Comparison of climate time series – Part 5: Multivariate annual cycles

This paper develops a method for determining whether two vector time series originate from a common stochastic process. The stochastic process considered incorporates both serial correlations and multivariate annual cycles. Specifically, the process is modeled as a vector autoregressive model with periodic forcing, referred to as a VARX model (where X stands for exogenous variables). The hypothesis that two VARX models share the same parameters is tested using the likelihood ratio method. The resulting test can be further decomposed into a series of tests to assess whether disparities in the VARX models stem from differences in noise parameters, autoregressive parameters, or annual cycle parameters. A comprehensive procedure for compressing discrepancies between VARX models into a minimal number of components is developed based on discriminant analysis. Using this method, the realism of climate model simulations of monthly mean North Atlantic sea surface temperatures is assessed. As expected, different simulations from the same climate model cannot be distinguished stochastically. Similarly, observations from different periods cannot be distinguished. However, every climate model differs stochastically from observations. Furthermore, each climate model differs stochastically from every other model, except when they originate from the same center. In essence, each climate model possesses a distinct fingerprint that sets it apart stochastically from both observations and models developed by other research centers. The primary factor contributing to these differences is the difference in annual cycles. The difference in annual cycles is often dominated by a single component, which can be extracted and illustrated using discriminant analysis.</p

Understanding the role of ocean dynamics in multi-year predictability

Recent studies have questioned the degree to which interactive ocean circulations are important for making useful predictions of the next decade. We investigate this question by identifying the most predictable patterns of global sea surface temperature in coupled atmosphere-ocean models. Remarkably, the most predictable patterns in models that include interactive ocean circulation are very similar to predictable patterns in models without interactive ocean circulations (i.e., models whose ocean is represented by a 50m-deep slab ocean mixed layer with no interactive currents). In addition, these patterns can be skillfully predicted in observational data using empirical models trained on simulations from either type of climate model. These results suggest that interactive ocean circulation is not essential for the spatial structure of multi-year predictability previously identified in coupled models and observations. However, the time scale of predictability, and the relation of these predictable patterns to other climate variables, is sensitive to whether the model supports interactive ocean circulations or not, especially over the North Atlantic. To understand this sensitivity, a hierarchy of ocean models coupled to stochastic atmospheric models are examined, ranging from slab mixed-layer models to a stochastically forced Stommel box model. The box model is able to reproduce many statistical characteristics of sea surface temperatures that are relevant to predictability. This model is then used to suggest hypotheses that can be tested about the role of ocean dynamics in multi-year predictability.Non UBCUnreviewedAuthor affiliation: George Mason U.Facult

Optimal Detection of Decadal Predictability

This document is a property certificate form for the subject contract

Predictability of Seasonal Precipitation Using Joint Probabilities

This paper tests whether seasonal mean precipitation is predictable using a new method that estimates and analyzes joint probabilities. The new estimation method is to partition the globe into boxes, pool all data within the box to estimate a single joint probability of precipitation for two consecutive seasons, and then apply the resulting joint probability to individual pixels in the box. Pooling data in this way allows joint probabilities to be estimated in relatively small sample sizes, but assumes that the transition probabilities of pixels in a box are homogeneous and stationary. Joint probabilities are estimated from the Global Precipitation Climatology Project data set in 21 land boxes and 5 ocean boxes during the period 1979-2008. The state of precipitation is specified by dry, wet, or normal terciles of the local climatological distribution. Predictability is quantified by mutual information, which is a fundamental measure of predictability that allows for nonlinear dependencies, and tested using bootstrap methods. Predictability was verified by constructing probabilistic and quantitative forecasts directly from the transition probabilities and showing that they have superior cross-validated skill than forecasts based on climatology, persistence, or random selection. Spring was found to be the most predictable season whereas summer was the least predictable season. Analysis of joint probabilities reveals that though the probabilities are close to climatology, the predictability of precipitation arises from a slight tendency of the state to persist from one season to the next, or if a transition occurs then it is more often from one extreme to normal than from one extreme to the other

Introducing Water Budget Constraint To Improve Land Data Assimilation Performance

A weak constraint is introduced in ensemble Kalman filters to reduce the water budget imbalance that occurs in land data assimilation. Two versions of the weakly constrained filter, called the weakly constrained ensemble Kalman filter (WCEnKF) and the weakly constrained ensemble transform Kalman filter (WCETKF), are proposed. The strength of the weak constraint is adaptive in the sense that it depends on the statistical characteristics of the forecast ensemble. The resulting filters are applied to assimilate synthetic observations generated by the Noah land surface model over the Red Arkansas River basin. The data assimilation experiments demonstrate that, for all tested scenarios, the constrained filters produce analyses with nearly the same accuracy as unconstrained filters, but with much smaller water balance residuals than un-constrained filters

Reducing water imbalance in land data assimilation: Ensemble filtering without perturbed observations

It is well known that the ensemble Kalman filter (EnKF) requires updating each ensemble member with perturbed observations in order to produce the proper analysis-error covariances. While increased accuracy in a mean square sense may be preferable in many applications, less accuracy might be preferable in other applications, especially if the variables being assimilated obey certain conservation laws. In land data assimilation, for instance, the update in soil moisture often produces a water balance residual, in the sense that the input water is not equal to output water. This study shows that suppressing the perturbation of observations in the EnKF and in the weakly constrained ensemble Kalman filter significantly improves the water balance residuals without significantly increasing the state errors

Improving land data assimilation performance with a water budget constraint

A weak constraint is introduced in ensemble Kalman filters to reduce the water budget imbalance that occurs in land data assimilation. Two versions of the weakly constrained filter, called the weakly constrained ensemble Kalman filter (WCEnKF) and the weakly constrained ensemble transform Kalman filter (WCETKF), are proposed. The strength of the weak constraint is adaptive in the sense that it depends on the statistical characteristics of the forecast ensemble. The resulting filters are applied to assimilate synthetic observations generated by the Noah land surface model over the Red Arkansas River basin. The data assimilation experiments demonstrate that, for all tested scenarios, the constrained filters produce analyses with nearly the same accuracy as unconstrained filters, but with much smaller water balance residuals than unconstrained filters

Response of the Madden Julian Oscillation and Tropical Atmosphere to changes in Oceanic Mixed Layer Depth Over the Indian Ocean

Abstract The Madden-Julian Oscillation (MJO) is a component of tropical variability that influences high-impact events such as hurricane activity and Asian monsoons on intraseasonal (2-8 weeks) time scales. However, the atmosphere-ocean dynamics responsible for the MJO are highly debated. To gain insight into MJO-Indian Ocean dynamics, we conduct climate model experiments where the ocean is replaced by a motionless slab whose thickness, called the mixed-layer-depth (MLD), varies in space but not in time. Changes in the MLD and ocean heat convergence over the Indian Ocean have no discernible impact on MJO propagation, predictability, or variability within the Community Earth System Model (CESM) version 1.2.1. This suggests that ocean dynamics may not be critical to the MJO over the Indian Ocean in this dynamical model (CAM5 coupled to motionless slab). To diagnose changes in intraseasonal variability beyond the MJO, a discriminant analysis technique is used to optimize differences in variability between experiments. This analysis reveals that differences caused by changing Indian Ocean MLDwere restricted mostly to local surface fluxes and could be explained by simple energy balance physics. Despite modeling adjustments intended to preserve the climate, the control slab has a warmer climate than the fully coupled model. The resulting changes in the mean climate are consistent with changes theoretically expected from global warming, particularly the ”wet-gets-wetter” mechanism

Assessing the fidelity of predictability estimates

Predictability is an intrinsic limit of the climate system due to uncertainty in initial conditions and the chaotic nature of the atmosphere. Estimates of predictability together with calculations of current prediction skill are used to define the gaps in our prediction capabilities, inform future model developments, and indicate to stakeholders the potential for making forecasts that can inform their decisions. The true predictability of the climate system is not known and must be estimated, typically using a perfect model estimate from an ensemble prediction system. However, different prediction systems can give different estimates of predictability. Can we determine which estimate of predictability is most representative of the true predictability of the climate system? We test three metrics as potential indicators of the fidelity of predictability estimates in an idealized framework-the spread-error relationship, autocorrelation and skill. Using the North American multi-model ensemble re-forecast database, we quantify whether these metrics accurately indicate a model's ability to properly estimate predictability. It is found that none of these metrics is a robust measure for determining whether a predictability estimate is realistic for El Nino-Southern oscillation events. For temperature and precipitation over land, errors in the spread-error ratio are related to errors in estimating predictability at the shortest lead-times, while skill is not related to predictability errors. The relationship between errors in the autocorrelation and errors in estimating predictability varies by lead-time and region