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Multiscale Hydrologic Remote Sensing: Perspectives and Applications
10.4.4 Model vaRiaBleS
10.4.4.1 Temperature and Precipitation
SRM operates using daily temperature and precipitation data corresponding to the
hypsometric mean elevation of each zone. Analysis of the SNOTEL data time series
indicated that, for temperature, there was a general altitudinal lapse rate, but that there
was a fair amount of scatter, possibly caused by microclimate effects associated with
individual stations. For precipitation, there was no apparent altitudinal gradient. In
order to maintain as robust of a time series data set as possible, a virtual station was
created, whose elevation was the arithmetic average of all 11 SNOTEL stations within
the basin. The temperature time series data were produced at this virtual station by
taking the average of the average daily temperature at each of the 11 SNOTEL stations when data for all 11 stations existed. Similarly, the precipitation time series data
were produced at the same virtual station by taking the arithmetic average of the daily
precipitation values at all 11 SNOTEL stations. This precipitation time series at virtual station is equivalent to the basin-wide average precipitation that would be calculated using the arithmetic mean method (Chow et al. 1988), which is appropriate since
no altitudinal or geographical pattern was evident among the precipitation stations.
10.4.4.2 Snow-Covered Area
SRM requires a daily time series of S, the fraction of SCA for each elevation zone
throughout the snowmelt season. These time series are known as CDCs. A fraction
of SCA was derived from the Terra satellite’s MODIS 8-day L3 global 500-m grid
composite SCA products (MOD10A2) available from the NSIDC (Hall et al. 2006).
This product uses an 8-day temporal filter to generate a composite snow cover image.
The primary purpose of the filter is to remove cloud cover. The filter examines a
series of eight consecutive daily remotely sensed snow cover images and assigns the
value of “snow” to every pixel for which a “snow” value was observed for that pixel
within any of the eight images. The first day of the 8-day sequence is assigned to the
composite snow cover image.
Ninety-six remotely sensed images were used, covering the period from February
to August each year from 2003 through 2006. Each image covered a large portion
of the northwestern United States. The snow cover images were processed in a GIS
software package to extract the portion corresponding to the basin area, delineate
the basin zones used in the SRM, and then calculate the fraction of SCA within each
elevation zone.
Since these were an 8-day product and SRM requires daily S values, that is, the
ratio of SCA to total zone area, as input data, a method was developed in which S was
represented with a Gaussian curve during the melt period as follows. Day of year was
used to represent the random variable, t, and S corresponded to 1 – F(z), where z is a
standard normal random variable derived from t as
z = (t – t 50 )/σ t ,
(10.8)
where t 50 is the day of year on which S = 50% within a given elevation zone based
on MODIS data, and σ t is the standard deviation of t required to cause the slope and
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
10.4.4 Model vaRiaBleS
10.4.4.1 Temperature and Precipitation
SRM operates using daily temperature and precipitation data corresponding to the
hypsometric mean elevation of each zone. Analysis of the SNOTEL data time series
indicated that, for temperature, there was a general altitudinal lapse rate, but that there
was a fair amount of scatter, possibly caused by microclimate effects associated with
individual stations. For precipitation, there was no apparent altitudinal gradient. In
order to maintain as robust of a time series data set as possible, a virtual station was
created, whose elevation was the arithmetic average of all 11 SNOTEL stations within
the basin. The temperature time series data were produced at this virtual station by
taking the average of the average daily temperature at each of the 11 SNOTEL stations when data for all 11 stations existed. Similarly, the precipitation time series data
were produced at the same virtual station by taking the arithmetic average of the daily
precipitation values at all 11 SNOTEL stations. This precipitation time series at virtual station is equivalent to the basin-wide average precipitation that would be calculated using the arithmetic mean method (Chow et al. 1988), which is appropriate since
no altitudinal or geographical pattern was evident among the precipitation stations.
10.4.4.2 Snow-Covered Area
SRM requires a daily time series of S, the fraction of SCA for each elevation zone
throughout the snowmelt season. These time series are known as CDCs. A fraction
of SCA was derived from the Terra satellite’s MODIS 8-day L3 global 500-m grid
composite SCA products (MOD10A2) available from the NSIDC (Hall et al. 2006).
This product uses an 8-day temporal filter to generate a composite snow cover image.
The primary purpose of the filter is to remove cloud cover. The filter examines a
series of eight consecutive daily remotely sensed snow cover images and assigns the
value of “snow” to every pixel for which a “snow” value was observed for that pixel
within any of the eight images. The first day of the 8-day sequence is assigned to the
composite snow cover image.
Ninety-six remotely sensed images were used, covering the period from February
to August each year from 2003 through 2006. Each image covered a large portion
of the northwestern United States. The snow cover images were processed in a GIS
software package to extract the portion corresponding to the basin area, delineate
the basin zones used in the SRM, and then calculate the fraction of SCA within each
elevation zone.
Since these were an 8-day product and SRM requires daily S values, that is, the
ratio of SCA to total zone area, as input data, a method was developed in which S was
represented with a Gaussian curve during the melt period as follows. Day of year was
used to represent the random variable, t, and S corresponded to 1 – F(z), where z is a
standard normal random variable derived from t as
z = (t – t 50 )/σ t ,
(10.8)
where t 50 is the day of year on which S = 50% within a given elevation zone based
on MODIS data, and σ t is the standard deviation of t required to cause the slope and