Motivated by the increasing energy consumption of supercomputing for weather and climate simulations, we introduce a framework for investigating the bit-level information efficiency of chaotic models. In comparison with previous explorations of inexactness in climate modelling, the proposed and tested information metric has three specific advantages: (i) it requires only a single high-precision time series; (ii) information does not grow indefinitely for decreasing time step; and (iii) information is more sensitive to the dynamics and uncertainties of the model rather than to the implementation details. We demonstrate the notion of bit-level information efficiency in two of Edward Lorenz’s prototypical chaotic models: Lorenz 1963 (L63) and Lorenz 1996 (L96). Although L63 is typically integrated in 64-bit ‘double’ floating point precision, we show that only 16 bits have significant information content, given an initial condition uncertainty of approximately 1% of the size of the attractor. This result is sensitive to the size of the uncertainty but not to the time step of the model. We then apply the metric to the L96 model and find that a 16-bit scaled integer model would suffice given the uncertainty of the unresolved sub-grid-scale dynamics. We then show that, by dedicating computational resources to spatial resolution rather than numeric precision in a field programmable gate array (FPGA), we see up to 28.6% improvement in forecast accuracy, an approximately fivefold reduction in the number of logical computing elements required and an approximately 10-fold reduction in energy consumed by the FPGA, for the L96 model.

This article presents a framework for interpreting the time‐lagged correlation of oceanographic data in terms of physical transport mechanisms. Previous studies have inferred aspects of ocean circulation by correlating fluctuations in temperature and salinity measurements at distant stations. Typically, the time lag of greatest correlation is interpreted as an advective transit time and hence the advective speed of the current. In this article, we relate correlation functions directly to the underlying equations of fluid transport. This is accomplished by expressing the correlation functions in terms of the Green's function of the transport equation. Two types of correlation function are distinguished: field–forcing correlation and field–field correlation. Their unique relationships to the Green's function are illustrated in two idealized models of geophysical transport: a leaky pipe model and an advective–diffusive model. Both models show that the field–forcing correlation function converges to the Green's function as the characteristic (time‐ or length‐) scale of forcing autocorrelation decreases. The leaky pipe model provides an explanation for why advective speeds inferred from time‐lagged correlations are often less than the speed of the main current. The advective–diffusive model reveals a structural bias in the field–field correlation function when used to estimate transit times.

The sea surface temperature (SST) record provides a unique view of the surface ocean at high spatiotemporal resolution and holds useful information on the kinematics underlying the SST variability. To access this information, we develop a new local matrix inversion method that allows us to quantify the evolution of a given SST perturbation with a response function and to estimate velocity, diffusivity, and decay fields associated with it. The matrix inversion makes use of the stochastic climate model paradigm—we assume that SST variations are governed by a linear transport operator and a forcing that has a relatively short autocorrelation time scale compared to that of SST. We show that under these assumptions, the transport operator can be inverted from the covariance matrices of the underlying SST data. The accuracy of the results depends on the length of the time series, and in general the inverted properties depend on the spatial and time resolution of the SST data. Future studies could use the methodology to explore the interannual variability of SST anomalies; to estimate the scale dependency of ocean mixing; and to estimate anomaly propagation, both at the surface and in the interior. The methodology can be easily used with any gridded observations or model output with adequate time and spatial resolution, and it is not restricted to SST. The inversion code is written in Python and distributed as a MicroInverse package through GitHub and the Python Package Index.

Abstract-Accurate forecasts of future climate with numerical models of atmosphere and ocean are of vital importance. However, forecast quality is often limited by the available computational power. This paper investigates the acceleration of a C-grid shallow water model through the use of reduced precision targeting FPGA technology. Using a double-gyre scenario, we show that the mantissa length of variables can be reduced to 14 bits without reducing the accuracy beyond the error inherent in the model. Our reduced precision FPGA implementation runs 5.4 times faster than a double precision FPGA implementation, and 12 times faster than a multi-threaded CPU implementation. Moreover, our reduced precision FPGA implementation uses 39 times less energy than the CPU implementation and can compute a 100x100 grid for the same energy that the CPU implementation would take for a 29x29 grid.

In this article we introduce a method to quantify the transport of sea surface temperature (SST) from SST fluctuations. Previous studies have estimated the advective transport of SST from time-lag correlation of SST anomalies. However this approach does not consider diffusive SST transport or relaxation to atmospheric temperatures. To quantify the transport more completely we use a response function (Greenʼs function) which solves the SST continuity equation for an impulsive forcing. The response function is estimated from SST anomalies using a fluctuation-dissipation approach. An assumption of spatial locality in the linear operator used to produce the response significantly improves the accuracy of the method. Using 100 years of data from a stochastically-forced prototypical SST model, the method estimates the SST transport response function to within 10% error. Decomposing the linear operator into symmetric, anti-symmetric, and divergent operators enables estimates of the modelʼs spatially dependent velocity vector, diffusivity tensor, and relaxation rate which converge at the same rate as the response function.