Climate

The baseline dataset contains 36 primary monthly climate variables. For applications in ecology, we provide many additional biologically relevant climate variables. Many of these additional variables need to be calculated using daily climate data, which are not available in ClimateNA. We estimated these variables based on empirical or mechanistic relationships between these variables calculated using daily observations and monthly climate variables from weather stations across the entire North America. We called these variables “derived climate variables”. Some of them have been developed in previous studies for smaller regions at the annual scale [12 (link), 13 ]. In this study, we developed the derived climate variables at monthly scale, then summed up to seasonal and annual scales. The steps included: 1) calculating derived climate variables for each month (e.g., degree days) from daily weather station data; 2) building relationships (or functions) between the derived climate variables and observed (or calculated) monthly climate variables; 3) applying the functions in ClimateNA to estimate derived climate variables using monthly climate variables generated by ClimateNA.
Observed daily climate data were obtained from 4,891 weather stations in North America from the Daily Global Historical Climatology Network (http://www.ncdc.noaa.gov). The distribution of the weather stations is shown in Fig 1. Due to the wide range of variation in climate in North America, no single linear, polynomial or nonlinear function was found to adequately reflect the relationships between degree-days and monthly climate variables. We therefore applied piecewise functions, which combine a linear function and a nonlinear function, to model these relationships between various forms of monthly degree-day variables and monthly temperatures. The degree-day variables include degree-days below 0°C (DD < 0), degree-days above 5°C (DD>5), degree-days below 18°C (DD<18) and degree-days above 18°C (DD>18). The general form of the piecewise functions of all degree-days (DD_m) is:
${DD}_m=\{\begin{array}{l}if{T}_m>k,\frac{a}{1+e^{-\left(\frac{T_m-T_0}{b}\right)}}\\ if{T}_m\le k,c+\beta T_m\end{array}$
where, T_m is the monthly mean temperature for the m month; k, a, b, T₀, c and β are the six parameters to be optimized.
For number of frost-free days (NFFD) and precipitation as snow (PAS), a sigmoid function was used to model the relationship between these monthly variables and monthly temperatures:
${NFFD}_m(orPAS)=\frac{a}{1+e^{-\left(\frac{T_m-T_0}{b}\right)}}$
where, T_m is the monthly minimum temperature for the m month; a, b and T₀ are the three parameters to be optimized.
To estimate the length of the frost-free period (FFP), the beginning the frost-free period (bFFP) and the end of the frost-free period (eFFP), we used the same polynomial functions as ClimateWNA [12 (link)] for bFFP and eFFP while the parameters were estimated based on observations from all weather stations in North America.
For extreme minimum temperature (EMT) and extreme maximum temperature (EXT) expected over a 30-year period, polynomial functions were used as follows:
$EMT=a+bTmin01+{cTmin01}^2+{dTmin12}^2+{eTD}^2$
$EXT=a+bTmax07+{cTmax07}^2+dTmax08+{eTmax08}^2+fTD$
where, a, b, c, d, e and f are the parameters to be optimized; Tmin01 and Tmin12 are monthly minimum temperature for January and December; Tmax07 and Tmax08 are monthly maximum temperature for July and August, respectively; and TD is continentality (the difference between the mean temperatures of the warmest and coldest months).
Monthly average relative humidity (RH %) is calculated from the monthly maximum and minimum air temperature following [21 ]. Monthly reference evaporation (Eref_m mm) is calculated from the monthly air temperature using the Hargreaves 1985 method [12 (link), 22 (link)]. It was evaluated against the ASCE Standardized Reference Evapotranspiration (ASCE EWRI 2005). If the monthly average air temperature is less than 0°C then Eref_m = 0. The monthly climatic moisture deficit (CMD_m mm) is 0 if Eref_m< P_m, where P_m is the monthly precipitation (mm), otherwise
${CMD}_m={Eref}_m-P_m$