φf (τf,i − ςfLi = βf + φfVi), USING TWO YEARS OF SMMR OBSERVATIONS WITH A FORMAT OF

(ASCENDING/DESCENDING) AND LSHM-MEMLS SIMULATIONS AT VALDAI WHILE ζf WAS MAINTAINED WITH β AND Φ FOR OPTICAL DEPTH τf

scattering coefficients are estimated for each frequency basedon snow density ρjs and snow correlation length pjec (m), ameasure of surface-to-volume ratio of an electromagneticallyequivalent distribution of spherical particles equivalent to theheterogeneous snow grain size distribution of the real snowpack[32], [34]. Specifically, the classification presented in Table I of[34] was used to estimate the snow correlation length for eachlayer based on the temporal evolution of layer snow density.

III. DATA DESCRIPTION

As detailed in Part 1 [1], PILPS standard forcing and RUC40MM5 meteorological data (40× 40 km2) are used to forcethe coupled modeling system at regional scale, respectively forValdai and CLPX 2002–2003 studies. For the evaluation ofsimulated emissions, microwave brightness temperatures fromSMMR, SSM/I, and AMSR-E are used in the same way as inPart 1. Note that, despite common SMMR heritage, the fre-quencies are slightly different (2–3% difference) for SSM/I andAMSR-E. Accordingly, the exact sensor-specific frequenciesare used in the MEMLS OSS. Even though brightness temper-ature products are resampled and projected on equal Area scal-able Earth (EASE)-grid at 25× 25 km2, the nominal footprintspatial resolutions of each sensor at different frequencies arevery different (e.g., coarser for SMMR and SSM/I and finer forAMSR-E roughly on a 1 : 3 ratio). In addition to the spatial scalegaps between atmospheric forcing, and consequently MLSHMresolution, satellite observations, and ground-based observa-tions, it is important to acknowledge that even at their nominalscale, there is uncertainty in the RUC40 and the ERA40 datasets, which can vary from day to day depending on weatherconditions and availability of observations for data assimilation(e.g., [27]). The atmospheric corrections follow [1] closely.

A detailed description of CLPX is provided by the Na-tional Snow and Ice Data Center (NSIDC) CLPX web-site (http://nsidc.org/data/clpx/) and [31]. Within the Frasermesoscale study area (MSA), snowpit measurements at varioustimes were conducted at the location of the ground-basedpassive microwave radiometer No. 7 (GBMR-7), and withinthe three intense study areas (Alpine, St. Louis Creek, andFool Creek). CLPX snowpit observation profiles are used toevaluate the multilayer formulation of the snow physics inthe MLSHM-ML. Snowpits are trenches that allow one-time

mapping of the vertical profiles of density and temperaturein the snowpack, as well as stratigraphic analysis. Note thatsnowpit measurements are destructive, and once excavated, it isnot possible to sample the same location again. This contrastswith nondestructive monitoring such as proposed by [44] forexample. Again, there is a large gap in spatial scales betweenthe snowpit data (point scale, near instantaneous) and the scaleof the RUC40 grid cell (40 km, hourly) that is used to force theMLSHM-ML. Thus, the simulated emissions represent the av-erage electromagnetic behavior at the RUC40 scale, which canbe interpreted as a regional mean. By comparing the MLSHM-ML profile predictions against several snowpit profiles, it ispossible to characterize the uncertainty associated with surfaceheterogeneity at the subgrid scale. The data sets are avail-able at http://nsidc.org/data/clpx/clpx_pits.gd.html for the in-tensive study areas (ISAs), and for GBMR-7 at http://nsidc.org/data/docs/daac/nsidc0165_clpx_gbmr/index.html [50], [51].

IV. RESULTS AND DISCUSSION: VALDAI

A. Snow Physics

Fig. 3(a)–(c) show the inter-annual variability of SWE, snowdepth, and snow density simulated by the MLSHM using bothsingle and multilayer formulations. The two formulations yieldvery similar SWE results, consistent with the mass balanceconstraint in the model and with the phase of precipitation forc-ing (all precipitation is specified in terms of water equivalentof rain, and when temperature is below freezing, then rainfallis accumulated as snow). Slight differences from one year toanother reflect different types of precipitation. For example,percolation of liquid water deep into the snowpack during rain-on-snow events is described differently in single and multilayerformulations. In addition, surface melting takes place at a fasterrate in the multilayer simulation, because the uppermost layerthat interacts with the atmospheric boundary is shallower thanthe single-layer model, the vertical temperature gradient iscaptured with better fidelity, and thus it warms faster for thesame energy forcing (radiation, turbulent heat fluxes).

Snow depth in the multilayer simulation is significantlylarger than in the single-layer case, and consequently the bulksnow density is lower. This difference is because the bulksnow density in the multilayer snowpack increases more slowlythan the density of the single layer. The parameterization of

http://nsidc.org/data/clpx/clpx_pits.gd.htmlforthein-tensivestudyareas(ISAs),andforGBMR-7athttp://nsidc.org/data/docs/daac/nsidc0165_clpx_gbmr/index.html




Fig. 3. MLSHM simulations in Valdai compared with ground-truth ob-servations as available. (a) Snow water equivalent, SWE. (b) Snow depth.(c) Snow density.

Fig. 4. Temporal evolution of the number of snow layers in the MLSHM-MLsimulation for the Valdai simulations.

compaction rate (see [1] and [20]) is very sensitive to thethickness of the layers considered to account for overburdeneffects: the integral of the density profile over a stack of verythin layers (Fig. 4) leads to lower bulk density than that for thesingle-layer snowpack.

Fig. 5. SMMR (red circle) and MLSHM-ML (blue dot) corrected brightnesstemperatures (Tappm) at 37 GHz (top: H-pol. bottom: V-pol.)

Fig. 6. SMMR (red circle) and MLSHM-ML (blue dot) corrected brightnesstemperatures (Tappm) at 21 GHz. (top: H-pol. bottom: V-pol.)

B. Microwave Emissions

Figs. 5–7 show the time series of MLSHM-ML simulationsafter applying local atmospheric correction (Tappm, [1]) com-pared against SMMR observations from 1978 to 1983 at 37,21, and 18 GHz, for horizontal and vertical polarizations (H-poland V-pol). Table II shows the summary error statistics betweenSMMR and multilayer and single-layer MLSHM simulationsafter atmospheric correction (Tappm) for ascending (11:00 A.M.LST) and descending (11:00 P.M. LST) paths. The same atmo-spheric correction scheme with parameters optimized locallyas described by [1] was used here (Table I). Because theseparameters lead to larger atmospheric transmissivity values for


Fig. 7. SMMR (red circle) and MLSHM-ML (blue dot) corrected brightnesstemperatures (Tappm) at 18 GHz. (top: H-pol. bottom: V-pol.)

H-pol than V-pol, and despite lower snowpack emissivities forH-pol, there is a significant increase in the corrected brightnesstemperatures in H-pol relative to V-pol, particularly during coldand dry winter conditions.

The mean absolute error (ME), root mean squared error(RMSE), and bias were calculated by comparing the MLSHMsimulated value y against the corresponding SMMR observa-tion y at the same frequency and polarization

ME =

∑|y − y|n

(17)

RMSE =

√∑(y − y)2

n(18)

Bias =∑ y − y

n. (19)

The MLSHM-ML SMMR OSS for V-pol exhibits neutral tomodest improvements in error statistics at all frequencies fordescending (nighttime) paths as compared to the single-layerformulation for V-pol, except with regard to bias at 37 GHzwhich decreases (∼3 K). There is no improvement for as-cending (daytime) paths. However, in the case of H-pol, theerror statistics improve dramatically at 18 and 37 GHz forboth ascending and descending paths (∼1–1.5 K at 18 GHz,and 2–3.5 K at 37 GHz), corresponding to a decrease of up to30% in the difference between V-pol and H-pol as comparedto single layer. Similar behavior can be found at 21 GHz fordescending though not ascending paths. Thus, the multilayerformulation does improve significantly the SMMR OSS per-formance for horizontal polarization, but results are somewhatneutral or mixed for vertical polarization during the day. Inempirical retrieval algorithms (e.g., [7]), H-pol is used to esti-

mate SWE, whereas V-polarization is an indicator of snowpackinternal structure, and thus volume scattering. Thus, the resultssuggest that the multilayer representation of the snowpack, ifnot accompanied by an improvement in the representationsof the vertical distributions of nonlinear interactions betweensnow hydrologic states and electromagnetic properties, is notsufficient to describe the impact of snowpack stratigraphy, andspecifically the vertical structure of snow density, on emissions.On the other hand, significant improvements in H-pol simu-lations with the MLSHM-ML, and particularly at 37 GHz forboth ascending and descending paths, suggest that there is greatpotential for SWE monitoring from space.

C. Coupled Hydrology-Emission Behavior

The lack of improvement for V-pol in ascending paths isattributed to excessive warming of the brightness temperaturesand degradation of the OSS skill particularly at the peak of theaccumulation and ripening phases in the daytime (Table II).Fig. 8 shows the temporal evolution of SWE, integrated vol-umetric LWC, 37-GHz H-pol simulated brightness tempera-tures with optimal atmospheric correction (Tappm, [1]) forthe 1982–1982 snow season, and the corresponding SMMRobservations. The brightness temperature reaches a minimumbefore the maximum SWE accumulation in Fig. 8, and thusthere is an increase in internal energy before melting starts,the so-called “ripening” phase of the snowpack during whichtemperatures increase until they reach 273.15 K. The lackof sensitivity of the microwave emission as SWE increasesabove 100 mm is similar to the saturation behavior identifiedby [47] for SWE values above the 150–200 mm range. Sincesignificant changes of correlation length and density with depthto account for depth hoar and other microphysical changes arenot explicitly described by the model and the parameterizationof correlation length as a function of snow density is basedon limited empirical data [32], [34], this study indicates that amore parsimonious parameterization of the temporal evolutionof snow microphysics (metamorphic processes) with depth isrequired to improve the OSS simulations for V-pol using theMLSHM-ML as compared to the MLSHM-SL in Valdai. Thatis, better understanding of the temporal evolution of snowcorrelation length with density is necessary.

The simulated density and temperature profiles at three timescorresponding to accumulation A1, ripening A2, and meltingA3 phases (Fig. 8) are shown in Fig. 9. Consistent with thecompaction model described in Section II, snow density in-creases from the top to the bottom layer. However, note how thetemperature of the top snow layer decreases between February(A1) and March (A2), and then rapidly increases betweenMarch (A3) and April. A3 exhibits a strong inversion withthe upper layer significantly warmer than the lower layers, anindication that the melting phase is underway toward March23rd. The yellow marker in Fig. 8 marks March 21st 1983at the beginning of the melt season. On this date, there wassignificant daytime superficial melt resulting in high LWC bothin the multi- and single-layer simulations. Fig. 10(a) showsthat the brightness temperature from the multilayer modelincreases during the afternoon while that from single layer is


TABLE IIERROR STATISTICS IN [K] OF BRIGHTNESS TEMPERATURES Tappm SIMULATED BY MLSHM-ML AT VALDAI FOR ASCENDING/DESCENDING SMMR

PATHS, AND RESPECTIVE CHANGE ∆ (SL-ML). HALL [35] REPORTED BIASES BETWEEN SMMR AND SSM/I OF −5.4 AND 1.0 FOR ASCENDING,AND −8.85 AND 4.59 FOR DESCENDING PATHS, RESPECTIVELY, AT 18–19 V AND 37 V GHz

Fig. 8. MLSHM-ML simulated brightness temperatures with atmosphericcorrection (Tappm, 37 GHz, H-pol) and snowpack hydrology during the 1982to 1983 snow season at Valdai. A1: Feb. 5th, A2: Mar. 15th, A3: Mar. 23rd,and Yellow Circle: March 21st.

relatively constant. The brightness temperature is determinedby two terms in (16) [Fig. 10(a)–(c)]: 1- outgoing radiation, Dn,and 2- surface transmissivity (1− sn+1 = r + t). Compared tochanges in Dn, the change of surface transmissivity betweensingle- and multilayer formulations is negligible. The surfaceemission is influenced by the surface emissivity, the comple-mentary of the summation of reflectivity and transmissivity.Fig. 10(d) shows that (r + t) sharply decreases after 16:00 LSTleading to significantly higher brightness temperatures in themultilayer snow simulation. This increase is explained by theincrease in volumetric LWC inside the snowpack duringthe afternoon shown in Fig. 10(e). First, superficial meltingaround noon increased the LWC of the multilayer snowpack,lower internal reflectivity and transmissivity, and rapid increaseof the outgoing radiation Dn. Second, rainfall at the end of theday further increases the LWC. As previously pointed out by [1]using the single-layer formulation, increases in LWC “warm”

Fig. 9. Simulated snow temperature and density profiles at Valdai correspond-ing to dates A1, A2, and A3 in Fig. 8.

the snowpack and lead to an increase in outgoing radiation Dn.The representation of the combined effects of intermittent surfi-cial melting and other surface heterogeneities such as complextopography and heterogeneous land use and land cover can onlybe described by improved spatial resolution of the model, whichin turn depends strongly on the meteorological forcing.


Fig. 10. (a) Brightness temperatures of single- and multilayer simulations for 37-GHz H-pol. (b) Outgoing emission Dn. (c) Air–snow interface reflectivity sn.(d) Summation of internal reflectivity and transmissivity. (e) Brightness temperature of multilayer simulation at 37-GHz H-pol superimposed with rainfall (gray)on March 21st, 1983, corresponding to the location of the yellow circle in Fig. 8.

V. RESULTS AND DISCUSSION: CLPX

A. Snow Physics

Fig. 11 shows the SWE [Fig. 11(a)], snow depth [Fig. 11(b)],and bulk snow density [Fig. 11(c)] evolution for the multilayerand the single-layer MLSHM simulations against snowpit ob-servations at GBMR-7 in the local scale observation station(LSOS) within the Fraser MSA (for location, see Fig. 2 of Part 1[1]). The results show that during accumulation and beginningof ripening phases, the two formulations lead to similar results,whereas there are significant differences during late ripeningand melting phases. Melting is faster in the single-layer case,and, based on snowpit observations, melting is faster in bothmodel formulations as compared to observations. The simu-lated snowpack never reaches the high density values observedin mid-May, and presumably the densification of the snowpackin March–May, particularly at mid-depths is underestimatedthough there are no snowpit observations in that period totest this hypothesis. Note that the model results correspondto the grid cell that contains the entire Fraser MSA usingRUC40 forcing; the GBMR-7 data in Fig. 11 are presented

for reference purposes only, and therefore some variability isexpected around the observed values. One important result formodeling microwave signatures is that in both formulations,and better so in the multilayer case, the overall changes in snowdensity profile during the accumulation season appear to bewell captured by the model. Fig. 12 shows the evolution of thenumber of snow layers in the model increasing up to 14 duringthe peak accumulation season.

Fig. 13 shows the snow temperature and snow density pro-files at three different times corresponding to the points markedwith C1 (12/19/2002), C2 (2/21/2003), and C3 (3/26/2003)in Fig. 11(a) from left to right, respectively. The number oflayers varies with time as per Fig. 12. The results are comparedagainst the snowpit data from three ISAs in the Fraser MSA:Fool Creek, St. Louis Creek, and Alpine, as well as LSOS(GBMR-7). Because the RUC40 meteorological forcing fore-casts are used to drive the MLSHM at spatial resolution close tothe scale of the entire Fraser MSA, snowpit observations fromvery distinct locations within Fraser provide a good measure ofthe spatial variability of the snow physical condition against thesimulated area averages over time. At C1, the temperature of


Fig. 11. MLSHM simulations of snowpack evolution in the Fraser MSAusing RUC40 forcing. GBMR-7 integrated snowpit observations are shown forreference. (a) Snow water equivalent, SWE. (b) Snow depth. (c) Snow density.[C1, C2, and C3 correspond to selected dates for further analysis: 12/19/2002,2/21/2003, and 3/26/2003, respectively; the red filled circle with cross hairs inpart (a) the end of the accumulation season proper].

the top layer is well below freezing at 257 K, while the layersunderneath display increasing temperatures up to the meltingpoint both in the observations and in the simulations. Thisillustrates the typical heat insulating effect due to sensible heatfluxes [33]: even though the ambient temperature is cold, theinternal layers adjacent to the soil maintain higher snowpacktemperatures at the bottom. At C2, there is an increase of snowdensity from the top to bottom layers due to overburden effects,while some observed density profiles have lower density in thebottom layers which can be attributed to depth hoar effects.Despite differences in snowpack density at C2, the temperatureprofiles agree well particularly considering that the differentprofiles were obtained at far apart snowpit locations withinthe Fraser MSA (see Fig. 2 in Part1) encompassing differentlandforms, orientation with respect to solar forcing, and het-

Fig. 12. Temporal evolution of the number of snow layers in the MLSHM-MLsimulation of snowpack for the Fraser MSA in the 2002–2003 season duringCLPX.

erogeneous surface characteristics. The increase in density inthe uppermost layers of the snowpit observations at C3 accom-panied by the nearly uniform temperature profiles suggests thepresence of refrozen liquid water that percolated down fromsurface layer melting. During the accumulation season, themodel consistently underestimates the top layer temperature byas much as 5 K on average. In particular, by the end of March,the temperatures of the upper layers in the model are still belowfreezing and the density profile exhibits a steep monotonic slopewith depth that contrasts with the complex profiles from snow-pit observations with uniform density at mid-depth. This canbe addressed in part by increasing the number of layers at thetop of the snowpack to better represent numerically the strongtemperature gradient at the snow–atmosphere interface in solv-ing the heat transfer equations. Note that different layers in theMLSHM do not need to have different physical or electromag-netic properties, as they are specified based on thickness alone.

In addition, refreezing of the surface melt water at nighttimemay lead to the formation of ice lenses and heterogeneitiesthat should have an impact on microwave emissivity. Indeed,larger differences in density in the upper layers of the snow-pack should have an impact also on the parameterization ofthe snow grain size distribution [34], [41]. By the end ofthe accumulation season, the model has difficulty to capturerapid changes in snowpack structure associated with transientmelt and intermittent wet snow regimes likely due to its coldsurface temperature bias. Table III shows the RMSE of snowtemperature and snow density for C1, C2, and C3 dates. TheRMSE of snow temperature and snow density show a largeincrease after the onset of melting season (C3), which illustratesthe model limitations to explain the movement of liquid waterand snow ripening processes in the rapidly vanishing snowpack.

Profiles of snow temperature and density profiles from threedifferent snopwits at three distinct locations within the FraserMSA (Alpine, Fool Creek, and St. Louise Creek) at 9:00, 12:00,and 15:00 LST on the same day, Feb. 20th, are shown in Fig. 14to examine the diurnal cycle during the accumulation season.Note the increase in top layer temperature during the day andthe effect of spatiotemporal variability in the propagation of theheat flux from the top to the bottom of the snowpack, whereas


Fig. 13. MLSHM-ML simulation of snow temperature and density profiles against snowpit observations at three ISAs (Fig. 4, [1]) throughout the Fraser MSAcorresponding to dates C1, C2, and C3 in Fig. 11: 12/19/2002, 2/21/2003, and 3/26/2003, respectively.

TABLE IIIROOT MEAN SQUARE ERRORS [RMSE] BETWEEN THE SIMULATED PROFILES OF SNOW TEMPERATURE

AND DENSITY AND SNOWPIT OBSERVATIONS AT FRASER, MSA SHOWN IN FIG. 13

Fig. 14. MLSHM-ML simulations of the diurnal cycle of the vertical profiles of snow temperature and density on Feb. 20th 2003 using RUC40 forcing againstsnow pit observations at the three ISAs (Fig. 4, [1]) within the Fraser MSA. From left to right: 9:00, 12:00, and 15:00 LST, respectively.

the density profiles do not change significantly. The snowpitdata at the Alpine site at 12 P.M. show densification at mid-depths due to the presence of the liquid water. By mid-afternoon(15:00 P.M.), the temperature profiles both in the measurementsand in the simulation show a linear increase of temperature atthe top layer in response to solar forcing, and they are in goodagreement, though the model underestimates the temperatures

on average by about 3–5 K. The top layer exhibits therefore amarked diurnal cycle, and more so at St. Louis Creek. St. LouisCreek is located in the valley below 3000 m a.s.l., while theother two locations are above 3000 m on the slopes, and thustopographic effects should be important in terms of exposurefor example as well as snow redistribution by boundary layerwinds, which cannot be captured by the model.


Fig. 15. (a) Temporal evolution of the simulated difference in brightnesstemperature (∆Tb = Tb19H− Tb37H) and simulated snow water equivalent(SWE), (b) same as (a) but for AMSRE-E and SSM/I observations.

Furthermore, Fig. 14 shows that in the dry snow regime,during the accumulation phase, the model and the observationscome close to agreement below the top layer before the end ofFebruary. Snowfall rarely occurs during the first three weeks ofFebruary, and the air temperature does not exceed the meltingpoint of 273.15 K (not shown), which implies that the mi-crowave behavior in February is controlled by radiative forcingat the air–snowpack interface and internal processes within thesnowpack.

B. Microwave Emissions

Fig. 15(a) shows the temporal evolution of the differ-ence of brightness temperatures ∆Tb between 19-GHZ and37-GHz H-pol along with the temporal evolution of SWE formultilayer and single layer MLSHM simulations. The objectivehere is to examine the relationship between SWE and ∆Tb

used in empirical retrieval algorithms (e.g., [7]). As the snowaccumulates, volume scattering effects during the ripeningphase in late April and early May are quite different in themultilayer and single-layer simulations. When melting initiatesin mid-May, the multilayer results exhibit more sensitivitythan the single layer for which the difference between 19and 37 H-pol brightness temperatures abruptly collapses. Sim-ilarly, Fig. 15(b) presents ∆Tb calculated from AMSR-E andSSM/I observations at their nominal frequencies, respectively,19.35- and 37-GHz H-pol for SSM/I, and 18.7- and 36.5-GHzH-pol for AMSR-E. The difference between 19- and 37-GHzH-pol brightness temperatures (∆Tb) increases during thesnow accumulation phase, though the magnitude is 10 K

smaller in the satellite-based observations as compared to theMLSHM simulations. That is, the range of the simulations islarger than that of the satellite observations. The convex shapeof the observations is not captured by the model during theaccumulation phase, though the timing and magnitude of therapid transition from dry to wet snow regime in mid-Marchis present in both simulations and observations. The differencein the accumulation phase is tentatively attributed to the com-paction rate parameterization and, as discussed earlier, the lackof an explicit parameterization of depth hoar effects which havea strong impact on density profiles, vertical structure of snowgrain size distribution, and ultimately volume scattering.

Note that SWE peaks in May, whereas ∆Tb in both simu-lations and observations reaches a maximum in early March[Fig. 15(a) and (b)]. This phase shift between the peak of theaccumulation season in the dry snow regime and the peak inthe wet snow regime (ripe snowpack) explains the ambiguityin the relationship between SWE and ∆Tb in retrieval al-gorithms. The profound effect of increased density as wellas depth hoar on brightness temperatures at 37 GHZ wasaddressed by [35] who pointed out differences on the orderof 20 to 40 K at 37-H GHz depending on layer thickness fordry snowpacks, and addressed by [41] in the context of verydense snow samples. The relationship between the differencein brightness temperatures and snow depth is more sensitive athigher frequencies (e.g., 37 GHz) because of the significant at-tenuation within the snowpack as expressed by the relationshipbetween γa and ε′′. To help address this problem with empiricalretrieval models, [36] implemented dynamical calibration of therelationship between ∆Tb and snow depth, and [8] exploredvarious empirical retrieval models and found that incorporatingexplicit dependencies on elevation, land-cover categories, andatmospheric conditions decreased ambiguity and improved per-formance. An alternative approach to address the challenge ofambiguity in retrieval is to develop an algorithm that optimallyderives the snow physical properties from the observationsusing a model such as MLSHM and a Bayesian approach[40], or for example using the MLSHM results to constrain adynamically calibrated empirical model such as [36].

Finally, the panels in Fig. 16 show the brightness temperatureresponses near 19-, 23-, and 37-GHz V-pol and H-pol, respec-tively, against AMSR-E observations for the entire period ofsimulation. MLSHM-ML SSM/I OSS results are not shown, buterror statistics are included in Table IV. The results capture wellthe seasonal cycle, particularly in the melting season and for37-GHz H-pol. In the accumulation season between Decem-ber and early March, during which the model is consistentlywarmer than the observations, the typical concave shape corre-sponding to increasingly lower temperatures before the onset ofmelt is not captured for AMSR-E at 36.5-GHz V-pol not unlikethe behavior reported by [1]. This is attributed in part to errorsin the vertical density profile, and thus the vertical structureof the snow correlation length. As discussed previously, themodel underestimates density particularly at mid-depths, andoverestimates density near the bottom of the snowpack due tothe lack of a depth hoar and vapor diffusion and depositionparameterizations during dry periods in the accumulation phase[35]. Nevertheless, spatial scale differences between sensors’


Fig. 16. Comparison of AMSR-E observed and MLSHM-ML simulated brightness temperatures at 18.7-, 23.8-, and 36.5-GHz H-pol and V-pol. Very coldanomalous temperatures in late May take place during a short weather transition.

footprint resolutions, re-gridded products, and the effectivescale of MLSHM simulations that are in this case determinedby the meteorological forcing are also expected to contribute tothe discrepancies.

Table IV shows a summary of error statistics includingresults from [38] as a reference. [38] used a version of theHUT model as well as DMRT and MEMLS coupled to VIC forsimulations at two sites within the Fraser MSA, February–May2003, thus including both dry and wet snow regimes over a four-month period. Overall, there are very small differences in errorstatistics between the single- and the multilayer simulations(measurement uncertainty alone is in the range of 0.5–1 K forSSM/I and AMSR-E). Results show clear gains in OSS skillonly for SSM/I at 37 GHz, in particular V-pol. This is in contrastwith the results obtained for Valdai, which suggests that snowstratigraphy is more complex in CLPX where the weather ismore variable and orographic effects are important as comparedto the northern (drier) latitudes and flatter topography of Valdai,and there is significant subgrid-scale variability in terms of landcover and landform. The improvement of error statistics of themultilayer OSS for V-pol in CLPX is better than for H-pol,even more so in the case of AMSR-E. Although the simulationperiod in this study is longer than previous studies (8 monthsversus weeks up to 4 months) and no surface observations were

used to specify snowpack properties or model parameters, thatis the model was run in full prognostic forward OSS modefrom snow hydrology to emissions, the errors statistics arecompetitive. This suggests that the MLSHM meets operationalreadiness requirements.

In summary, because the CLPX multilayer results do notsignificantly improve for horizontal polarization as compared toValdai, further analysis is required with regard to: 1) improve-ment of the representation of snow densification processes,particularly the effect of metamorphosis on compaction rate,and separate parameterization of correlation length for lay-ers that undergo intermittent melting and freezing leading tothe formation of ice occlusions for example (i.e., ice lenses,[49]); 2) explicit parameterization of depth hoar effects; and3) sensitivity analysis of the horizontal and vertical scatteringcoefficients to grain size correlation length and density on alayer-by-layer basis. Another critical aspect that must be ac-counted for is the role of subgrid scale variability of the topog-raphy as well as land cover, specifically vegetation (e.g., [48]).

C. Coupled Hydrology-Emission Behavior

The challenge of space-time intermittency in snowpack ra-diometric properties is examined next focusing on surficial


TABLE IVMODEL ERROR STATISTICS [MULTILAYER (SINGLE-LAYER)] AND CHANGE ∆ INTERCOMPARISON USING

THE CORRELATION LENGTH pcc BASED ON THE CLASSIFICATION BY [34] FOR THE FRASER MSADURING CLPX: SSM/I, AMSR-E, AND [38]. SINGLE-LAYER SIMULATION RESULTS ARE FROM [1]

Fig. 17. Sensitivity analysis of brightness temperature affected by volumetricliquid water content (lwn and lwn−1) in the two uppermost layers from 6 P.M.LST on May 14th through 6 A.M. on May 18th 2003 during CLPX. Notethe nocturnal freezing of volumetric liquid water in the top layer after mid-night LST.

snowpack melting. When it occurs, the liquid water movesdownward from the top to the adjacent lower layers before itrefreezes. This begs the question of which layer will contributemore to the microwave emission from the snowpack surface.Fig. 17 shows the temporal evolution of volumetric LWC (lw)in the two uppermost layers along with brightness temperatureat 37-GHz H-pol for a short window from 6 P.M. LST onMay 14th through 6 A.M. on 20th 2003 in the Fraser MSAduring CLPX. Note the convergence of brightness temperaturesto the physical snowpack temperature in response to afternoonwarming and transient melting induced by solar forcing. Thereis very strong correlation between the top layer LWC and thesurface brightness temperature, whereas changes in volumetricLWC in the second layer do not show a significant impact onthe brightness temperature. That is, the top layer controls theradiometric signature of the snowpack when there is surficialmelting. Combined with spatial heterogeneity, the occurrence

of intermittent surface melting and subsequent refreezing at thescale of the MLSHM simulations could be a leading cause ofthe drop of OSS skill during daytime (e.g., SSMR in Valdai), aswell as the mixed error statistics for H-pol and V-pol during theripening and early melting phases in CLPX.

VI. CONCLUSION

The MLSHM-ML leads to improved results particularly inthe case of horizontal polarization for the SMMR OSS inValdai compared with the single-layer physics [1]. In the caseof CLPX, performance was generally neutral as compared tothe MLSHM-SL except for SSM/I at 37-GHz H-pol and V-pol,and for AMSR-E at all frequencies in V-pol. General improve-ment of the OSS performance at 37 GHz for all three sensors(SMMR, SSM/I, and AMSR-E) indicates there is value inthe multilayer physics, particularly given the well-documentedsensitivity of snowpack emissions to snow physical propertiesat this frequency ([23], [26], [32] among others). The multilayerformulation further facilitates physically based inquiry into theprocesses that govern the coupled snow hydrology and radio-metric behaviors by focusing on vertical structure. Comparisonagainst snowpit data show that the model captures the overallevolution of the snowpack throughout the entire 2002–3003cold season in Colorado within the range of uncertainty de-termined by the spatial variability of the snowpit observations,including the vertical structure of snow temperature and snowdensity, particularly for dry snow conditions across the FraserMSA, and despite spatial scale differences. A cold bias of(3–5 K) was quantified for the top snow layers during theaccumulation season, which does not persist after the onset ofripening and melting processes as compared to observations.


Finally, the results obtained with the coupled multilayerMLSHM-ML for CLPX without calibration are competitivewith results obtained from emissivity models supplied by directobservations of snowpack characteristics (e.g., [18], [38], and[39]). Nevertheless, the results show that a multilayer repre-sentation of snow physics does not necessarily improve resultsas compared to the single-layer model, if the key governingprocesses that map the snowpack layers to snow stratigraphy,in the MLSHM-ML via the snow density profile, are not welldescribed and, or parameterized in the model. Note that, as dis-cussed in [1], fractional vegetation cover effects were neglectedin this study, but even if the values are very small, an explicitrepresentation should improve the results particularly for V-pol[52]–[54].

There are three types of physical processes that requireimproved model parameterizations: 1) densification and therepresentation of snow metamorphic processes, and particularlythe formation of depth hoar in dry cold climates during thewinter season, which has implications for both snow densityand snow grain size distribution, and has long been recognizedas a major challenge [35], [55], [56]; 2) the simulation of thesnowpack energy balance, and specifically the diurnal cycleof snowpack surface temperature, and snowpack–canopy inter-actions; and 3) explicit representation of intermittent surficialmelting in MEMLS. Furthermore, water percolation processesassociated with the effect of abrupt and intermittent melting inearly spring need to be further investigated [39]. During the fastmelting snow season, as the melting water percolates throughthe layered snowpack, multidirectional routing of liquid waterwithin the snowpack over complex terrain should also be ac-counted for, including outflow through intermediate layers aswell as lateral redistribution of liquid water interflow, and theunderlying matrix beneath the snowpack needs to be consideredsuch as ice lenses or lakes [46].

Finally, and independent of model physics, the two studiesshow that the utility of the MLSHM is ultimately determinedby the spatial resolution of the model, and the uncertaintyassociated with the representation of subgrid scale variability.The differences between Valdai and CLPX, and separatelybetween the SSM/I and AMSR-E OSS within CLPX suggestthat even though all satellite-based observations are used atthe same EASE-grid resolution, the influence of the originalnominal footprint resolution carries through the resampling andprojection: for H-pol, improvements (losses) in the MLSHM-ML simulation skills are much smaller (larger) for the higherresolution AMSR-E frequencies than for SSM/I. On the otherhand, use of meteorological forcing from the local tower at theGMR-7 location greatly improves the simulations at the localscale. Because the spatial resolution of the MLSHM is onlylimited by the spatial resolution of the meteorological forcing,there is great potential in improving performance and opera-tional utility in remote regions using high-resolution numericalweather prediction forecasts.

ACKNOWLEDGMENT

The authors are thankful to the Reviewers and Editors fortheir comments and suggestions.

REFERENCES

[1] D. Kang and A. P. Barros, “An evaluation of a coupled snow hydrologyand microwave emission model for data-sparse regions,” IEEE Trans.Geosci. Remote Sens., 2011, to be published.

[2] A. Wiesmann and C. Mätzler, “Microwave emission model of lay-ered snowpacks,” Remote Sens. Environ., vol. 70, no. 3, pp. 307–316,Dec. 1999.

[3] C. Mätzler and A. Wiesmann, “Extension of the microwave emissionmodel of layered snowpacks to coarse grained snow,” Remote Sens.Environ., vol. 70, no. 3, pp. 317–325, Dec. 1999.

[4] A. Rango, “Progress in snow hydrology research,” IEEE Trans. Geosci.Remote Sens., vol. GRS-24, no. 1, pp. 47–53, Jan. 1986.

[5] Intergovernmental Panel on Climate Change, Climate change 2007:The physical science basis, summary for policymakers, Geneva,Switzerland, 2007.

[6] P. W. Mote, “Trends in snow water equivalent in the Pacific northwestand their climatic causes,” Geophys. Res. Lett., vol. 30, no. 12, p. 1601,Jun. 2003.

[7] A. T. C. Chang, J. L. Foster, and D. K. Hall, “Nimbus-7 derived globalsnow cover parameters,” Ann. Glaciol., vol. 9, pp. 39–44, 1987.

[8] P. R. Singh and T. Y. Gan, “Retrieval of snow water equivalent usingpassive microwave brightness temperature data,” Remote Sens. Environ.,vol. 74, no. 2, pp. 275–286, Nov. 2000.

[9] C. R. Madrid, Ed., The Numbus-7 User’s Guide. Greenbelt, MD: GSFC,1978.

[10] J. W. Rivers, Jr., “Defense meteorological satellite program (DMSP),”in Proc. IEEE Int. Conf. Commun. 1G61/5, Philadelphia, PA, Jun. 1982,vol. 1, pp. 13–17.

[11] K. Imaoka, A. Shibata, N. Nakagawa, Y. Nakajima, H. Haijima,H. Tanaka, and T. Imatani, “Airborne microwave radiometer for AMSRand AMSR-E project,” in Proc. SPIE: Microw. Remote Sens. Atmos.Environ. II, 2000, vol. 4152, pp. 303–309.

[12] J. J. Horan, “Nimbus: The vanguard of remote sensing,” IEEE Spectr.,vol. 15, no. 11, pp. 36–43, 1978.

[13] R. H. Eather, “DMSP calibration,” J. Geophys. Res., vol. 84, no. A8,pp. 4134–4144, 1979.

[14] T. P. Nosek and P. Thomas, “The EOS AQUA/AURA experience:Lessons learned on design, integration, and test of earth-observing satel-lites,” in Collection Tech. Papers—AIAA Space Conf. Expo., 2004, vol. 3,pp. 1916–1923.

[15] M. Hallikainen, J. Pulliainen, L. Kurvonen, and J. Grandell, “The HUTbrightness temperature model for snow-covered terrain,” in Proc. Int.Geosci. Remote Sens. Symp., 1997, vol. 2, pp. 622–624.

[16] J. Lemmetyinen, J. I. Pulliainen, J. Rees, A. Kontu, and Y. Qiu, “Multiple-layer adaptation of HUT snow emission model: Comparison with experi-mental data,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 7, pp. 2781–2794, Jul. 2010.

[17] L. Tsang, C. Chen, A. T. C. Chang, J. Guo, and K. Ding, “Dense mediaradiative transfer theory based on quasicrystalline approximation withapplications to passive microwave remote sensing of snow,” Radio Sci.,vol. 35, no. 3, pp. 731–749, 2000.

[18] K. M. Andreadis, D. Liang, L. Tsang, and D. P. Letenmaier, “Charac-terization of errors in a coupled snow hydrology-microwave emissionmodel,” J. Hydrometeorol., vol. 9, no. 1, pp. 149–164, 2008.

[19] M. Tedesco and E. J. Kim, “Intercomparison of electromagnetic modelsfor passive microwave remote sensing of snow,” IEEE Trans. Geosci.Remote Sens., vol. 44, no. 10, pp. 2654–2666, Oct. 2006.

[20] R. Jordan, “A one-dimensional temperature model for a snow cover,” U.S.Army Corps Eng., Washington, DC, Special Rep. 91-16, 1991.

[21] E. Brun, P. David, M. Sudul, and G. Brunot, “A numerical model tosimulate snow cover stratigraphy for operational avalanche forecasting,”J. Glaciol., vol. 38, no. 128, pp. 13–22, 1992.

[22] M. Lehning, C. Fierz, and C. Lundy, “An objective snow profile com-parison method and its application to SNOWPACK,” Cold Regions Sci.Technol., vol. 33, no. 2/3, pp. 253–261, Dec. 2001.

[23] C. Mätzler, “Advances in microwave emission models for snow and ice,”in Proc. 2nd Workshop Remote Sens. Model. Surf. Properties, Toulouse,France, 2009, pp. 9–11.

[24] E. Devonec and A. P. Barros, “Exploring the transferability of a land-surface hydrology model,” J. Hydrol., vol. 265, no. 1–4, pp. 258–282,Aug. 2002.

[25] P. Gloersen and F. T. Barath, “A scanning multichannel microwave ra-diometer for Nimbus-G and SeaSat-A,” IEEE J. Ocean. Eng., vol. OE-2,no. 2, pp. 172–178, Apr. 1977.

[26] J. L. Foster, A. T. C. Chang, and D. K. Hall, “Comparison of snowmass estimates from a prototype passive microwave algorithm and a snow


depth climatology,” Remote Sens. Environ., vol. 62, no. 2, pp. 132–142,Nov. 1997.

[27] S. M. Uppala, P. W. Kallberg, A. J. Simmons, U. Andrae, V. Da CostaBechtold, M. Fiorino, J. K. Gibson, J. Haseler, A. Hernandez, G. A. Kelly,X. Li, K. Onogi, S. Saarinen, N. Sokka, R. P. Allan, E. Andersson,K. Arpe, M. A. Balmaseda, A. C. M. Beliaars, L. Van De Berg, J. Bidlot,N. Bormann, S. Caires, F. Chevallier, A. Dethof, M. Dragosavac,M. Fuentes, S. Hagenmann, E. Holm, B. J. Hoskins, L. Isaksen, P. A. E. M.Janssen, R. Jenne, A. P. McNally, E. Holm, B. J. Hoskins, L. Isaksen,P. A. E. M. Janssen, R. Jenne, A. P. McNally, J. F. Mahfouf, J. J. Morcrette,N. A. Ravner, R. W. Saunders, P. Simon, A. Sterl, K. E. Trenberth,A. Untch, D. Vasilievic, P. Viterbo, and J. Woolen, “The ERA-40 re-analysis,” Q. J. R. Meteorol. Soc., vol. 131, no. 612, pp. 2961–3012,Oct. 2005.

[28] A. Henderson-Seller, Z. L. Yang, and R. E. Dickinson, “The project forintercomparison of land-surface parameterization schemes,” Bull. Amer.Meteorol. Soc., vol. 74, no. 7, pp. 1335–1350, Jul. 1993.

[29] A. Henderson-Sellers, A. Pitman, P. K. Love, P. Irannejad, andP. Chen, “The project for intercomparison of land surface parameteri-zation schemes (PILPS): Phases 2 and 3,” Bull. Amer. Meteorol. Soc.,vol. 76, no. 4, pp. 489–504, Apr. 1995.

[30] C. A. Schlosser, A. G. Slater, A. Robock, A. J. Pitman, K. Y. Vinnikov,A. Henderson-Sellers, N. A. Speranskaya, K. Mitchell, A. Boone,H. Braden, F. Chen, P. Cox, P. de Rosnay, C. Desborough, andR. E. Dickenson, “Simulations of a boreal grassland hydrology atValdai, Russia: PILPS phase 2(d),” Monthly Weather Rev., vol. 128, no. 2,pp. 301–321, Feb. 2000.

[31] D. Cline, K. Elder, B. Davis, J. Hardy, G. E. Liston, D. Imel, S. H. Yueh,A. J. Gasiewski, G. Koh, R. L. Armstrong, and M. Parsons, “Overview ofthe NASA cold land processes field experiment,” in Proc. SPIE—Int. Soc.Opt. Eng., 2003, vol. 4894, pp. 361–372.

[32] A. Wiesmann and C. Mätzler, “Radiometric and structural measurementsof snow samples,” Radio Sci., vol. 33, no. 2, pp. 273–289, 1998.

[33] L. Cohen, D. Helmig, W. Neff, A. A. Grachev, and C. W. Fairall,“Boundary-layer dynamics and its influence on atmospheric chemistry atSummit, Greenland,” Atmos. Environ., vol. 41, no. 24, pp. 5044–5060,2007.

[34] C. Mätzler, “Relation between grain-size and correlation length of snow,”J. Glaciol., vol. 48, no. 162, pp. 461–466, Jun. 2002.

[35] D. K. Hall, “Influence of depth hoar on microwave emission from snowin northern Alaska,” Cold Reg. Sci. Technol., vol. 13, no. 3, pp. 225–231,Apr. 1987.

[36] R. E. J. Kelly and A. T. C. Chang, “Development of a passive microwaveglobal snow depth retrieval algorithm for Special Sensor MicrowaveImager (SSM/I) and Advanced Microwave Scanning Radiometer-EOS(AMSR-E) data,” Radio Sci., vol. 38, no. 4, pp. 8076–8088, Jul. 2003,DOI:10.1020/2002RS002648.

[37] C. Mätzler, “Ground-based observations of atmospheric radiation at 5,10, 21, 35, and 94 GHz,” Radio Sci., vol. 27, no. 3, pp. 403–415,May/Jun. 1992.

[38] R. Wójcik., K. Andreadis, M. Tedesco, E. Wood, T. Troy, andD. Lettenmeier, “Multimodel estimation of snow microwave emissionduring CLPX 2003 using operational parameterization of microphysicalsnow characteristics,” J. Hydrometeorol., vol. 9, no. 6, pp. 1491–1505,Dec. 2008.

[39] J. Martinec and J. , “Meltwater percolation through an alpine snowpack,”in Proc. Avalanche Formation, Movement and Effects (Proc. Davos Symp.Sep. 1986), 1987, pp. 255–264, IAHS Publ. no. 162.

[40] M. Durand, N. P. Motlotch, and S. A. Margulis, “A Bayesian approachto snow water equivalent reconstruction,” J. Geophys. Res. D, Atmos.,vol. 113, no. D20, p. D20 117, Oct. 2008.

[41] A. M. Toure, K. Goita, A. Royer, C. Mätzler, and M. Schneebeli, “Near-infrared digital photography to estimate snow correlation length for mi-crowave emission modeling,” Appl. Opt., vol. 47, no. 36, pp. 6723–6733,Dec. 2008.

[42] S. G. Benjamin, J. M. Brown, K. J. Brundage, D. Devenyi, D. Kim,B. E. Schwartz, T. G. Smirnova, T. L. Smith, and A. Marroquin, “Im-provements in aviation forecasts from the 40-km RUC,” in Proc. 7th Conf.Aviation, Range Aerosp. Meteorol., Long Beach, CA, Feb. 1997, pp. 411–416, Preprints.

[43] M. J. Butt and R. E. J. Kelly, “Estimation of snow depth in the UK usingthe HUT snow emission model,” Int. J. Remote Sens., vol. 29, no. 14,pp. 4249–4267, Jul. 2008.

[44] D. Kang and A. P. Barros, “Introducing an L-band snow sensor systemfor in situ monitoring of changes in water content—Full-system testing,”IEEE Trans. Geosci. Remote Sens. Sci., vol. 49, no. 3, pp. 908–919,Mar. 2011.

[45] M. Sturm and C. S. Benson, “Vapor transport, grain growth and depth-hoar development in the subarctic snow,” J. Glaciol., vol. 43, no. 143,pp. 42–59, 1997.

[46] A. Kontu, S. Kemppainen, J. Lemmetyinen, J. Pulliainen, andM. Hallikainen, “Determination of snow emission on lake ice from air-borne passive microwave measurements,” in Proc. IGARSS, Boston, MA,Jul. 2008, pp. IV-1046–IV-1049.

[47] E. Schanda, C. Mätzler, and K. Kunzi, “Microwave remote sensing ofsnow cover,” Int. J. Remote Sens., vol. 4, no. 1, pp. 149–158, 1983.

[48] M. Schwank, M. Stahli, H. Wydler, J. Leuenberer, C. Mätzler, andH. Fluhler, “Microwave L-band emission of freezing soil,” IEEE Trans.Geosci. Remote Sens., vol. 42, no. 6, pp. 1252–1261, Jun. 2004.

[49] S. H. Yueh, S. J. Dinardo, A. Akqiray, R. West, D. W. Cline, and K. Elder,“Airborne Ku-band polarimetric radar remote sensing of terrestrial snowcover,” IEEE Trans. Geosci. Remote Sens., vol. 47, no. 10, pp. 3347–3364,Oct. 2009.

[50] M. J. Brodzik, R. Armstrong, and M. Savoie, Global EASE-Grid 8-dayBlended SSM/I and MODIS Snow Cover. Boulder, CO: National Snowand Ice Data Center. Digital media, 2007.

[51] M. Tedesco, R. E. J. Kelly, J. L. Foster, and A. T. C. Chang, AMSR-E/AquaDaily L3 Global Snow Water Equivalent EASE-Grids V002. Boulder,CO: National Snow and Ice Data Center. Digital media, 2004, updateddaily.

[52] C. Derksen, A. Walker, and B. Goodison, “A comparison of 18 winterseasons of in situ and passive microwave-derived snow water equivalentestimates in Western Canada,” Remote Sens. Environ., vol. 88, no. 3,pp. 271–282, Dec. 2003.

[53] C. Derksen, P. Toose, A. Rees, L. Wang, M. English, A. Walker, andM. Sturm, “Development of a tundra-specific snow water equivalentretrieval algorithm for satellite passive microwave data,” Remote Sens.Environ., vol. 114, no. 8, pp. 1699–1709, Aug. 2010.

[54] A. Langlois, A. Royer, and K. Gota, “Analysis of simulated and space-borne passive microwave brightness temperatures using in situ measure-ments of snow and vegetation properties,” Can. J. Remote Sens., vol. 36,no. S1, pp. S135–S148, 2010.

[55] A. B. Tait, “Estimation of snow water equivalent using passive microwaveradiation data,” Remote Sens. Environ., vol. 64, no. 3, pp. 286–291,Jun. 1998.

[56] L. S. Koenig and R. Forster, “Evaluation of passive microwave snowwater equivalent algorithms in the depth hoar-dominated snowpack of theKuparuk River Watershed, Alaska, USA,” Remote Sens. Environ., vol. 93,no. 4, pp. 511–527, Dec. 2004.

Do Hyuk Kang received the B.A. degree in geog-raphy from Seoul National University, Seoul, Korea,the M.S. degree in civil engineering from ColoradoState University, Fort Collins, and the Ph.D. degreein civil engineering from Duke University, Durham,NC, in December 2010.

His research interests include the applications ofL band sensors to measure geophysical layers anda hydrology model coupled with forward models ofpassive and active microwave remote sensing.

Ana P. Barros (M’94–SM’04) received the diplomain civil engineering with majors in structures and hy-draulics and the M.Sc. degree in ocean engineeringfrom the Faculty of Engineering, University of Porto,Porto, Portugal, the M.Sc. degree in environmentalscience and engineering from the Oregon Gradu-ate Institute, Oregon Health and Science University,Portland, and the Ph.D. degree in civil engineeringfrom the University of Washington, Seattle, in 1985,1988, 1990, and 1993, respectively.

She was a Faculty Member with The PennsylvaniaState University, University Park, and with Harvard University, Cambridge,MA. She is currently a Professor of engineering with Duke University,Durham, NC.

ieee transactions on geoscience and remote sensing 1...

Documents