Statistical transfer functions
10-day observation data for temperature and precipitation were collected from 661
meteorological stations scattered across China from 1961 to 2010 (National Meteorological
Information Center of China: www.nmic.gov.cn) (Supplement 3). A digital elevation model
(DEM) from the Shuttle Radar Topography Mission (SRTM) of China at a spatial resolution
of 90m  90m (http://srtm.csi.cgiar.org) was upscaled into a DEM at a spatial resolution of
1km  1km using a bilinear resampling approach. The DEM was used as auxiliary data to
develop the STFs for MAT and MAP.
A statistical analysis of the time series data from the 661 meteorological stations during
the 1961 to 2010 period, using the DEM as secondary data, indicates that MAT from 1961 to
2010 exhibits spatial stationarity, while MAP does exhibit spatial non-stationarity (Wang et al,
2012). MAT can be modeled as a linear function of a set of independent variables; local
variations in rates of change are allowed for MAP so that the coefficients in the model are
localized rather than using global estimates. In other words, regression coefficients for MAP
are determined locally and not globally.
For the simulation of MAT from 1961 to 2010, HASM-OLS, a combination of HASM
with the linear equation of OLS, was developed due to the spatial stationarity of MAT. Owing
to the spatial non-stationarity of MAP during the 1961 to 2010 period, HASM-GWR-BC, an
integration of HASM with the GWR equation of Box-Cox transformation of MAP, was
developed.
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1 STF of MAT
A statistical transfer function (STF) of MAT was formulated using minimized residuals
output from a high accuracy and high speed method for surface modeling (HASM) with an
ordinary least squares (OLS) linear equation that used latitude and elevation as independent
variables. The linear equation of an ordinary least squares (OLS) between observed and
simulated temperatures from 1961 to 2010, with a correlation coefficient of 0.96, can be
formulated as,
Ts  38.552  0.705  La  0.003 Ele  Te
(1)
where Ts represents the MAT simulated by OLS on a national level during 1961 to 2010
period; La = latitude; Ele = elevation, and Te is the residual.
The residuals of MAT from 1961 to 2010 were calculated by comparing the simulated
values using the OLS equation (1) with the observed MAT from all meteorological stations.
The residuals at all meteorological stations are used to drive HASM and interpolate residuals
at every grid cell. The total number of 1km  1km grid cells was 19,606,916 for a rectangle
of computational domain covering China. The simulated MAT from 1961 to 2010 at every
grid cell i , in which i  1, 2,...,19606916 , can be formulated as,

Tsi  t   ols  xT  HASM Tk  t   ols  xT

(2)
()
where x  1, Lat , Ele  , θols   38.552,0.705,0.003 , T k t is the MAT observed in the
year of t at the meteorological station k .
2 STF of MAP
Most atmospheric moisture is derived by the evaporation of ocean water and controlled by the
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transportation of air masses from the tropics to the polar areas. During this transportation, air
masses cool, leading to continuous condensation and rain-out from low to high latitudes on
both hemispheres (van der Veer et al. 2009). Latitude and longitude can be used to reflect the
influence of general circulation and continentality on precipitation. Spatial variability of
precipitation in complex terrain is caused by the dependence of precipitation on altitude and
windward effects (Franke et al. 2008). A statistical analysis of precipitation data from the 661
meteorological stations demonstrates that precipitation has a close relationship with
topographic aspect, the sky view factor, latitude, longitude and elevation.
Let x  1, Lo, La, Ele, ICA, SVF  , in which La represents latitude, Lo refers to
longitude, Ele is elevation, ICA the impact coefficient of aspect on precipitation, and
SVF the sky view factor. Then the STF of MAP under a BOX-COX transformation can be
formulated as an equation of geographical weight regression (HASM-GWR-BC),

Psi  t   θ gwr  xT  HASM  0.475  Pk  t    θ gwr  xT

T
where  gwr  x  W  x
Psi
is
the

1

(3)
 x  W   0.475  Pk  t   ; W is the geographical weight matrix；
simulated
MAP


at
the
grid
cell
i ( i  1, 2,...,19606916 );
 0.475  Pk  t    Pk0.475  t   1 / 0.475 is a BOX-COX transformation of annual mean
precipitation Pk  t  at observation station k in the year t .
The sky view factor can be formulated as (Yue, 2011),
SVF 
1  cos(  ( Slope /180))
2
æ
where Slope = arctan ç f x
è
(4)
2ö
( ) + ( f y ) ÷ø
2
1
2
×57.3, f y 
f
f
, fx 
and z  f  x, y  is a
x
y
digital elevation model.
The value of each cell in an aspect grid indicates the direction in which the cell's slope
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faces from north. Aspect is measured clockwise in degrees with 0° representing due north,
90° due east, 180° due south and 270° due west. Because of the considerable effects of the
Southwest and Southeast Monsoons, i.e. the effect of warm and wet airflow from the Pacific
Ocean and Indian Ocean, our data shows that southern aspects have the highest amounts of
precipitation. Therefore, an impact coefficient of 1 is given to slopes facing due south (ICA).
Further, a value of -1 is given to ICA due north. A value of 0 is given to flat areas. The ICA
can be expressed as (Yue, 2011),
 cos(  (Aspect /180))
Asp  
0
slope area
flat area
(5)
References
Franke J, Haentzschel J, Goldberg V, Bernhofer C (2008) Application of a trigonometric approach to the
regionalization of precipitation for a complex small-scale terrain in a GIS environment. Meteorological
Applications 15: 483-490
van der Veer G, Voerkelius S, Lorentz G, Heiss G, Hoogewerff JA (2009) Spatial interpolation of the deuterium
and oxygen-18 composition of global precipitation using temperature as ancillary variable. Journal of
Geochemical Exploration 101: 175-184
Wang CL, Yue TX, Fan ZM, Zhao N, Sun XF (2012) HASM-based climatic downscaling model over
China. Journal of Geo-Information Science 14(5): 599-610 (in Chinese)
Yue TX (2011) Surface Modelling: High Accuracy and High Speed Methods. CRC Press, New York
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