Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Do laws influence the cost of real estate brokerage services? A state fixed effects approach

A FTC-DOJ study argues that state laws and regulations may inhibit the unbundling of real estate brokerage services in response to new technology. Our data show that 18 states have changed laws in ways that promote unbundling since 2000. We model brokerage costs as measured by number of agents in a state-level annual panel vector autoregressive framework, a novel way of analyzing wasteful competition. Our findings support a positive relationship between brokerage costs and lagged house price and transactions. We find that change in full-service brokers responds negatively (by well over two percentage points per year) to legal changes facilitating unbundling