Potential increase in floods in California’s Sierra Nevada under future climate projections

Abstract

California’s mountainous topography, exposure to occasional heavily moisture-laden storm systems, and varied communities and infrastructures in low lying areas make it highly vulnerable to floods. An important question facing the state—in terms of protecting the public and formulating water management responses to climate change—is “how might future climate changes affect flood characteristics in California?” To help address this, we simulate floods on the western slopes of the Sierra Nevada Mountains, the state’s primary catchment, based on downscaled daily precipitation and temperature projections from three General Circulation Models (GCMs). These climate projections are fed into the Variable Infiltration Capacity (VIC) hydrologic model, and the VIC-simulated streamflows and hydrologic conditions, from historical and from projected climate change runs, allow us to evaluate possible changes in annual maximum 3-day flood magnitudes and frequencies of floods. By the end of the 21st Century, all projections yield larger-than-historical floods, for both the Northern Sierra Nevada (NSN) and for the Southern Sierra Nevada (SSN). The increases in flood magnitude are statistically significant (at p <= 0.01) for all the three GCMs in the period 2051–2099. The frequency of flood events above selected historical thresholds also increases under projections from CNRM CM3 and NCAR PCM1 climate models, while under the third scenario, GFDL CM2.1, frequencies remain constant or decline slightly, owing to an overall drying trend. These increases appear to derive jointly from increases in heavy precipitation amount, storm frequencies, and days with more precipitation falling as rain and less as snow. Increases in antecedent winter soil moisture also play a role in some areas. Thus, a complex, as-yet unpredictable interplay of several different climatic influences threatens to cause increased flood hazards in California’s complex western Sierra landscapes.

Appendix: Test of significance for flood magnitude

For two regression-based estimates of log-transformed flood magnitudes with recurrence interval of r years, f₁ ~ N(m₁,s₁) (e.g., from simulated historical annual-flood series) and f₂ ~ N(m₂,s₂) (from simulated future annual-flood series), the probability that f₂ > f₁ is

$$ \int_{{ - \infty }}^{{ + \infty }} {\frac{1}{{\sqrt {{2\pi {s_2}}} }}{e^{{ - \frac{1}{2}\left( {\frac{{x - {m_2}}}{{{s_2}}}} \right)2}}}} \int_{{ - \infty }}^x {\frac{1}{{\sqrt {{2\pi {s_1}}} }}{e^{{ - \frac{1}{2}\left( {\frac{{y - {m_1}}}{{{s_1}}}} \right)2}}}dydx} $$

or, after rearranging the problem in a more readily generalized form,

$$ \int_{{ - \infty }}^{{ + \infty }} {\frac{{{s_1}}}{{\sqrt {{2\pi {s_2}}} }}{e^{{ - \frac{1}{2}{{\left( {x - \left( {{m_2} - {m_1}} \right)/{s_1}} \right)}^2}s_1^2/s_2^2}}}} \left[ {\frac{1}{{\sqrt {{2\pi }} }}\int_{{ - \infty }}^x {{e^{{ - \frac{{{y^2}}}{2}}}}} dy} \right]dx $$

Upon numerical integration of this distribution for various values of (s₂/s₁) and (m₂-m₁)/s₁, and then identification of the values μ_s2/s1 of (m₂-m₁)/s₁ corresponding to Prob(f₂ > f₁) = 0.95 or 0.99 as a function of s₂/s₁ (Fig. 8), the null hypothesis that f₂ <= f₁ can be rejected (at p = 0.05 and p = 0.01 levels) when (m₂-m₁)/s₁ > μ_s2/s1.

Fig. 8

Values μ = (m₂−m₁)/s₁ as a function of s₂/s₁ where the probability that f₁ ~ N(m₁,s₁) is greater than f₂ ~ N(m₂,s₂) is 0.95 or 0.99