Spatial variability of shortwave radiative fluxes in the context of snowmelt
modeling
Yingtao Ma1, Rachel T. Pinker1
Laura M. Hinkelman2, Jessica Lundquist3, Chuan Li1 and Karl Lapo4
1
Department of Atmospheric and Oceanic Science
Computer and Space Sciences Building
University of Maryland
College Park, MD 20742
2
Joint Institute for the Study of the Atmosphere and Ocean
University of Washington
Seattle, WA 98195-5672
3
Department of Civil and Environmental Engineering
University of Washington
Seattle, WA, USA
4
Department of Atmospheric Sciences
University of Washington
Seattle, WA, USA
Revision:
12/20/2013
1
Abstract
Net radiative fluxes make up about 80% of the energy balance over snow covered surfaces.
Therefore, the greatest potential source of error in simulating snowmelt rates and timing is
related to such fluxes. The situation is complicated over mountainous terrain due to slope effects
on the radiative fluxes and the heterogeneous distribution of snow. It is important to model
accurately the snow melt in such regions. Due to the large extent of snow-cover and scarcity of
ground observations, use of remotely sensed data is an attractive option for estimating radiative
fluxes. Most of the available methodologies have been applied to low spatial resolutions of the
satellite observations that do not capture the spatial variability of snow cover which needs to be
accounted for accurate estimates of the surface fluxes. The objective of this study is to utilize
observations of high spatial resolution as available from the Moderate Resolution Imaging
Spectro-radiometer (MODIS) to derive surface shortwave (SW) radiative fluxes in complex
terrain, with attention to the impact of slopes on the amount of radiation received. The
methodology developed has been applied to several water years (January to July during 2003,
2004, 2005 and 2009) over the western part of the United States, and the available information
was used to derive metrics on spatial and temporal variability in the SW fluxes. To better
understand the difficulties in the validation process of the satellite derived quantities, issues of
scale are also addressed. It is planned to apply the findings from this study for testing
improvements in Snow Water Equivalent (SWE) estimates.
Key words: shortwave radiative fluxes on slopes; satellite radiative fluxes.
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1.
Introduction
1.1
Background
Snow-covered mountain ranges are a major source of water supply for run-off and
groundwater recharge. Snowmelt supplies as much as 75% of surface water in basins of the
western United States [Beniston, 2006]. Factors that affect the rate of snow melt include
incoming shortwave and longwave radiation, surface albedo, snow emissivity, snow surface
temperature, sensible and latent heat fluxes, ground heat flux, and energy transferred to the
snowpack from deposited snow or rain [Gray and Prowse, 1992; Pomeroy et al., 2003]. The net
radiation generally makes up about 80% of the energy balance [Male and Granger, 1981; Marks
and Dozier, 1992; Cline, 1997]. Therefore, the greatest potential sources of error in simulating
snowmelt rates and timing are errors in solar and longwave radiation inputs.
Complex terrain poses a great challenge for obtaining the needed information on radiative
fluxes from satellites due to elevation issues, spatially-variable cloud cover, rapidly changing
surface conditions during snow fall and snow melt, lack of high quality ground truth for
evaluation of the satellite based estimates, as well as scale issues between the ground
observations that are exposed to the entire sky dome and the small satellite footprint when high
spatial resolution observations are used. The situation in the region of our interest is unique due
to orographic effects of the mountains on cloud formation affecting their frequency distribution
on the two sides of the mountains. Moreover, the Great Central Valley of California is
frequented by the tule fog (Figure 1) that forms from late fall through early spring, the official
period being November 1 to March 31. It is a radiation fog, which occurs when the relative
humidity is high during rapid night cooling and is usually confined to below 2,000 feet. The
moisture for the fog formation is supplied by the ocean which is also a source of nuclei for the
3
condensation of the water vapor. As will be shown in the results section, only high resolution
satellite observations can capture the unique complex terrain radiation/cloud/fog conditions.
These challenges will be addressed in this study.
While observations from very high resolution satellites like Landsat [e. g., Rosenthal and
Dozier, 1996] are very useful for determining fractional snow cover, such observations are at low
temporal resolution and as such, their practical applicability is restricted. Our approach utilizes
routinely available observations from current satellites (e. g., MODIS) and can serve as a
prototype for use of future operational satellites, both polar orbiting and geostationary (see
further discussion in Section 5).
1.2
Study Objectives
Modeling and prediction of snowmelt in the Western US suffers from a lack of
information on energy balance components. Most available information on surface radiative
fluxes from satellites is at spatial resolutions between 0.5-2.5o. The objective of this study is to
derive SW radiative fluxes (a key parameter in the surface energy budget) at the highest readily
available resolution (5-km) using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) [King et al., 1992; Platnick et al., 2003]. The auxiliary information on
atmospheric and surface properties at this scale is also available from MODIS. It is expected that
this information will improve the quality of snowpack modeling by accounting for the spatial
variability of the energy that drives the melting. We will address the intrinsic difficulties to
evaluate the fluxes derived at 5-km resolution due to discrepancies between the satellite and
ground instrument views and use an indirect approach to demonstrate that the high resolution
fluxes are of better quality. The methodology used in this study is described in section 2, results
are presented in section 3, distribution of SW fluxes on slopes is described in section 4 and a
summary and discussion are given in section 5.
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2.
Methodology
Observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument
on the Terra and Aqua satellites [King et al., 2013] are used to produce surface radiative fluxes
as needed for modeling various land surface processes in complex terrain, such as snowmelt,
potential evapotranspiration (ET), or Net Primary Productivity (NPP). The basic inference
scheme implemented for the retrieval of shortwave (SW) fluxes is described by Wang and Pinker
[2009] (Version 1), where it was evaluated at 10 (~111 km) spatial resolution. Additional
evaluation of Version 1 products is presented in Pinker et al. [2009], Niu et al. [2010], and Niu
and Pinker [2011]. Feasibility to implement the methodology at 5-km and application of results
to address certain aspects of scale issues over flat terrain are illustrated in Su et al. [2008];
topographic effects and high spatial and temporal variability in snow cover were not accounted
for previously. Changes implemented in the methodology will be described in what follows.
2.1
Model for shortwave (SW) fluxes Version 2.0 (V2.0)
The model used in this study is a modified version of the algorithm described by [Wang and Pinker,
2009]; details are also presented in Randles et al. [2013]. Briefly, shortwave (SW) radiative fluxes are
computed in seven spectral intervals (0.2-0.4, 0.4-0.5, 0.5-0.6, 0.6-0.7, 0.7-1.19, 1.19-2.38, 2.38-4.0 μm)
assuming a plane-parallel, vertically inhomogeneous, scattering and absorbing atmosphere. Water vapor
absorption is parameterized following Ramaswamy and Freidenreich [1992] and Chou et al. [1999].
Ozone absorption in the ultraviolet and in the visible is computed following Lacis and Hansen [1974].
The single scattering properties and vertical profiles of aerosols were derived from the Optical Properties
of Aerosols and clouds (OPAC) software package [Hess et al., 1998]. Five atmospheric aerosol vertical
profiles (continental, desert, maritime, Arctic and Antarctic) are used with the inference scheme. Cloud
extinction coefficients, single scattering albedos, and asymmetry factors are computed from the
parameterizations of Slingo [1989] and Edwards et al. [1996)] for water clouds and from Chou et al.
[2002] for ice clouds. Multiple scattering is dealt with the delta-Eddington approximation following
5
Joseph et al. [1976]. Vertical atmospheric profiles are from the standard atmospheres of Kneizys et al.
[1980]. TOA solar spectral irradiance data are from MODTRAN 3. Data sources for model input are
described in Table 1.
To calculate the shortwave fluxes over Western US at 5-km, the cloud fraction, cloud optical
depth and cloud drop size are first re-gridded to 5-km from 1-km data. The 5-km cloud drop size
is calculated as the mean of all pixel values within the 5 x 5 block. The 5-km cloud optical depth,
𝜏5𝑘𝑚 is calculated using log averaging, namely:
𝜏5𝑘𝑚 = exp⁡(̅̅̅̅̅̅̅̅̅̅̅
ln(𝜏1⁡𝑘𝑚 ))
For the MODIS Level-2 swath data, the cloud phase information (water or ice clouds) is
hidden in a parameter named “Quality_Assurance_1 km”. Aside from quality control
information, it also provides a flag to indicate the cloud phase and layer properties for each 1-km
pixel. The 5-km cloud fraction and phase is aggregated from each 5x5 pixel block. Pixels flagged
as “Undetermined” are treated as missing; pixels with layer information determined (single or
multi-layer clouds) but with phase labeled as “Unknown” are classified as water clouds.
Information on surface albedo is needed to account for multiple reflection of shortwave
radiation between the surface and the atmosphere. In this study, the surface albedo is derived
from “The Filled Land Surface Albedo Product” and the MODIS daily and weekly snow
products (MOD10C1, MYD10C1, MOD10C2 and MYD10C2). The first one is developed from
the Terra/MODIS Land Surface Albedo Product (MOD43B3) by the MODIS atmosphere team.
It gives spatially complete albedo maps for snow-free land surface at 1 minute resolution. To
couple it with the 5-km radiative transfer calculations, the 1 minute snow-free albedo data are
resampled to 5-km grids. For deriving albedo of snow covered areas, snow information at a daily
time scale and at 0.05º spatial resolution is used as available from both Terra (MOD10C1) and
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Aqua (MYD10C1); if both are available, an average is used. If no information is available at
daily time scale, the 8-day composite is used. In the original MODIS inference scheme [Wang
and Pinker, 2009], the spectral reflectance for snow was assumed to be 0.9 for visible sand 0.6
for the near-infrared (NIR) parts of the spectrum. In the updated version, the surface spectral
reflectance in the presence of snow is derived from a combination of snow cover percentage and
the MODIS surface reflectance products which are provided as a five-year (2000-04)
climatological statistics of spectral reflectance (the underlying surface types are aggregated
according to the International Geosphere-Biosphere Program (IGBP) classification) (Moody et
al., 2007) (Table 3).
2.2
Available V2.0 product
The improved version of the SW inference scheme is used to produce instantaneous pixel
level (5-km) SW fluxes from Terra and Aqua observations. The product generated is provided
swath by swath corresponding to the MODIS level-2 data; each pixel is identifies by its
coordinates and time of observation. This product covers an area of the western United States
from the eastern foothills of the Rocky Mountains to the Pacific Ocean bounded by (350-500 N,
1250-1150 W) (Figure 2) from January through July of 2003, 2004, 2005 and 2009. A gridded
instantaneous product at 0.05o resolution is also derived and an example is shown in Figure 3.
All pixels falling in a grid are averaged to give a mean value. Some grid boxes are not covered
by observations. These are filled with the average values from the surrounding 3x3 grids. This
filling process is repeated twice; to avoid the use of too many filled boxes, the process stops after
two iterations. As can be seen from the figure, after two iterations some grid cells are still empty.
Daily mean fluxes are also computed for the gridded data. Instantaneous values from
Terra and Aqua are first normalized to daily mean solar zenith angle and then averaged to give
7
an estimate of the daily flux. Due to the swath overlap at higher latitudes, for some regions, there
are up to 6 observations available per day depending on the day of the year and location. In the
following sections, the instantaneous pixel and gridded fluxes are evaluated against ground
observations. The gridded instantaneous and daily fluxes are used to investigate spatial and
temporal variability of the SW↓ fluxes in the study area. In section 5, an approach to apply
topographic correction is developed and described; subsequently, it is applied to the
instantaneous gridded values.
3.
Evaluation of MODIS V2.0 SW↓ flux products
3.1
Ground observations
Ideally, ground observations from mountain sites during the snow season should be used in
evaluating these satellite products. Such observations are difficult to make due to limited access
to the sites during snowfall, and therefore, the data are often not of the highest quality. We used
observations from well-maintained mountain sites, as detailed in Table 2. These data were
augmented with observations from the Baseline Surface Radiation Network (BSRN) network
[Ohmura et al., 1998] (http://www.gewex.org/bsrn.html) (previously known as the SURFRAD
Network in the U. S. [Augustine et al., 2005]) (with an emphasis on stations with winter snow
cover) to serve as a benchmark for the evaluation of model performance under “ideal”
maintenance conditions. We used two sites from the BSRN network, namely, Fort Peck, MT
(FTP) (48.1o N, 105.1o W), and Table Mountain, Boulder, CO (TBL) (40.1o N, 105.2o W) as well
as a flat terrain site at Bondville, IL (BON) (40o N, 88.4o W); comparison of model performance
is
stratified by surface conditions (flat, elevated, mountain, snow-free, snow-covered).
Information on snow conditions is based on the Interactive Multi-sensor Snow and Ice Mapping
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System (IMS) daily northern hemisphere snow and ice cover data at 4 km resolution as provided
at: ftp://sidads.colorado.edu/pub/DATASETS/NOAA/G02156/4km. In addition, data from three
high-quality West Coast stations (Burns, Eugene, and Hermiston, OR [Vignola et al., 2007;
Riihimaki, et al., 2009] as available from http://solardat.uoregon.edu/SolarData.html were used.
For evaluation of the satellite estimates against ground truth, used are the instantaneous pixel
level products; all satellite retrievals within 50 km radius around the selected ground
measurement stations were extracted to create match-up files around these stations.
3.2
Scale issues
There is an inherent inconsistency of scale when matching satellite estimates at 5-km with
ground observations. Ground instruments (radiometers) usually have a field of view (FOV) of
around 1700 looking upward, and therefore, the actual sky area that contributes to the measured
downward flux is generally much larger than 5-km. Downward observed fluxes integrate the
entire FOV of the instrument and incorporate the distribution of aerosol and cloud conditions
within the FOV. The 5-km footprint fills part of this FOV. Under the assumptions used in the
radiative transfer computations of the satellite algorithm, the calculated 5-km SW↓ flux is
equivalent to the flux under a plane parallel sky with the optical depth of the cloud and/or aerosol
slab specified by the values retrieved for the 5-km pixel. Thus, the more representative the 5-km
footprint is of the scale viewed by the radiometer, the closer agreement can be expected between
the satellite retrievals and the ground observations. One can expect better evaluation results
under relatively uniform stratus cloud or clear sky conditions than under broken cumulus clouds.
Experiments to illustrate such issues are described in next section.
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3.3
Optimal time and space scales for evaluation
Almost all evaluations of satellite retrievals against ground observations rely on the
assumption that the temporal averaging at a fixed ground point are equivalent to the spatial
averaging derived from the satellite observations. The validity of this assumption for
atmospheric radiation fields is still under active investigation [Hakuba et al., 2013]. Since the
satellite estimates of SW↓ radiative fluxes are of high spatial resolution, and the ground
measurements from the SURFRAD/BSRN and University of Oregon stations are available at 1minute temporal resolution, it is possible to investigate the impact of scale on the comparison
results.
For evaluation of the satellite estimates against ground observations, all satellite retrievals
that are within 50 km radius around the selected SURFRAD/BSRN, University of Oregon, and
mountain stations that were extracted to create match-up files around these stations, will be used.
Comparisons against ground observations that have 1-minute data averaged over time intervals
of (10, 20, 30, and 60 min) are performed over the flat terrain sites. Instantaneous MODIS-based
SW↓ fluxes from the pixel level products are compared to ground observations from
SURFRAD sites averaged over a range of time intervals (10, 20, 30, and 60 min) and spatial
scales (5, 10, 25, 50 km radius) (Table 4). The combination of 60 min averages of ground
observations and 50 km radius spatial averages of satellite estimates yielded the best results as
measured by bias, standard deviation, and correlation coefficient (a circle with a radius of 50 km
(diameter 100 km) is about the size of a 1° grid box). This combination will be used in
subsequent evaluations.
10
3.4
Evaluation of instantaneous SW↓
Evaluation of MODIS SW↓ fluxes at SURFRAD sites of FPK and BON was performed
at instantaneous and daily time scales using the pixel level 5-km observations from each
overpass (“swath”) averaged over a radius of 50 km and matched with ground observations
averaged over an hour; snow and no snow conditions as determined from the IMS data were
evaluated independently (Figure 4). For no snow conditions, observations made during 2005
were used. Since the number of cases with snow conditions is lower as compared to no snow
ones, cases from the year 2004 were also added to the snow cases. The bias between the
observations and the satellite-based SW↓ radiative flux is larger when the sites are snow covered
(note that the sample sizes are not the same). It is difficult to determine the source of error in
these comparisons. It is notoriously difficult to distinguish between snow and clouds using
satellite radiances [Wang and Key, 2003; Curry, 2006] while the radiometers during snow-fall
are vulnerable to problems from snow on the domes or to slippage in their mounting systems.
Evaluation of instantaneous and daily SW↓ for the three Oregon sites combined (Burns, Eugene
and Hermiston) (http://solardat.uoregon.edu/SolarData.html) during 03/01/2005-07/31/2005 are
shown in (Figure 5). Here, no distinction was made between snow and no snow conditions.
Comparison of the MODIS 5-km pixel level instantaneous SW↓ fluxes for 01/01/2009 to
06/30/2009 was also performed at Mountain Stations as described in Table 2 where concurrent
SWE measurements are made. As evident from Table 5, the stations USNR and RSH may have
been problematic and when excluded from the evaluation (Figure 6 (right)) the results show a
bias of (2.7 %), while the scatter is about (23%).
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3.5
Indirect evaluation of V.20 products
The evaluation presented earlier addresses the need to match the satellite observations
with ground observations meaningfully. Since the systematic evaluation that followed was done
at the lower spatial resolution, it does not resolve the question of whether there is a benefit in the
higher spatial resolution information as compared to information derived from lower resolution.
Additional insight on this issue can be gained from Figure 7. The upper left panel shows the 5km SW↓ product as obtained from Level 2 MODIS/Terra observations. The upper right panel
shows results after the 5-km data were aggregated into 10 grid boxes. To obtain the 1⁰ data from
5-km MODIS input, the 5-km swath data were first gridded to 0.05⁰ resolution and then upscaled to a 1⁰ grid by taking a 20x20 grid cell average. The lower right panel shows the SW↓ as
derived from MODIS/Terra Level 3 information that is provided at 10 resolution using the same
algorithm. The lower left panel shows the difference between the two 10 products. As evident,
the differences are in the range of -15 to 25 W/m2. In Figure 8, the two types of 1⁰ satellite
retrievals from MODIS on the Terra and Aqua satellites were evaluated against ground
observations from the six mountain stations listed as Set 2 in Table 2. Data from these sites for
the time period 12/01/2004 to 05/31/2005 is used after being subjected to additional strict quality
control (QC) tests. In the figure, the left column shows results from Terra and the right column
from Aqua. The upper panel shows results for 1⁰ product up-scaled from the 5-km data and the
lower panel shows results for the 1⁰ product inferred from the MODIS level 3 data. The
preliminary results indicate that the agreement with ground measurements is better for the 10
product aggregated from the 5-km estimates for the MODIS/Terra product. For the
MODIS/Aqua product, the aggregated 1⁰ fluxes from the 5-km data yield higher correlation and
12
smaller standard error but somewhat larger bias than for Terra. Additional evaluation for longer
time periods needs to be undertaken.
4.
Spatial and temporal variability
A better measure of the spatial and temporal variability of SW↓ and snow cover are of
interest in formulating parameterizations of the surface energy budget and snow-melt.
Snow information is also important for correct accounting for multiple reflection bewteen
surface and atmosphere in the radiative tranfer computations that estimate surface SW↓ fluxes.
Here we use the radiative flux products developed in this study and available information on
snow distribution to examine their spatial and temporal variability.
4.1
Spatial and temporal variability of snow cover
We focus on the red boxes illustrated in the left panel of Figure 9 and denoted as WA, ID,
CA. They are defined as follows:
1. 'sub-area CA' (121.4o W, 118.4o W, 36.5o N, 39.5o N) is around the locations of sites
DAN and TUM (see Table 2).
2. 'sub-area ID' (117.3o W, 116.3o W, 42.5o N, 43.5o N) is in Idaho around the location of
site RME.
3. 'sub-area WA' (122.5o W, 120.5o W, 45.9o N, 47.9o N) is in the Cascades from the
Washington-Oregon border to just north of Snoqualmie Pass.
The middle panel of Figure 9 shows the monthly mean snow cover in units of % combined
from the MODIS instantaneous snow products from Terra and Aqua, while the right panel shows
the day-to-day variability in snow covered area (%). Missing daily snow cover values are filled
with MODIS 8-day snow products. The day-to-day variability is calculated as the standard
devation (STD) of daily values for the month of January, 2005, at each pixel. The calculation is
13
based on the gridded data; each pixel is of 0.05 degree resolution (5-km). Even at the 5-km
resolution, the spatial snow variability is significant and so is the day to day variability.
Therefore, the 5-km MODIS observations should improve the coupling between the spatial
variability of these crucial parameters in estimating snow-melt.
4.2
Spatial and temporal variability of SW fluxes
The variability of both radiative fluxes and snow distribution is of importance for SWE
modeling. Here, an attempt is made to learn about such variability in each of three sub-domains
where a dense network of ground observations relevant for snow-melt modeling is available, for
future testing of SWE models. In Figure 10, the left column shows the monthly mean values of
SW↓ radiative flux for January 2005. The middle column shows the frequency distribution of
daily values for the corresponding month and sub-domain. The right column shows the temporal
standard deviation for the sub-domain for the month. The white lines show the county
boundaries. The spatial variability of SW↓ in the three sub-domains for January of 2005 is
presented in Figure 11. Left column shows the monthly mean spatial variability. The spatial
variability is calculated within a 9x9 box around each grid point at a daily time scale, namely, the
temporal average of the daily scale variability for the month. The middle column shows the
frequency distribution of the spatial variability for the whole month of January 2005. The right
column shows the spatial variability of the monthly mean flux over an area of 9x9 grid cells.
Each row is for a specified sub domain.
Time series of spatial means and relative standard deviations of daily mean fluxes for
the three intensive evaluation subdomains as defined in Figure 9 are shown in Figure 12. The
relative standard deviations (Rel. Std. Dev) are relative to the area mean. The sizes of these subdomains are 3ºx3º (CA), 2ºx2º (WA) and 1ºx1º (ID). Calculations are based on daily mean values.
14
As evident, the mean values start to increase around March, somewhat earlier in the lower
latitudes, and the temporal relative variability is similar in the three domains.
As seen, the representativeness of a location to an extended surrounding area depends on
the spatial heterogeneity of the area. As seen in Figure 11, where time average spatial variability
for three sub areas (CA, ID and WA) is shown (left column) there are locations where SW↓
radiation changes rapidly in a short distance. For example, in the CA sub-area, along the edges of
the California basins, large flux gradient can be observed. This corresponds to the transition from
the “tule” fog covered California basin during winter season to the high elevation mountain area.
One would expect less representativeness of an observation located within this region to its
surroundings.
Spatial variability can be systematic or non-systematic. The topographic pattern shown in
the CA subarea is an example of systematic spatial variability. The south-north change of solar
radiation caused by the Sun-Earth geometry is another example of the systematic spatial
variability. Non-systematic variability is mainly causes by sub-grid processes such as the cloud
formation and movement, aerosol pattern and so on. Figure 12 shows the time series of mean
fluxes and the mean spatial standard deviation for the three sub areas. The mean spatial
variability changes with time. The relative variability in the ID subarea is less than the other two
subareas. The larger variability in the CA comparing to ID is mainly due to the terrain of the
region. A larger domain size, 3ºx3º of CA vs. 1ºx1º of ID may also contribute to the larger mean
spatial variability.
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5.
Topographic corrections
5.1
Model development
In mountainous regions, local topographic effects due to complex terrain may cause
significant variation in the radiation budget. For SW↓, the variation is mainly induced by the
changes of illumination angle, shadowing, and limited sky view factor along with reflection from
surrounding terrain. The slope and aspect of the receiving surface determine the flux density of
the incident radiation. Shadowing blocks the solar beam from reaching the surface and is
especially important under low sun conditions or in valleys. Sky view restrictions limit the
amount of diffuse radiation that reaches the surface. A common approach to computing the solar
irradiance in mountainous terrain is a two-step process. Initially, downwelling irradiance is
computed for a flat lower boundary. Subsequently, corrections are applied to the inferred SW↓
to derive the radiant flux received by the tilted surface within its surrounding topography.
Usually, the resolution of the terrain is higher than the grid size used in the radiative transfer
calculation.
Treatment of topographic effects for retrieving SW↓ radiation fluxes from satellite
observations has been investigated in several studies (Dozier and Frew [1990], Dubayah et al.
[1990], Muller and Scherer [2005], Chen et al. [2006], Helbig et al. [2009], Lai et al. [2010],
Lee et al. [2011]). The approach for topographic correction applied in many studies follows the
formulation:
𝐹(𝑥) = 𝜒𝐹𝐵 cos(γ0 ) /cos⁡(γ0h ) + 𝐹𝐷 ∙ 𝑓𝑠𝑘𝑦 (𝑥) + 𝛼̅(𝐹𝐷 + 𝐹𝐵 )(1 − 𝑓𝑠𝑘𝑦 (𝑥))
(2)
The first term on the right-hand side represents the solar beam radiation incident on a
tilted plane. The second term is the downwelling diffuse radiation restricted by a sky view factor
16
(calculated as the percentage of the upper hemisphere that is not obstructed by surrounding
terrain). The last term denotes the reflected radiation from the surrounding terrain. This last term
is not present when a horizontal lower boundary is assumed. The 𝐹𝐵 and 𝐹𝐷 terms are the direct
and diffuse components of the SW↓ flux, respectively without topographic correction. The
additional terms are:
γ0 is the solar incidence angle measured from the tilted surface normal to the solar direction
γ0h is the solar incident angle to a horizontal receiving plane
𝑓𝑠𝑘𝑦 (𝑥) is sky view factor, or the fraction of the upper hemisphere that is viewable sky, as
opposed to blocked by the surrounding terrain
𝛼̅ is the surface albedo averaged over the grid box.
In our treatment of Eq. 2, the definition of terrain configuration factor (1 − 𝑓𝑠𝑘𝑦 (𝑥)) is
different from the one used in Dozier and Frew [1990] where the terrain configuration factor is
approximated as the difference between two sky view factors, where one is the sky view factor
for an infinity long slope and the other is the sky view factor obtain by Eq. 4 below. The Dozier
and Frew [1990] definition ignores the radiation coming from the terrain under the horizon.
As is, (Eq. 2) is highly simplified with following approximations:
1. Diffuse sky radiation is isotropic
2. Heterogeneity of surface albedo and SW↓ in each individual grid is ignored
3. Impact of complex terrain on multiple reflections between surface and atmosphere is
ignored.
4. Atmospheric scattering and absorption between slopes are ignored.
5. Surface is a Lambertian reflector.
17
6. Due to terrain reflection, there will be radiation exchange between neighboring grid cells.
This is called the “edge effect”. The simplified approach assumes that the size of a grid
cell is large enough so that the edge effect can be neglected.
Given the above assumptions, the topographical correction to SW↓ radiation is basically a
geometrical problem. For a receiving plane with tilt angle 𝜃𝑟 and azimuth angle 𝜙𝑟 , the solar
angle, which is the angle between the sunbeam and receiving plane normal, is given as:
cos(γ0 ) = cos(𝜃0 ) cos(𝜃𝑟 ) + sin⁡(𝜃0 )sin⁡(𝜃𝑟 )cos⁡(𝜙𝑟 − 𝜙0 )
(3)
If cos(γ0 ) < 0, the receiving point is self-shaded.
The sky view factor by definition is [Dozier and Frew, 1990]
1
1
2𝜋
ℎ
𝑓𝑠𝑘𝑦 = 𝜋 ∫𝑠𝑘𝑦 cos(γ) 𝑑Ω = 𝜋 ⁡ ∫0 𝑑𝜙 ∫0 𝜙 sin⁡(𝜃)cos⁡(γ)𝑑𝜃
(4)
namely, the fractional area of sky dome viewed from the location 𝑥 projected onto the tilted
receiving plane where γ is the angle between the receiving surface normal and Ω direction. 𝜃 and
𝜙 are zenith and azimuth angle, respectively, 𝑑Ω = sin⁡(𝜃)𝑑𝜃𝑑𝜙, ℎ𝜙 is the horizon angle
measured from zenith downward to horizon, as shown in Figure 13.
Since
cos(γ) = cos(𝜃) cos(𝜃𝑟 ) + sin⁡(𝜃)sin⁡(𝜃𝑟 )cos⁡(𝜙 − 𝜙𝑟 )
(5)
Dozier and Frew [1990)] expressed Eq. (4) as:
ℎ𝜙
1 2𝜋
𝑓𝑠𝑘𝑦 = ⁡∫ 𝑑𝜙 ∫ sin(𝜃) [cos(𝜃) cos(𝜃𝑟 ) + sin⁡(𝜃)sin⁡(𝜃𝑟 )cos⁡(𝜙 − 𝜙𝑟 )]𝑑𝜃⁡
𝜋 0
0
2𝜋
1
=
⁡∫ 𝑑𝜙[cos(𝜃𝑟 ) sin2 (ℎ𝜙 ) + sin(𝜃𝑟 ) cos(𝜙 − 𝜙𝑟 ) (ℎ𝜙 − sin⁡(ℎ𝜙 )cos⁡(ℎ𝜙 ))]⁡
2𝜋 0
(6)
𝑛
1
≅
⁡∑[cos(𝜃𝑟 ) sin2 (ℎ𝜙𝑖 ) + sin(𝜃𝑟 ) cos(𝜙𝑖 − 𝜙𝑟 ) (ℎ𝜙𝑖 − sin(ℎ𝜙𝑖 ) cos(ℎ𝜙𝑖 ))]∆𝜙𝑖
2𝜋
𝑖=1
Equation (6) must be evaluated numerically.
18
A digital elevation model (DEM) is needed to determine the shaded-or-unshaded indicator
function χ, the solar incidence angle γ0 , and the sky view factor fsky . The DEM used in this
study is the HYDRO1k database developed by the National Center for Earth Resources
Observation and Science (EROS) of the U.S. Geological Survey (USGS)
(http://webgis.wr.usgs.gov/globalgis/metadata_qr/metadata/hydro1k.htm;
https://lta.cr.usgs.gov/HYDRO1K). It is based on the USGS' 30 arc-second digital elevation
model of the world (GTOPO30) database. The HYDRO1k, on a continent-by-continent basis and
at a resolution of 1-km, provides hydrologically corrected DEMs along with a suite of five
ancillary data sets including slope angle, azimuth angle and two other data sets (not required in
this study) (wee focus on the subarea CA).
To numerically calculate the shaded-or-un-shaded indicator function 𝜒, the solar incidence
angle γ0 , and the sky view factor 𝑓𝑠𝑘𝑦 , we first obtain the local horizons for each 1-km terrain
cell. The local horizons are determined within a rectangular box of 40x40 km size centered at
each cell. Around the center of each cell, the 360o azimuth is divided into 64 sections. For each
section, a maximum elevation angle is determined as the representative elevation angle of the
section from all 1 km cells located within the section. For a central cell 𝑖, the elevation angle
between cell 𝑖 and another cell 𝑗 in the section is calculated as
𝑧 −𝑧
tan(𝛽𝑖𝑗 ) = |𝑥𝑗−𝑥𝑖 |
𝑗
(7)
𝑖
where 𝑧𝑗 and 𝑧𝑖 denotes the altitudes of the two cells
|𝑥𝑗 − 𝑥𝑖 | is the distance between the two cells
𝜋
𝛽𝑖𝑗 is the elevation angle from cell 𝑖 to cell 𝑗⁡given⁡as 𝛽𝑖𝑗 = 2 − ℎ𝜙,𝑖𝑗
19
The elevation angle is measured from the horizon as shown in Figure 13; if cell 𝑗 is lower than
cell 𝑖, 𝑧𝑗 − 𝑧𝑖 is set to zero. If a receiving cell is not tilted, obstruction of the sky is solely caused
by its surrounding cells (𝑗 ≠ 𝑖). For a tilted receiving cell, part of the sky view from the center of
the cell may be blocked by its own slope. To take this into account, the elevation angle from the
center point to cell itself, or the slope angle of the cell is accounted for as well.
The sky view factor 𝑓𝑠𝑘𝑦 is calculated using Eq. 4 with 𝑛 = 64. For the direct solar beam, the
solar azimuth direction is first checked to see which dissected azimuth section it falls in. Then,
the solar zenith angle is compared against the representative horizon angle of the corresponding
section. If the sun is lower than the horizon angle, the shaded-or-un-shaded indicator function 𝜒
is set to zero, otherwise it is set to one. Self-shadowing is determined by the cosine of the solar
incidence angle as shown in Eq.3.
With all radiant and geometrical parameters being available, the dowelling radiation flux
onto a tilted receiving plane in mountainous terrain can be estimated by Eq. 2. For our study, 𝐹𝐵
and 𝐹𝐷 are obtained directly from the radiative transfer calculation without the need to estimate
the two components from the global flux as is typically done when only the total solar flux is
available from parameterizations or measurements. One should note that the 5-km is the
resolution at which the radiative fluxes are computed assuming average surface elevation. The
actual resolution of the radiative fluxes after the topographic correction depends on the
resolution of the DEM used. Dozier and Frew [1990] use 100-m resolution DEMs; the
topographic correction method described here can be applied to any resolution DEM independent
of the resolution of the radiation fluxes.
The extent to which the radiation coming from below the horizon can be ignored depends on
the surface type of the slope that reflects the radiation. If the below-horizon surface happens to
20
be snow covered with high albedo, ignoring the radiation from that part of the terrain may cause
large differences in the computed fluxes. Since for most of the earth surfaces the portion of
received radiation that comes from the surrounding terrain is less than 3% [Chen, 2006] and even
less for domain average values, large differences should not be expected.
5.2
Impact of the topographic correction
Figure 14 shows an example of the impact of topography on SW↓ in sub area CA for
20:25 UTC, January 14, 2005. These images are at 1-km resolution, namely, the 5-km radiative
fluxes were downscaled according to the DEM used (1 km resolution). The two stages of
correction are considered separately. The upper left panel of Figure 14 shows the original flux
before the topographic correction. The upper middle panel shows the result after correction for
horizontal receiving surface. This is the typical situation of ground instruments that are set up to
measure SW↓. In this situation, the topographic effects are mainly the shadowing from
neighboring mountains and the sky view restriction effect. The upper right panel shows the SW↓
on a tilted slope corrected for the topographic effects. Differences between the corrected and
uncorrected fluxes for horizontal receiving surface, as shown in the lower middle panel, are less
than 10 W/m2 for most of the mountain region, although they range from -15 to +20 W/m2. The
lower right panel shows the differences between after and before corrections for situation when
the receiving surface is the slope itself. In this situation, where some sloped surfaces face the sun
directly and receive incoming solar radiation with increased flux density, the difference can be as
large as 400 W/m2.
We have conducted an evaluation of the satellite retrievals against ground observations at
two stations in sub-area CA (“DAN” and “TUM” in Table 2) before and after topographic
correction for the period of 01/12/2004 to 01/04/2005 (Figure 15). Ground data were quality
21
controlled and averaged to hourly intervals. Only those observations that did not fail any quality
control criteria are used in this comparison. Ground observations with time stamps falling in +/30 minute window around the satellite overpass time are selected for comparison. The satellite
retrievals used are instantaneous values obtained over the stations. Satellite swath data are first
gridded to 0.05° and then topographically corrected assuming a level receiving surface. The
topographic correction is done at 1-km resolution following the DEM data set HDRYO1k. After
slope correction, we get an image of 1-km resolution.
Since the ground data are hourly, four different sizes (NoAvg, 5-km, 10 km, 50 km) of area
average are tried for satellite retrievals. In the figures, “AvgR” gives the radius of the average
area. “NoAvg” means no average was applied and the ground observations are compared against
the nearest 1-km resolution satellite retrievals. Cases with satellite flux values larger than three
times the standard deviation from the measured values are deemed outliers and excluded from
statistical calculations. For these two locations, topographic correction makes little difference to
the comparisons except for large area average results (AvgR=50 km). The reason may be that
there is no blockage of the direct solar component at these two stations at the satellite overpass
times. Since the radiometers are oriented in a horizontal plane, topography affects only the
diffuse sky component, which is limited by surrounding terrain, and the reflected component
from the surrounding terrain. The latter two components are small compared to the direct
component. It should be noted that the lack of strong topographic effect on a level receiving
surface shown here does not imply that the topographic correction is unnecessary. As shown in
Fig. 15, the radiative flux received by a sloped surface is very different from that received by a
level surface because of the cosine effect. For surface energy budget calculations in complex
22
terrain, this slope effect must be taken into account. Also, for those locations where solar shading
does occur, such as in a deep valley, topographic correction is critical.
6. Summary
An inference scheme for deriving SW↓ fluxes from MODIS observations was modified to
allow implementation with MODIS 5-km observations with special attention to snow conditions
on the ground. This required the development of procedures to replace missing variables in the
MODIS database with independent observations (i.e., aerosols from MISR or water vapor from
NOAA/NCAR reanalysis). The inferred fluxes were evaluated against well maintained and
calibrated ground stations that follow the rigorous requirements of the BSRN protocols as well as
against dedicated observations in the mountainous region of interest where snow water
equivalent (SWE) is observed. The methodology was implemented for several water years,
providing the first consistent information of sufficient duration to be useful for SWE estimation.
The evaluation experiments conducted revealed difficulties in matching ground stations with
high resolution satellite observations. As such, the results obtained can be viewed as an initial
evaluation before a more rigorous approach is developed. Yet the results are comparable to those
of products derived at lower resolutions, and as such, the spatial variability shown with the 5-km
data can be considered as real.
To obtain an indirect evaluation of the quality of the 5-km data, the following experiment
was conducted. The 5-km results were aggregated into 10 degree resolution and an independent
product was produced from radiances prepared at 10 resolution for implementation at such scale.
These two 10 products were then compared to ground observations at the mountain sites. As
evident from Figures 8, the first product based on the 5-km observations is in better agreement
with the surface measurements. Moreover, as seen from Figure 10, the monthly mean fluxes
over the CA sub-domain clearly show the location of Lake Tahoe and Mammoth Lake that
23
receive less radiation than the surrounding area. Lake Tahoe in the Sierra Nevada is at a surface
elevation of 6,225 ft and is the largest alpine lake in North America. Lake Mammoth is also in
CA at an elevation of 7,880 ft. It also clearly shows the reduced radiation over the fog covered
areas and the effect of clouds on the up-slopes. Such realistic depiction of these features typical
to complex terrain are not seen in the 10 product shown in Figure 7. The spatial variability of
SW↓ fluxes is shown in Figure 11 for January 2005. The left column shows the monthly mean
spatial variability calculated within a 9x9 box around each grid point at daily time scale, namely,
the temporal average of the daily scale variability for the month. As seen for the sub-domain of
CA, the fog covered area, the mountain slopes with changing cloud conditions, the relatively
clear mountain tops, and the coastline are extremely well depicted in this plot as well as in the
right column that shows the spatial variability of the monthly mean flux, computed by deriving
the monthly mean first and then computing the 9x9 spatial variability. Again, Lake Tahoe and
Mammoth Lake are distinctly seen showing large variability in space and time corresponding to
the variability in cloud formation over these lakes.
While the MODIS observations include relatively high spatial variability, the temporal
frequency of the observations is limited. In mountainous regions affected by topography and
temporal shading effects, additional attention needs to be given to such restrictions in the process
of evaluation on daily time scales. In particular, how well the diurnal cycle is represented when
only two observations per day are available must be assessed. Experiments with these data sets
will allow us to determine the combination of spatial and temporal sampling that provides
optimum SWE model performance. We anticipate that the use of these satellite data will greatly
improve the accuracy of snow models, providing substantial benefits to our understanding of
snow melt processes and to the snow model stakeholder community. We will provide an ftp site
24
with instantaneous data for each swath gridded to 0.05o and each pixel labeled with the time of
orbit overpass. We will also provide gridded data at 0.05o for daily values based both on
observations from both the Terra and Aqua satellites.
The work presented here can serve as a precursor for possible operational products that
can advance snowmelt modeling. For instance, the Joint Polar Satellite System (JPSS) of
NOAA’s next generation polar-orbiting operational environmental satellite system was launched
in October 2011, and the launch of the second satellite in the JPSS Program is planned for early
2017 (the JPSS-1). JPSS will provide operational continuity of satellite-based observations and
products for NOAA Polar-orbiting Operational Environmental Satellites (POES). The JPSS
Program includes a series of advanced spacecraft and sensitive instruments such as the Visible
Infrared Imager Radiometer Suite (VIIRS) that combines the radiometric accuracy of the
Advanced Very High Resolution Radiometer (AVHRR), which is currently flown on the NOAA
polar orbiters, with the high spatial resolution of the Operational Linescan System (OLS) flown
on DMSP. VIIRS will provide users with spectral coverage from 0.412 μm to 12.00 μm in 22
bands; imagery at ~375 m nadir resolution in 5 bands; moderate resolution (~750 m at nadir)
radiometric quality data. The MODIS based methodology is transferable to this system. Another
relevant system is the Geostationary Operational Environmental Satellite - R Series (GOES-R),
the next generation of geosynchronous environmental satellites, which will provide atmospheric
and surface measurements of the Earth’s Western Hemisphere, to be launched in 2015. The
GOES-R series of satellites (GOES-R, S, T, & U) will extend the availability of these systems
through 2036 and provide information relevant to snow-melt modeling in rugged terrain with
prospects for operational implementation.
Acknowledgements
25
The work was supported under NASA grant NNX11AF54G from the NASA Science of Terra
and Aqua Program to the University of Washington and benefited from support under NASA
grant NNX08AN40A from the Science Mission Directorate-Division of Earth Science. Thanks
are due to the NASA GES DISC Giovanni for the MODIS data, to the various MODIS teams
that produced data used in this study, and to the Baseline Surface Radiation Network for
observations used in the evaluation
26
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36
Table 1.
Model Input to V2.0
Time, Geolocation and Sun
Position
Aerosol
Time, Longitude, Latitude and Solar
Zenith Angle.
Collection 5.1 MOD07_L2 (Terra)
and MYD07_L2 (Aqua);
Aerosol Optical Depth
Cloud
Water Cloud Fraction
Water Cloud Optical Depth
Water Cloud Droplet Effective Radius
Ice Cloud Fraction
Ice Cloud Optical Depth
Ice Cloud Droplet Effective Radius
Cloud Top Pressure
Total Column Ozone
Total Column Precipitable Water
Collection 5.1 MOD04_L2 (Terra)
and MYD04_L2 (Aqua); MISR data
used when MODIS missing.
Collection 5.1 MOD06_L2 (Terra)
and MYD06_L2 (Aqua).
Profile
Surface
Surface Elevation
Surface Pressure
Surface Albedo
Daily and weekly snow
Collection 5.1 MOD07_L2 (Terra)
and MYD07_L2 (Aqua); NCEP
reanalysis data are used to fill
MODIS missing values.
Collection 5.1 MOD07_L2 (Terra)
and MYD07_L2 (Aqua);
Filled Land Surface Albedo from
MODIS;
MOD10C1, MOD10C2(Terra) and
MYD10C1, MYD10C2(Aqua);
37
Table 2. Locations and ID codes for selected mountain snow study stations.
Site ID
USFmf
USFuf
USFwf
USGLE
USMe2
USMe3
DAN
TUM
GLEES
USNR
RSH
RXP
Site Name
Set 1 of Mountain Stations
FLAGSTAFF MANAGED FOREST
FLAGSTAFF UNMANAGED FOREST
FLAGSTAFF WILDFIRE
GLACIER LAKES ECOSYSTEMS
STUDY SITE
METOLIUS INTERMEDIATE PINE
METOLIUS SECOND YOUNG PINE
Set 2 of Mountain Stations
Dana Meadows
Tuolumne Meadows
Glacier lakes ecosystems study site
Niwot ridge
Reynolds creek sheltered site
Reynolds creek ridge site
State
Lat
Lon
Elev (m)
AZ
AZ
AZ
35.1426
35.089
35.4454
-111.727
-111.762
-111.772
2160
2180
2270
WY
OR
OR
41.3644
44.4523
44.3154
-106.239
-121.557
-121.608
3190
1253
1005
CA
CA
WY
CO
ID
ID
37.897⁰
37.873⁰
41.3644⁰
40.033⁰
43.186⁰
43.186⁰
119.257⁰
119.35⁰
106.2394⁰
105.5464⁰
116.7831⁰
116.7831⁰
BSRN and Oregon sites
38
Table 3.
Five-year (2000-04) averaged spectral surface albedo in the presence of snow
aggregated by IGBP surface classifications for wavelengths of 0.55 m, 1.24 m,
0.3-0.7 m, and 0.7-5.0 m (based on Moody et al., 2007).
IGBP surface scene
Evergreen needle forest
Evergreen broad forest
Deciduous needle forest
Deciduous broad forest
Mixed forest
Closed shrubs
Open shrubs
Woody savanna
Savanna
Grassland
Wetland
Cropland
Urban
Crop mosaic
Permanent snow
Barren/desert
White-sky snow albedo by wavelength (m)
0.55
1.24
0.3-0.7
0.7-5.0
0.36
0.24
0.31
0.27
0.49
0.31
0.44
0.38
0.42
0.26
0.39
0.33
0.43
0.26
0.35
0.31
0.39
0.25
0.32
0.29
0.48
0.29
0.42
0.36
0.72
0.37
0.68
0.56
0.46
0.28
0.44
0.37
0.59
0.31
0.57
0.47
0.72
0.39
0.70
0.59
0.70
0.32
0.66
0.55
0.76
0.40
0.69
0.58
0.54
0.30
0.50
0.42
0.66
0.36
0.59
0.50
0.94
0.45
0.89
0.74
0.87
0.42
0.78
0.65
39
Table 4.
Obs.
Sat.
radius
5 km
10 km
25 km
50 km
Evaluation experiments of instantaneous SW fluxes from MODIS at different
time and space scales against ground observations.
10 Min
20 Min
30 Min
CC: 0.92
STD: 119.7
Bias: -15.3
CC: 0.93
STD: 106.4
Bias: -14.6
CC: 0.94
STD: 102.0
Bias: -11.8
N/A
CC: 0.92
STD: 117.8
CC: 0.94
STD: 103.4
CC: 0.94
STD: 96.5
N/A
Bias: -16.8
Bias: -15.7
Bias: -14.4
CC: 0.92
STD: 119.6
CC: 0.94
STD: 103.0
CC: 0.95
STD: 93.8
Bias: -15.5
Bias: -14.1
Bias: -13.2
N/A
N/A
N/A
60 Min
N/A
CC: 0.94
STD: 95.1
Bias: -8.5
40
Table 5.
DAN
TUM
RSH
RXP
GLEES
USNR
Statistical results for each mountain site used in Figure 6.
CC
0.89
0.82
0.83
0.83
0.81
0.77
Bias
2.79
20
77.8
38.5
5.39
40
STD
134
167
164
158
161
189
41
List of Figures
Figure 1.
Fog over the flat terrain in CA as seen from the GOES 11 satellite.
Figure 2.
Study area with location of various observational sites.
Figure 3.
Illustration of the gridding process for instantaneous SW↓ data in W/m2 for
2004/12/04/1810 after gap filling.Grid size is 0.05o. Missing values in each grid
cell are filled with the average from the 3x3 adjacent values. The gridding process
goes through two iterations. Boxes indicate sub-domains for further analysis.
Figure 4.
Evaluation of MODIS swath SW↓ fluxes at SURFRAD sites of FPK and BON for
a) instantaneous fluxes under no snow conditions, 2005; b) instantaneous for
snow conditions during 2004 and 2005; c) daily for (a) conditions; d) daily for (b)
conditions.
Figure 5.
Evaluation of MODIS swath SW↓ fluxes during 03/01/2005-07/31/2005 for a)
instantaneous fluxes b) daily fluxes over 3 sites in Oregon (Burns, Eugene and
Hermiston) combined (http://solardat.uoregon.edu/SolarData.html).
Figure 6.
Evaluation of MODIS swath instantaneous SW↓ during 01/01/2005 to 07/31/2005
at left) mountain sites of DAN, TUM, GLEES, USNR, RSH, RXP; right) without
USNR and RSH sites. Statistical results for each site are presented in Table 5.
Figure 7.
An example of instantaneous SW↓ fluxes at different grid resolutions in the subarea CA (121.4⁰ W - 18.4⁰ W, 36.5⁰ N - 39.5⁰ N) for 01/01/2005 from
MODIS/Terra satellite. Upper-left: 0.05⁰ results from the MODIS level-2 5 km
resolution swath input. Upper-right: 1⁰ result aggregated from the 0.05⁰ results.
Lower-right: 1⁰ results from MODIS Level-3 1⁰ data. Lower-left: Difference
42
between the two 1⁰ results. The red box indicates the location of the subarea CA.
The white lines are the coast and states boundaries. To obtain the 1⁰ data from 5km MODIS input, the 5-km swath data were first gridded to 0.05⁰ resolution and
then downscaled to 1⁰ grid by taking 20x20 grid average.
Figure 8.
Evaluation of the 1⁰ satellite retrievals from MODIS/Terra (Left column) and
MODIS/Aqua (right column) against 6 ground observational sites over the
western USA region for the time period 12/2004 to 05/2005. Upper panel: 1⁰
result up scaled from the MODIS 5-km data; Lower panel: 1⁰ result inferred from
the MODIS level-3 one-degree resolution data. The ground data are for the six
mountain stations listed as Set 2 in Table 2.
Figure 9.
The left panel is the topography of the region with the three focus sites
(WA, ID, CA) marked by red boxes. The blue spots show the locations of
available ground observation stations. The middle panel shows the monthly mean
snow covered area in units of % averaged from the MODIS daily snow products
while the right panel shows the day to day variability in snow cover area. The
calculation is based on the 0.05° resolution grided data for January 2005.
Figure 10.
The left column shows the monthly mean values of surface SW↓ flux for January
2005. The middle column shows the frequency distribution of daily values for the
corresponding month and subdomain. The right column shows the temporal
standard deviation for the subdomain in the month.
Figure 11.
Spatial variability of SW↓ flux in the 3 subdomains for January 2005. Left
column shows the monthly mean spatial variability. The spatial variability is
calculated within a 9x9 box around each grid point at daily time scale, namely, the
43
temporal average of the daily scale variability for the month. The middle column
shows the frequency distribution of the spatial variability for whole month of
January 2005. The right column shows the spatial variability of the monthly mean
flux, computed by getting monthly mean first and then derive the 9x9 spatial
variability. Each row is for a specified sub area.
Figure 12.
Spatial means and relative standard deviations of daily mean fluxes
for the three intensive evaluation subdomains. The relative standard deviations
(Rel.Std.Dev) are relative to the area mean. The sizes of these sub-domains are
3ºx3º (CA, 121.4ºW, 118.4ºW, 36.5ºN, 39.5ºN), 2ºx2º (WA, 122.5ºW, 120.5ºW,
45.9ºN, 47.9ºN) and 1ºx1º (ID, 117.3ºW, -116.3ºW, 42.5ºN, 43.5ºN).
Figure 13.
Topographic correction parameters.
Figure 14.
Impact of surface topography on solar radiation for subdomain CA for 20:25UTC,
January 14, 2005. Upper left: downwelling solar radiation before topographic
correction. Upper middle: SW downwelling flux after topographic correction over
a horizontal receiving surface. Upper right: SW downwelling flux incident on the
slope face. Lower left: surface elevation of the domain. Lower middle: Difference
between after and before (after-before) topographic correction for horizontal
receiving surface. Lower right: Difference for a slope face.
Figure 15.
Evaluation of satellite retrievals against ground observations at two stations
(independently) in sub-area CA (“DAN”, 119.257o W, 37.897o N and “TUM”,
119.35o W, 37.873o N), from 12/01/2004 to 04/30/2005. Left: before topographic
correction; Right: after topographic correction. Ground data are hourly averaged
and quality controlled. Only those observations that did not fail any criteria are
44
used in this comparison. Ground observations with time stamp falling in +/-30
minute window around the satellite pass time are selected for comparison.
45
Figure 1.
Fog over the flat terrain in CA as seen from the GOES 11 satellite.
46
Figure 2.
Study area with location of various observational sites.
47
Figure 3. Illustration of the gridding process for instantaneous SW↓ data in W/m2 for
2004/12/04/1810 after gap filling.Grid size is 0.05o. Missing values in each grid cell are
filled with the average from the 3x3 adjacent values. The gridding process goes through
two iterations. Boxes indicate sub-domains for further analysis (results over Colorado not
presented here).
48
Figure 4.
Evaluation of MODIS SW↓ fluxes at SURFRAD sites of FPK and BON for a)
instantaneous fluxes under no snow conditions, 2005; b) instantaneous for snow
conditions during 2004 and 2005; c) daily for (a) conditions; d) daily for (b)
conditions.
49
Figure 5.
Evaluation of MODIS swath SW↓ fluxes during 03/01/2005-07/31/2005
for a) instantaneous fluxes b) daily fluxes over 3 sites in Oregon (Burns, Eugene
and Hermiston) combined (http://solardat.uoregon.edu/SolarData.html).
50
Figure 6.
Evaluation of MODIS swath instantaneous SW↓ during 01/01/2005 to 07/31/2005
at left) mountain sites of DAN, TUM, GLEES, USNR, RSH, RXP; right) without
USNR and RSH. Statistical results for each site are presented in Table 5.
51
Figure 7.
An example of instantaneous SW↓ fluxes at different grid resolutions in the subarea CA (121.4⁰ W - 18.4⁰ W, 36.5⁰ N - 39.5⁰ N) for 01/01/2005 from
MODIS/Terra satellite. Upper-left: 0.05⁰ results from the MODIS level-2 5 km
resolution swath input. Upper-right: 1⁰ result aggregated from the 0.05⁰ results.
Lower-right: 1⁰ results from MODIS Level-3 1⁰ data. Lower-left: Difference
between the two 1⁰ results. The red box indicates the location of the subarea CA.
The white lines are the coast and states boundaries. To obtain the 1⁰ data from 5km MODIS input, the 5-km swath data were first gridded to 0.05⁰ resolution and
then downscaled to 1⁰ grid by taking 20x20 grid average.
52
Figure 8.
Evaluation of the 1⁰ satellite retrievals from MODIS/Terra (Left column) and
MODIS/Aqua (right column) against 6 ground observational sites over the western USA
region for the time period 12/2004 to 05/2005. Upper panel: 1⁰ result up scaled from the
MODIS 5-km data; Lower panel: 1⁰ result inferred from the MODIS level-3 one-degree
resolution data. The ground data are for the six mountain stations listed as Set 2 in Table 2.
.
53
Figure 9. The left panel is the topography of the region with the three focus sites
(WA, ID, CA) marked by red boxes. The blue spots show the locations of available
ground observation stations. The middle panel shows the monthly mean snow
covered area in units of % averaged from the MODIS daily snow products while the
right panel shows the day to day variability in snow cover area. The calculation is
based on the 0.05° resolution grided data for January 2005.
54
Sub area: CA
Sub area: ID
Sub area: WA
Figure 10.
The left column shows the monthly mean values of surface SW↓ flux for January
2005. The middle column shows the frequency distribution of daily values for the
corresponding month and subdomain. The right column shows the temporal
standard deviation for the subdomain in the month.
55
Sub area: CA
Sub area: ID
Sub area: WA
Figure 11.
Spatial variability of SW↓ flux in the 3 subdomains for January 2005. Left
column shows the monthly mean spatial variability. The spatial variability is calculated
within a 9x9 box around each grid point at daily time scale, namely, the temporal average
of the daily scale variability for the month. The middle column shows the frequency
distribution of the spatial variability for whole month of January 2005. The right column
shows the spatial variability of the monthly mean flux, computed by getting monthly
mean first and then derive the 9x9 spatial variability. Each row is for a specified sub area.
56
Area Mean, CA
Rel.Std.Dev, CA
Figure 12. Spatial means and relative
standard deviations of daily mean fluxes for
the three intensive evaluation subdomains.
Area Mean, ID
The relative standard deviations (Rel.Std.Dev)
are relative to the area mean. The sizes of
these sub-domains are 3ºx3º (CA, 121.4ºW,
Rel.Std.Dev, ID
118.4ºW, 36.5ºN, 39.5ºN), 2ºx2º (WA,
122.5ºW, 120.5ºW, 45.9ºN, 47.9ºN) and
1ºx1º (ID, 117.3ºW, -116.3ºW, 42.5ºN,
Area Mean, WA
43.5ºN).
Rel.Std.Dev, WA
Zenith
57
Before
After-level
After-slope
Diff.-level
Diff.-slope
Figure 14. Impact of surface topography on solar radiation for subdomain CA for 20:25UTC,
January 14, 2005. Upper left: downwelling solar radiation before topographic correction.
Upper middle: SW downwelling flux after topographic correction over a horizontal
receiving surface. Upper right: SW downwelling flux incident on the slope face. Lower
left: surface elevation of the domain. Lower middle: Difference between after and before
(after-before) topographic correction for horizontal receiving surface. Lower right:
Difference for a slope face.
58
59
Figure 15.
Evaluation of satellite retrievals against ground observations at two stations
(independently for each station) in sub-area CA (“DAN”, 119.257o W, 37.897o N and
“TUM”, 119.35o W, 37.873o N), from 12/2004 to 04/2005. Left: before topographic
correction; Right: after topographic correction. Ground data are hourly averaged and
quality controlled. Only those observations that did not fail any criteria are used in this
comparison. Ground observations with time stamp falling in +/-30 minute window
around the satellite pass time are selected for comparison.
60