Bioclimatic indices for use in studies of ecosystem function, species distribution, and vegetation dynamics under changing climate scenarios depend on estimates of surface fluxes and other quantities, such as radiation, evapotranspiration and soil moisture, for which direct observations are sparse. These quantities can be derived indirectly from meteorological variables, such as near-surface air temperature, precipitation and cloudiness. Here we present a consolidated set of simple process-led algorithms for simulating habitats (SPLASH) allowing robust approximations of key quantities at ecologically relevant timescales. We specify equations, derivations, simplifications, and assumptions for the estimation of daily and monthly quantities of top-of-the-atmosphere solar radiation, net surface radiation, photosynthetic photon flux density, evapotranspiration (potential, equilibrium, and actual), condensation, soil moisture, and runoff, based on analysis of their relationship to fundamental climatic drivers. The climatic drivers include a minimum of three meteorological inputs: precipitation, air temperature, and fraction of bright sunshine hours. Indices, such as the moisture index, the climatic water deficit, and the Priestley–Taylor coefficient, are also defined. The SPLASH code is transcribed in C++, FORTRAN, Python, and R. A total of 1 year of results are presented at the local and global scales to exemplify the spatiotemporal patterns of daily and monthly model outputs along with comparisons to other model results.

Despite the existence of dense networks of meteorological monitoring stations around the world, plant ecophysiology and biogeography suffer from a lack of globally distributed observational data, especially those central to the estimation of ecosystem-level photosynthesis, including photosynthetic photon flux density and soil moisture. To overcome this deficiency, we present simple process-led algorithms for simulating habitats (SPLASH) for generating driving datasets for ecological and land-surface models (e.g., monthly carbon and water fluxes or seasonal plant functional trait distributions) from more readily available meteorological observations.

SPLASH is a continuation of the STASH (static shell) model, which was
originally developed for modeling the climatic controls on plant species
distributions at a regional scale

Despite their long history of use, no single publication documents the algorithms of the STASH model. This work aims to fill that gap to allow for the continued development and use of these algorithms. As the new incarnation of STASH, SPLASH provides the same physically based soil-moisture accounting scheme with updated and corrected analytical expressions for the calculation of daily radiation, evapotranspiration, and soil moisture. Included in this documentation are the equation derivations, variable definitions, and information regarding model assumptions and limitations. One notable improvement is that we have discontinued the approximation of constant angular velocity in the orbit of Earth around the Sun. This version is thus suitable for palaeoclimate applications, whereby orbital precession (as well as changes in obliquity and eccentricity) influences the seasonal distribution of insolation. SPLASH also includes explicit consideration of elevation effects on biophysical quantities.

Key model outputs include daily insolation (incoming solar radiation at the
top of the atmosphere) and net surface radiation (

Input values of latitude,

We present SPLASH comprehensively re-coded in a modular framework to be
readable, understandable, and reproducible. To facilitate varied application
requirements (including computational speed), four versions of the code (C++,
FORTRAN, Python, and R) are available in an online repository (see
Sect.

In line with the intention of the original STASH algorithms, we also present bioclimatic indices at the monthly and annual timescales to exemplify the analytical applications of the SPLASH model outputs.

The implementation of the soil-moisture accounting scheme follows the steps
outlined by

To solve the simple “bucket model” represented by Eq. (

The calculation of

Nomenclature.

Constants and Standard Values.

The distance factor,

The last term,

While the three orbital parameters (i.e.,

The daily top-of-the-atmosphere solar radiation,

The sunset angle can be calculated as the hour angle when the solar radiation
flux reaches the horizon (i.e., when

The net surface radiation,

The calculation of

Here,

To account for the occurrences when the net surface radiation flux
does not cross the zero datum,

Complementary to

Figure

Example of the net radiation flux curve between the hours of solar
noon (i.e.,

The daily photosynthetically active radiation in units of photon flux
density,

The daily condensation,

The barometric formula may be used to estimate the atmospheric pressure,

The evaporative supply rate,

The evaporative demand rate,

Daily equilibrium evapotranspiration,

The daily demand, which is equal to the daily potential evapotranspiration,

The calculation of daily actual evapotranspiration,

The analytical solution to

Figure

Example of actual evapotranspiration curve between the hours of
solar noon (i.e.,

The calculation of daily runoff, RO, is based on the excess of daily soil
moisture without runoff compared to the holding capacity,

With analytical expressions for

The calculation of RO in Eq. (

One application of the SPLASH model is for the estimation of the surface fluxes required
for the calculation of bioclimatic indices. Typically described at longer
timescales (e.g., monthly or annually), the daily SPLASH fluxes can be
integrated to monthly and annual totals:

The following sections describe three common bioclimatic indices.

There exists a long history that includes several variants of the moisture
index, MI, also commonly referred to as the aridity index, AI, or
moisture ratio, MR

The climatic water deficit,

The Priestley–Taylor coefficient,

The methodology described in Sect.

The SPLASH model was run at six locations across North America (see
Fig.

Map of Köppen–Geiger climate regions across North America

The first year of the simulation (i.e., 1991) was iterated (approximately
twice) until the daily soil moisture, initialized at zero, reached
equilibrium, after which the model was spun-up for eight years (i.e.,
1992–1999). The results, shown in Figs.

Daily simulations of net radiation,

Figure

Figure

Figure

Figure

Figure

Figure

Monthly SPLASH results of evapotranspiration,

Figure

Figure

The hot arid desert region presents a more extreme case as shown in
Fig.

In contrast, at the equatorial monsoonal site, shown in
Fig.

Similar to the hot arid desert, at the high elevation of the cold arid
steppe, shown in Fig.

For the global simulation, 0.5

Global mean net downward surface radiation flux (

The SPLASH simulations were driven by the data described above, one pixel at a time, starting each pixel with an empty bucket and terminating when a steady state of soil moisture was reached between the first and last day of the year. Following the spin-up to equilibrate the soil moisture, the model was driven once again to produce daily simulations of net radiation and soil moisture.

Figure

Overall, the SPLASH model produces a reasonable simulation of the latitudinal
gradients and seasonal shifts of net surface radiation flux. The differences
between SPLASH and CERES EBAF net downward radiative flux are highlighted in
Fig.

Figure

Global mean relative soil moisture (

Overall, the SPLASH model simulates soil-moisture patterns similar to the
NCEP CPC model results. The differences between the SPLASH and NCEP CPC model
results are highlighted in Fig.

The results presented in Sect.

While the methodology presented in Sect.

Over the years, a common misconception has developed regarding the
calculation of daily actual evapotranspiration (as defined by

The code, in four programming languages (C++, FORTRAN, Python, and R), is
available on an online repository under the GNU Lesser General Public License
(

For the C++ version, the code was successfully compiled and executed using the GNU C++ compiler (g++ v.4.8.2) provided by the GNU Compiler Collection (Free Software Foundation, Inc., 2016). It utilizes the C numerics library (cmath), input/output operations library (cstdio), and the standard general utilities library (cstdlib), and it references the vector container and string type.

For the FORTRAN version, the code was successfully compiled and executed using the PGI Fortran compiler (pgf95 v.16.1-0) provided by The Portland Group – PGI Compilers and Groups (NVIDIA Corporation, 2016) and the GNU Fortran compiler (gfortran v.4.8.4) provided by the GNU Compiler Collection (Free Software Foundation, Inc., 2016).

For the Python version, the code was successfully compiled and executed using Python 2.7 and Python 3.5 interpreters (Python Software Foundation, 2016). It requires the installation of third-party packages, including NumPy (v.1.10.4 by NumPy Developers, 2016) and SciPy (v.0.17.0 by SciPy Developers, 2016) and utilizes the basic date- and time-type (datetime), logging facility (logging), Unix-style pathname pattern extension (glob), and miscellaneous operating system interface (os) modules.

For the R version, the code was successfully compiled and executed using R-3.2.3 “Wooden Christmas-Tree” (The R Foundation for Statistical Computing, 2015).

The four variables used to calculate the water-to-energy conversion factor,

The temperature-dependent equation for the slope of the saturation vapor
pressure–temperature curve,

The temperature-dependent equation for the latent heat of vaporization,

The temperature and pressure dependence of the density of water,

The equation for

The coefficients for

Coefficients of

The temperature and pressure dependence of the psychrometric constant,

I. C. Prentice, M. T. Sykes, and W. Cramer developed the original model theory and methods. A. V. Gallego-Sala, B. J. Evans, H. Wang, and T. W. Davis contributed to model improvements. R. T. Thomas, R. J. Whitley, B. D. Stocker, and T. W. Davis transcribed the new model code and ran simulations. The paper was prepared with contributions from all authors.

The authors declare that they have no conflict of interest.

This work was primarily funded by Imperial College London as a part of the
AXA Chair Programme on Biosphere and Climate Impacts. It is a contribution to
the Imperial College initiative on Grand Challenges in Ecosystems and the
Environment, and the Ecosystem Modelling And Scaling Infrastructure (eMAST)
facility of the Australian Terrestrial Ecosystem Research Network (TERN).
TERN is supported by the Australian Government through the National
Collaborative Research Infrastructure Strategy (NCRIS). BDS funded by the
Swiss National Science Foundation (SNF) and the European Commission's 7th
Framework Programme, under grant agreement number 282672, EMBRACE project. WC
contributes to the Labex OT-Med (no. ANR-11-LABX-0061) funded by the French
government through the A