arXiv subjects

Ryan L. Sriver

Publications and source records attributed to Ryan L. Sriver.

3 recordsLinked to original sources

arXiv2026

Single-point statistical moments of the nonhomogeneous stochastic advection equation in the small correlation length limit

This paper presents the derivation of closed-form expressions of the single-point statistical moments of a solution to a nonhomogeneous stochastic advection equation with a linear relaxation. While analytical solutions exist for homogeneous systems, nonhomogeneous cases have traditionally relied on intensive numerical simulations. Here, we provide an analytical framework for calculating single-point statistical moments by first obtaining the solution to the stochastic advection equation via the method of characteristics, from which the moments are derived. Explicit, closed-form expressions for the first four moments are derived as functions of the characteristic length scale of the stochastic velocity field and the spatial derivatives of time-mean profile of the field. The analytical results are validated against numerical simulations, demonstrating excellent agreement across a range of physical parameters. The resulting theory acts as a generalized ``equation-of-state" style approach for predicting variability and non-Gaussian statistical behavior directly from the macroscopic mean state, providing applicability across transport systems with a wide range of time and length scales, including geology, hydrology, and atmospheric sciences.

physics.flu-dyn↗

arXiv2026

Analytical Model for the Higher Order Moments of Midlatitude Atmospheric Temperature Distributions

Observed distributions of atmospheric temperature are non-Gaussian. Therefore, moments beyond variance are necessary in determining the frequency of extreme temperature events. Here we propose a simple kinematic model for atmospheric mid-latitude temperature variability based on symmetric advection from a non-symmetric background temperature profile. We then use this model to derive analytical expressions for the higher order moments of temperature distributions. Our results show that nonzero skewness and kurtosis arise due to the nonlinearity of the time-mean meridional temperature profile. The analytical model matches an idealized Held-suarez atmospheric model, indicating nonlinearity of time-mean temperature in latitude is the dominant contribution to nonzero skewness and kurtosis in synoptic temperature variations. Model analysis further shows decrease in higher order moments due to climate change come roughly equally from changes in mixing length and changes in the background temperature profiles.

physics.ao-ph↗

arXiv2023

Convolutional GRU Network for Seasonal Prediction of the El Niño-Southern Oscillation

Predicting sea surface temperature (SST) within the El Niño-Southern Oscillation (ENSO) region has been extensively studied due to its significant influence on global temperature and precipitation patterns. Statistical models such as linear inverse model (LIM), analog forecasting (AF), and recurrent neural network (RNN) have been widely used for ENSO prediction, offering flexibility and relatively low computational expense compared to large dynamic models. However, these models have limitations in capturing spatial patterns in SST variability or relying on linear dynamics. Here we present a modified Convolutional Gated Recurrent Unit (ConvGRU) network for the ENSO region spatio-temporal sequence prediction problem, along with the Niño 3.4 index prediction as a down stream task. The proposed ConvGRU network, with an encoder-decoder sequence-to-sequence structure, takes historical SST maps of the Pacific region as input and generates future SST maps for subsequent months within the ENSO region. To evaluate the performance of the ConvGRU network, we trained and tested it using data from multiple large climate models. The results demonstrate that the ConvGRU network significantly improves the predictability of the Niño 3.4 index compared to LIM, AF, and RNN. This improvement is evidenced by extended useful prediction range, higher Pearson correlation, and lower root-mean-square error. The proposed model holds promise for improving our understanding and predicting capabilities of the ENSO phenomenon and can be broadly applicable to other weather and climate prediction scenarios with spatial patterns and teleconnections.

physics.ao-ph↗