Abstract. Solar energetic particle (SEP) event onset is analyzed using simulated data. A large number of simulations using different coronal and interplanetary (IP) scattering conditions are performed. Protons in the energy range of 0.13-57 MeV are considered. The simulated data are analyzed employing a velocity dispersion analysis (VDA) to the proton-flux onset times in 16 energy channels. As a result of the analysis, the apparent coronal release time, t 0 , and the apparent IP path length, s, of the first-observed particles are obtained. It is shown that typical IP scattering conditions, i.e., 1-GV radial mean free path of Λ rr = 0.1-1 AU with a ∝P 1/3 rigidity dependence, lead to apparent path lengths of s ∼ 1-2 AU, consistent with observations. Thus, SEP events with s ∼ 2 AU can simply be explained as a result of IP scattering. Models with coronal mean free paths small enough to enable proton acceleration to high energies in quasi-parallel shocks close to the Sun are shown to yield VDA results in agreement with observations, at least with Λ rr > ∼ 0.3. As a result of IP scattering, the inaccuracy of the release times is tens of minutes in events with s > ∼ 2 AU, which may prevent accurate timing of particle release using the VDA method in such events. Low contrast between the time-of-maximum intensity of the studied SEP event and the pre-event background intensity and/or a large difference between the forms of the respective energy spectra may also lead to errors in derived onset times. Best timing results (with errors typically less than 10 min) are obtained for large IP mean free paths, Λ rr > ∼ 0.3 AU (typically resulting in small values of s < ∼ 1.5 AU), and large intensity contrast between the SEP event and the pre-event background.

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We explore the optimal regulation of forest carbon and albedo for climate change mitigation. We develop a partial equilibrium market-level model with socially optimal carbon and albedo pricing and characterize optimal land allocation and harvests. We numerically assess the policy's market-level impacts on land allocation, harvests, and climate forcing, and evaluate how parameter choices (albedo strength, productivity of forest land, and carbon and albedo prices) affect the outcomes. Carbon pricing alone leads to an overprovision of climate benefits at the expense of food and timber production. Complementing the policy with albedo pricing reduces these welfare losses.

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