Evaluating a modified point-based method to downscale cell-based climate variable data to high-resolution grids

Abstract

To address the demand for high spatial resolution gridded climate data, we have advanced the Daymet point-based interpolation algorithm for downscaling global, coarsely gridded data with additional output variables. The updated algorithm, High-Resolution Climate Downscaler (HRCD), performs very good downscaling of daily, global, historical reanalysis data from 1° input resolution to 2.5 arcmin output resolution for day length, downward longwave radiation, pressure, maximum and minimum temperature, and vapor pressure deficit. It gives good results for monthly and yearly cumulative precipitation and fair results for wind speed distributions and modeled downward shortwave radiation. Over complex terrain, 2.5 arcmin resolution is likely too low and aggregating it up to 15 arcmin preserves accuracy. HRCD performs comparably to existing daily and monthly US datasets but with a global extent for nine daily climate variables spanning 1948–2006. Furthermore, HRCD can readily be applied to other gridded climate datasets.

Appendices

Appendix A. Modified cosine interpolation

Modified cosine interpolation is more consistent with cell-based data than other interpolation methods because it more heavily weights the nearest input point with respect to the quadrant containing the output point rather than calculating a weight based on a linear distance from the input point. HRCD uses a fourth-power cosine function to constrain input values to the four nearest-neighbor cells and to mitigate input cell boundary effects on the interpolated surface (Zhao et al. 2005):

$$ {{D_i} = {\text{co}}{{\text{s}}^4}\left[ {\left( {\frac{\pi }{{2}}} \right) \cdot \left( {\frac{{{d_i}}}{{{d_{i{ \max }}}}}} \right)} \right]\quad i = {1,2,3,4}} $$

(A1)

$$ {{W_i} = \frac{{{D_i}}}{{\sum\nolimits_{i = {1}}^4 {{D_i}} }}} $$

(A2)

$$ {V = \sum\nolimits_{i = {1}}^4 {\left( {{W_i} \cdot {V_i}} \right)} }, $$

(A3)

where i is the index of one of four nearest-neighbor input cell centers, D _i is the nonlinear distance between the output cell center and input cell center i (dimensionless), d _i is the great circle distance between the output cell center and input cell center i (meter), d _imax is the great circle distance-passing through the output cell center—from input cell center i to the latitude–longitude boundary defined by the four nearest-neighbor input cell centers (meter), W _i is the interpolation weight for input cell center i (dimensionless), V _i is the climate variable value at input the cell center i, and V is the interpolated climate variable value at the output cell center (Fig. 12).

Fig. 12

Modified cosine interpolation. In this study the output interpolation point is the center of the output cell. d_i is the great circle distance between input cell center i (1–4) and the output interpolation point. d _imax is the great circle distance between input cell center i and the latitude/longitude boundary defined by the four input cell centers, passing through the interpolation point

This d _imax constrains weights by the latitude-longitude boundary defined by the four nearest-neighbor input cell centers. Zhao et al. (2005) defines d _imax as the maximum great circle distance between any two of the four input cell centers. Thus, D _i  = W _i  = 0 only when the output cell center lies on the great circle associated with d _imax. In all other cases, with distortion increasing with latitude due to meridian convergence, inappropriately high weights can occur because d _imax extends beyond the latitude–longitude boundary defined by the four nearest-neighbor input cell centers. Our d _imax, however, ensures that D _i is based on the relative position of the interpolation point within the four input cell centers.

Appendix B. Humidity variable conversion

For the daily input data described in Section 2.2, T _DEW (degree Celcius) is calculated from pressure and specific humidity via average vapor pressure using the inverse of the Magnus–Tetens formula (Campbell and Norman 1998):

$$ {e = {610}{.70} \cdot { \exp }\left( {\frac{{{17}{.38} \cdot {T_{\text{DEW}}}}}{{{T_{\text{DEW}}} + {239}{.0}}}} \right)} $$

(B1)

and

$$ {e = \frac{{{\text{PRES}} \cdot {\text{SH}}}}{{\left( {\frac{{{M_{\text{wv}}}}}{{{M_{\text{da}}}}} \cdot \left( {{1} - {\text{SH}}} \right)} \right) \cdot \left( {{1} + \frac{\text{SH}}{{\frac{{{M_{\text{wv}}}}}{{{M_{\text{da}}}}} \cdot \left( {{1} - {\text{SH}}} \right)}}} \right)}}}, $$

(B2)

where e is the average vapor pressure (Pascal), PRES is the input average surface pressure (Pascal), SH is the average specific humidity (kilograms water vapor (kilograms per dry air + water vapor)), M _wv is the molecular mass of water vapor (18.0148 × 10⁻³ kg mol⁻¹), and M _da is the molecular mass of dry air (28.9644 × 10⁻³ kg mol⁻¹).

After interpolation, T _DEW is converted back to e using Eq. 2 and then converted to VPD by (Pascal):

$$ {{\text{VPD}} = {e_s} - e} $$

(B3)

and

$$ {T_{\text{DAY}}} = {0}{.725} \cdot \,{T_{{\text{MAX}}\,}} + {0}{.275} \cdot \,{T_{\text{MIN}}}\,, $$

(B4)

where e _s is the average saturation vapor pressure (Pascal) calculated by Eq. (2) with T _DAY (degree Celcius) in place of T _DEW, and T _MAX and T _MIN are maximum and minimum daily temperatures, respectively (degree Celcius). We also used Eqs. (B1), (B3), and (B4) to convert verification data (Section 2.3) to VPD.

When T _AVG and PRES input data are available, elevation-adjusted PRES is estimated by the hypsometric equation (Holton 1992):

$$ {{Z_2} - {Z_1} = \frac{{RT}}{g} \cdot { \ln }\left[ {\frac{{{P_1}}}{{{P_2}}}} \right]} $$

(B5)

The elevation-adjusted PRES is used with Eqs. (B1)–(B4) to calculate an output SH.