Daymet: Annual 2-degree Tile Summary Cross-Validation Statistics for North America

This data set provides annual summary cross-validation statistics for minimum temperature (tmin), maximum temperature (tmax), and daily total precipitation (prcp) of "Daymet: Daily Surface Weather Data on a 1-km Grid for North America, Version 2" (Thornton et al., 2014). The cross-validation statistics were generated by the Daymet model algorithm from the station-based daily observations and predictions and are summarized for each of the 2-degree by 2-degree tiles in the regimen in which Daymet is derived. Data are available for the temporal period 1980 through 2014, the most recently processed calendar year of Daymet Version 2.

Summarized by tile are average and period-of-record mean absolute error (MAE) and bias statistics for the input weather observations of tmin, tmax, and prcp.  Also available are tile-wide values of total ground weather stations, total station-days evaluated, and mean observed input parameter values. Summary statistics are also available for the Gaussian distribution functions, used in the Daymet interpolation method, as mean and standard deviations of the radius of the kernel weights and x, y, and z components of the 3-dimensional regression formula.

The data are distributed as shape files that represent the 2-degree by 2-degree tile structure in which the Daymet model estimates are derived.  The annual cross-validation statistics are provided as a separate shape file for the North American domain for each of the three variables for each year of available Daymet input data (i.e., 3 files/year for 35 years).

Also provided are the complete time series of annual summary cross-validation statistics for the three Daymet input parameters in comma separated files (*.csv).  There is one file for each of the three parameters for each tile.

Figure 1 shows four different annual tile-wide summary cross-validation statistics for 1980 daily precipitation; mean absolute error (MAE) for single day predictions ("daymae"), mean prediction bias ("bias"), mean absolute error for period of record predictions ("pormae"), and mean absolute error as a percentage for period of record predictions (“pormpae”).

Project:  Daymet

This data set provides annual tile-wide summary cross-validation statistics for minimum temperature (tmin), maximum temperature (tmax), and daily total precipitation (prcp) of the Daymet data set (Daymet: Daily Surface Weather Data on a 1-km Grid for North America, Version 2), for the temporal period 1980 through 2014, the most recently processed calendar year of Daymet. The cross-validation statistics were generated by the Daymet model algorithm from the station-based daily observations and predictions and summarized for each of the 2-degree by 2-degree tile regimen in which Daymet is derived.

Average and period-of-record mean absolute error (MAE) and bias statistics for the input weather observations of tmin, tmax, and prcp were calculated along with tile-wide values of total ground weather stations per tile, total station days, and mean observed values per tile. The Gaussian distribution kernel weights and 3-dimensional regression components from the interpolation methodology are reported for the three variables. 

Related Data Set:

Thornton, P.E., M.M. Thornton, B.W. Mayer, N. Wilhelmi, Y. Wei, R. Devarakonda, and R.B. Cook. 2014. Daymet: Daily Surface Weather Data on a 1-km Grid for North America, Version 2. Data set. Available on-line [http://daac.ornl.gov] from Oak Ridge National Laboratory Distributed Active Archive Center, Oak Ridge, Tennessee, USA. http://dx.doi.org/10.3334/ORNLDAAC/1219

 

The annual cross-validation statistics are provided for North America as a separate shape file for each of the three variables for each year of available Daymet input data (i.e., 3 files/year for 35 years).

Also the complete time series of annual cross-validation statistics for a variable is provided in a single comma separated file (*.csv).  There is one file for each of the three variables.

Shape Files

Daymet cross-validation data are available as shape files for North America – Mexico, USA, and Canada south of 52N – with a spatial resolution of 2 degrees. 

The shape files geometric polygon structure represents the 2 degree x 2 degree tile “grid” in which the Daymet model is processed and output. 

Three shape files with cross-validation statistical information for each of the three Daymet daily weather input variables minimum temperature (tmin), maximum temperature (tmax), and total precipitation (prcp) are available each year of available Daymet data. There are a total of 105 shape files.

The North American shape files are zipped for convenience and contain five files (*.dbf,*.prj,*.shp,*.shp.xml, and *.shx).

File names follow this syntax:   xval_pppp_yyyy.shp  (*.zip)

Where:

xval distinguishes these as Daymet cross-validation data files;

pppp is the respective Daymet input meteorological variable (tmin, tmax, and prcp); and

yyyy is year. 

 

Data Dictionary:

Fields within each shape file contain the tile-wide summary cross-validation statistics. 

Shape files for temperature (tmin and tmax) Cross-Validation Statistics have these attributes.

Field	Units/format	Description
Xmin	decimal degrees	Approximate minimum longitude of tile
Xmax	decimal degrees	Approximate maximum longitude of tile
Ymin	decimal degrees	Approximate minimum latitude of tile
Ymax	decimal degrees	Approximate maximum latitude of tile
year	YYYY	Daymet processing year
tileid		Daymet Tile ID
nstns3x3	stations	number of stations in 3x3 tile region surrounding the central tile (tileid)
nstns	stations	number of stations evaluated (tileid)
nstndays	days	number of station-days evaluated (tileid)
rad90mean	meter	mean: radius capturing 90% of filter kernel weight
rad90std	meter	standard deviation:  radius capturing 90% of filter kernel weight
daymae	degrees Celsius	mean absolute error for single-day predictions
pormae	degrees Celsius	mean absolute error for period-of-record predictions
bias	degrees Celsius	mean prediction bias
tamean	degrees Celsius	mean observed temperature (tmin and tmax)
xlrmean	degrees C/meter	3-d regression: mean x-component
xlrstdv	degrees C/meter	3-d regression: among-station std dev of x-component
ylrmean	degrees C/meter	3-d regression: mean y-component
ylrstdv	degrees C/meter	3-d regression: among-station std dev of y-component
zlrmean	degrees C/meter	3-d regression: mean z-component
zlrstdv	degrees C/meter	3-d regression: among-station std dev of z-component

 

Shape files for precipitation (prcp) Cross-Validation Statistics have these attributes.

Field	Units/format	Description
Xmin	decimal degrees	Approximate minimum longitude of tile
Xmax	decimal degrees	Approximate maximum longitude of tile
Ymin	decimal degrees	Approximate minimum latitude of tile
Ymax	decimal degrees	Approximate maximum latitude of tile
year	YYYY	Daymet processing year
tileid		Daymet Tile ID
nstns3x3	stations	number of stations in 3x3 tile region surrounding the central tile (tileid)
nstns	stations	number of stations evaluated (tileid)
nstndays	days	number of station-days evaluated (tileid)
rad90mean	meter	mean: radius capturing 90% of filter kernel weight
rad90std	meter	standard deviation:  radius capturing 90% of filter kernel weight
daymae	cm/day	mean absolute error for single-day predictions
pormae	cm/day	mean absolute error for period-of-record predictions
pormpae	%	mean absolute error as a percentage, for period of record predictions
bias	cm/day	mean prediction bias
ppmean	cm/day	mean observed daily total precipitation
xlrmean	1/meter	3-d regression: mean x-component
xlrstdv	1/meter	3-d regression: among-station std dev of x-component
ylrmean	1/meter	3-d regression: mean y-component
ylrstdv	1/meter	3-d regression: among-station std dev of y-component
zlrmean	1/meter	3-d regression: mean z-component
zlrstdv	1/meter	3-d regression: among-station std dev of z-component

 

User’s Notes

• When “nstns” is zero (0), no input weather station data are available within that tile.  All attributes are recorded as nodata (-9999) or "nan".
• When “nstns” have very low values (e.g. 1, 2, or 3) denoting limited input data available for that tile, values for the 3-dimensional regression components may be set to “nan” where the regressions algorithm failed.
• Floating point precision has been carried forward from the Daymet model for all attributes.

 

Spatial Data Properties

Spatial Representation:  vector

Vector Format:  shape file

Nodata Value:  -9999

Spatial Reference Properties

Type:  Geographic

"GEOGCS['GCS_WGS_1984',  

                DATUM['WGS_1984',      

                SPHEROID['WGS_84',6378137.0,298.257223563]],  

                PRIMEM['Greenwich',0.0],  

                UNIT['Degree',0.0174532925199433]]"

 

Comma Separated Files

The complete time series (1980-2014) of annual cross-validation statistics for a variable is provided in a single comma separated file (*.csv) -- one file for each of the three variables.

 

File names follow this syntax:   xval_pppp_yyyy-yyyy.csv

Where:

xval distinguishes these as Daymet cross-validation data files;

pppp is the respective Daymet input meteorological variable (tmin, tmax, and prcp); and

yyyy-yyyy is the range of annual summary statistics included in the file. 

 

Data File Columns:

The first column in the *.csv files (pppp) indicates the variable and the remaining columns are the same as the attribute fields in the respective temperature and precipitation shape files.

Example data records:  xval_tmin_1980-2014.csv

pppp,year,tileid,nstns3x3,nstns,nstndays,rad90mean,rad90stdv,daymae,pormae,bias,tamean,xlrmean,xlrstdv,ylrmean,ylrstdv,zlrmean,zlrstdv tmin,1980,9402,274,7,2440,70869.69598,3407.694504,2.247534956,1.569762955,-0.036558511,19.78422131,-1.63E-06,1.84E-05,-5.50E-07,2.05E-05,-0.005625534,0.00070347 tmin,1980,9403,349,1,365,67391.66637,0,1.408607311,0.362330488,-0.362330488,21.44794521,-9.75E-06,0,1.86E-05,0,-0.0055475,0 … tmin,2014,12661,23,1,359,269892.1173,0,2.086786393,1.725761521,1.725761521,-3.542896936,nan,nan,nan,nan,nan,nan tmin,2014,12662,23,6,2069,222924.8585,26394.05484,1.495518096,0.671129179,-0.241127927,-1.305219913,7.61E-06,2.87E-06,-8.33E-06,2.53E-06,-0.00783864,0.001134132 tmin,2014,12663,27,0,0,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999

 

Example data records:  xval_tmax_1980-2014.csv

pppp,year,tileid,nstns3x3,nstns,nstndays,rad90mean,rad90stdv,daymae,pormae,bias,tamean,xlrmean,xlrstdv,ylrmean,ylrstdv,zlrmean,zlrstdv tmax,1980,9402,268,7,2470,70098.68631,3536.915168,1.598939817,0.705968608,-0.152744454,32.04473684,2.16E-05,1.58E-05,8.47E-05,2.29E-05,-0.007316183,0.00049859 tmax,1980,9403,343,2,698,65768.2673,6.410693902,3.53901007,3.336011606,-0.636168483,37.17492837,4.52E-06,6.95E-06,-3.18E-05,1.86E-05,-0.006291728,0.000134242 … tmax,2014,12661,23,1,361,269892.1173,0,1.570174058,0.808686223,0.808686223,5.394459834,nan,nan,nan,nan,nan,nan tmax,2014,12662,23,6,2080,222924.8585,26394.05484,1.581390139,0.61139589,0.066809276,6.296346154,1.34E-05,2.98E-06,-1.39E-05,3.08E-06,-0.006621289,0.001530597 tmax,2014,12663,27,0,0,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999,-9999

 

Example data records:  xval_prcp_1980-2014.csv

pppp,year,tileid,nstns3x3,nstns,nstndays,rad90mean,rad90stdv,daymae,pormae,pormpae,bias,ppmean,xlrmean,xlrstdv,ylrmean,ylrstdv,zlrmean,zlrstdv prcp,1980,9402,293,8,2783,49416.6094,3629.13058,0.367402143,0.14272381,43.16201199,-0.082371536,0.320970176,6.49E-09,3.37E-06,-4.16E-07,6.38E-06,8.10E-05,6.13E-05 prcp,1980,9403,371,2,730,51252.8156,18.26042728,0.177868655,0.150577116,638.1771137,0.00203571,0.124616438,-7.88E-07,5.19E-07,-4.45E-07,9.38E-07,4.07E-05,3.93E-06 … prcp,2014,12661,23,1,356,191164.8662,0,0.261805432,0.096687587,25.53091608,-0.096687587,0.378707865,3.01E-07,0,4.36E-08,0,0.000184898,0 prcp,2014,12662,22,5,1717,161737.6659,26601.34836,0.309491565,0.054964155,18.88746257,0.023351956,0.326435644,3.82E-07,8.93E-07,-7.82E-08,4.97E-07,0.000305412,0.000173946 prcp,2014,12663,24,0,0,-9999,-9999,-9999,-9999,-9999,-9999,nan,-9999,-9999,-9999,-9999,-9999,-9999

 

User’s Notes

• When “nstns” is zero (0), no input weather station data are available within that tile.  All attributes are recorded as nodata (-9999) or "nan".
• When “nstns” have very low values (e.g. 1, 2, or 3) denoting limited input data available for that tile, values for the 3-dimensional regression components may be set to “nan” where the regressions algorithm failed.
• Floating point precision has been carried forward from the Daymet model for all attributes.

The Daymet cross-validation analysis are used to characterize the sensitivity of Daymet model methods to the variation of parameters and to estimate the prediction errors associated with the final selected parameters.  The general cross-validation protocol is to withhold one observation at a time from a sample, generating a prediction error for the withheld case by comparing with the observed value, and repeating over all observations in the sample to generate an average prediction error.  The mean absolute error and bias are the basic error prediction error statistics.  MAE does not exaggerate the influence of outliers as would a root mean square error and provides a more robust parameterization framework.  Both the absolute value and sign of the prediction are considered in the generation of MAE and bias, respectively.

Occurrence of No Data and Not A Number (nan) field values

For tiles that had no input weather stations located within the 2 degree by 2 degree tile processing extent (e.g. nstns = 0), there are no cross-validation data available.  For these tiles, the nodata values are represented with -9999  or "nan" values.  For tiles with very low weather station inputs (e.g. nstns <= 3), it is often the case that the 3-dimensional regression components calculations failed.  In those cases, the regression values are represented with “nan” values in the attribute fields.

Figure 2.  Daymet cross-validation showing the number of station-days evaluated, "nstndays", per 2-degree by 2-degree Daymet tile for 1980 precipitation.

Figure 3.  Daymet cross-validation showing the number of station-days evaluated, "nstndays", per 2-degree by 2-degree Daymet tile for 1980 maximum temperature.

 

Cross-validation Protocol

The Daymet cross-validation summary statistics are used to test the sensitivity of Daymet model methods to the variation of parameters and to estimate the prediction errors associated with the final selected parameters. 

The general cross-validation protocol is to withhold one observation at a time from the sample, generating a prediction error for the withheld case by comparing with the observed value, and repeating over all observations in the sample to generate an average prediction error.  The mean absolute error and bias are the basic error prediction error statistics.  MAE does not exaggerate the influence of outliers as would a root mean square error and provides a more robust parameterization framework.  Both the absolute value and sign of the prediction are considered in the generation of MAE and bias, respectively.

The mean absolute error for single prediction days, or "daymae" is determined as below:

                          

The bias for the single prediction days is determined as below:

                              

The mean absolute error for the period of record predictions, or pormae, is determined as below:

 

Figure 4.  Daymet cross-validation tile-wide summary statistics for 1980 maximum temperature -- mean absolute error for single day predictions ("daymae").

 

Figure 5.  Daymet cross-validation tile-wide summary statistics for 1980 maximum temperature -- mean prediction bias ("bias").

 

Figure 6.  Daymet cross-validation tile-wide summary statistics for 1980 maximum temperature -- mean absolute error for period of record predictions ("pormae”).

 

Data Sources

The Daymet model requires spatially referenced ground observations of daily maximum and minimum temperature and precipitation. These observations have been obtained from a number of sources throughout this current Daymet campaign.

• The ground observations for the United States came from two main sources.
  • The first is the Cooperative Summary of the Day network of weather stations archived and distributed by the National Climate Data Center (NCDC). These data have recently come under the umbrella and are distributed as part of the Global Historical Climatology Network (GHCN)-Daily (Menne et al., 2012) data set.
  • The second source of surface observation data for the United States is the SNOwpack and TELemetry (SNOTEL) data set managed and distributed by the Natural Resources Conservation Service (NRCS). These stations are primarily in high elevation regions in the Western US and Alaska and are principle in maintaining critical snow pack information.
• Canadian surface observations were provided by the Government of Canada (Environment Canada) and through the GHCN-Daily data set.
• The Servicio Meteorológico Nacional provided surface weather observations within Mexico.

Menne, M.J., I. Durre, R.S. Vose, B.E. Gleason, and T.G. Houston, 2012:  An overview of the Global Historical Climatology Network-Daily Database. Journal of Atmospheric and Oceanic Technology, 29, 897-910, doi:10.1175/JTECH-D-11-00103.1

Thornton, P.E., M.M. Thornton, B.W. Mayer, N. Wilhelmi, Y. Wei, R. Devarakonda, and R.B. Cook. 2014. Daymet: Daily Surface Weather Data on a 1-km Grid for North America, Version 2. ORNL DAAC, Oak Ridge, Tennessee, USA. http://dx.doi.org/10.3334/ORNLDAAC/1219

Thornton, P.E., S.W. Running, and M.A. White. 1997. Generating surfaces of daily meteorological variables over large regions of complex terrain. Journal of Hydrology 190: 214 - 251. http://dx.doi.org/10.1016/S0022-1694(96)03128-9

Thornton, P.E., H. Hasenauer, and M.A. White. 2000. Simultaneous estimation of daily solar radiation and humidity from observed temperature and precipitation: An application over complex terrain in Austria. Agricultural and Forest Meteorology 104:255 - 271. http://dx.doi.org/10.1016/S0168-1923(00)00170-2

Thornton, P.E. and S.W. Running. 1999. An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity, and precipitation. Agriculture and Forest Meteorology. 93:211 - 228. http://dx.doi.org/10.1016/S0168-1923(98)00126-9