Climate and Land-Use Controls on Surface Water Diversions in the Central Valley, California

California’s Central Valley (CV) is one of the most productive agricultural regions in the world, enabled by the conjunctive use of surface water and groundwater. We investigated variations in the CV’s managed surface water diversions relative to climate variability. Using a historical record (1979−2010) of diversions from 531 sites, we found diversions are largest in the wetter Sacramento basin to the north, but most variable in the drier Tulare basin to the south. A rotated empirical orthogonal function (REOF) analysis finds 72% of the variance of diversions is captured by the first three REOFs. The leading REOF (35% of variance) exhibited strong positive loadings in the Tulare basin, and the corresponding principal component time-series (RPC1) was strongly correlated (ρ > 0.9) with contemporaneous hydrologic variability. This pattern indicates larger than average diversions in the south, with neutral or slightly less than average diversions to the north during wet years, with the opposite true for dry years. The second and third REOFs (20% and 17% of variance, respectively), were strongest in the Sacramento basin and San Francisco Bay−Delta. RPC2 and RPC3 were associated with variations in agricultural- and municipal-bound diversions, respectively. RPC2 and RPC3 were also moderately correlated with 7-year cumulative precipitation based on lagged correlation analysis, indicating that diversions in the north and central portions of the CV respond to longer-term hydrologic variations. The results illustrate a dichotomy of regimes wherein diversions in the more arid Tulare are governed by year-to-year hydrologic variability, while those in wetter northern basins reflect land-use patterns and low-frequency hydrologic variations

Stability of jammed packings I: the rigidity length scale

In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low frequency vibrational properties of jammed amorphous sphere packings can be understood in terms of a length scale, called l*, that diverges as the system becomes marginally unstable. Despite the tremendous success of this theory, it has been difficult to connect the counting argument that defines l* to other length scales that diverge near the jamming transition. We present an alternate derivation of l* based on the onset of rigidity. This phenomenological approach reveals the physical mechanism underlying the length scale and is relevant to a range of systems for which the original argument breaks down. It also allows us to present the first direct numerical measurement of l*.Comment: 8 pages, 5 figure

Finite-Size Scaling at the Jamming Transition

We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a non-trivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both 2 and 3 dimensions, indicating an upper critical dimension of 2.Comment: 5 pages, 3 figure