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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. [ABSTRACT FROM AUTHOR]

As the climate changes, it is important to understand the effects on the environment. Changes in wildland fire risk are an important example. A stochastic lattice-based wildland fire spread model was proposed by Boychuk et al. (2007), followed by a more realistic variant (Braun andWoolford, 2013). Fitting such a model to data from remotely sensed images could be used to provide accurate fire spread risk maps, but an intermediate step on the path to that goal is to verify the model on data collected under experimentally controlled conditions. This paper presents the analysis of data from small-scale experimental fires that were digitally video-recorded. Data extraction and processing methods and issues are discussed, along with an estimation methodology that uses differential equations for the moments of certain statistics that can be derived from a sequential set of photographs from a fire. The interaction between model variability and raster resolution is discussed and an argument for partial validation of the model is provided. Visual diagnostics show that the model is doing well at capturing the distribution of key statistics recorded during observed fires. [ABSTRACT FROM AUTHOR]

The 2014-2018 drought over South Africa's winter rainfall zone (WRZ) created a critical water crisis which highlighted the region's drought and climate change vulnerability. Consequently, it is imperative to better understand the climatic characteristics of the drought in order to inform regional adaptation to projected climate change. In this paper we investigate the spatio-temporal patterns of drought intensity and the recent rainfall trends, focusing on assessing the consistency of the prevailing conceptual model of drought drivers with observed patterns. For this we use the new spatial subdivision for the region encompassing the WRZ introduced in our companion paper (Conradie et al., 2022). Compared to previous droughts since 1979, the 2014-2018 drought in the WRZ core was characterised by a markedly lower frequency of very wet days (exceeding the climatological 99.5th percentile daily rainfall -- including dry days) and of wet months (SPI1 > 0:5), a sub-seasonal attribute not previously reported. There was considerable variability in the spatial footprint of the drought. Short-term drought began in the south-western core WRZ in spring 2014. The peak intensity gradually spread north-eastward, although a spatially near-uniform peak is seen during mid-2017. The overall drought intensity for the 2015--2017 period transitions radially from most severe in the WRZ core to least severe in the surroundings. During 2014 and 2015, the drought was most severe at those stations receiving the largest proportion of their rainfall from westerly and north-westerly winds; by 2018, those stations receiving the most rain from the south and south-east were most severely impacted. This indicates an evolving set of dynamic drivers associated with distinct rain-bearing synoptic flows. No evidence is found to support the suggestion that the drought was more severe in the mountain catchments of Cape Town's major supply reservoirs than elsewhere in the core nor that rain day frequency trends since 1979 are more negative in this subdomain. Rainfall and rain day trend rates also exhibit some connections to the spatial seasonality structure of the WRZ, although this is weaker than for drought intensity. Caution should be applied in assessing South African rain day trends given their high sensitivity to observed data shortcomings. Our findings suggest an important role for zonally asymmetric dynamics in the region's drought evolution. This analysis demonstrates the utility of the spatial subdivisions proposed in the companion paper by highlighting spatial structure in drought intensity evolution linked to rainfall dynamics. [ABSTRACT FROM AUTHOR]

The goal of the attribution of individual events is to estimate whether and to what extent the probability of an extreme climate event evolves when external conditions (e.g., due to anthropogenic forcings) change. Many types of climate extremes are linked to the variability of the large-scale atmospheric circulation. It is hence essential to decipher the roles of atmospheric variability and increasing mean temperature in the change of probabilities of extremes. It is also crucial to define a background state (or counterfactual) to which recent observations are compared. In this paper we present a statistical framework to determine the dynamical (linked to the atmospheric circulation) and thermodynamical (linked to slow forcings) contributions to the probability of extreme climate events. We illustrate this methodology on a record precipitation event that hit southern United Kingdom in January 2014. We compare possibilities for the creation of two states (or "worlds") in which probability change is determined. These two worlds are defined in a large ensemble of atmospheric model simulations (Weather@Home factual and counterfactual simulations) and separate periods (new: 1951-2014, and old: 1900- 1950) in reanalyses and observations. We discuss how the atmospheric circulation conditioning can affect the interpretation of extreme event attribution. We eventually show the qualitative coherence of results between the choice of worlds (factual/counterfactual vs. new/old). [ABSTRACT FROM AUTHOR]

Recent heatwaves such as the 2021 Pacific Northwest heatwave have shattered temperature records across the globe. The likelihood of experiencing extreme temperature events today is already strongly increased by anthropogenic climate change, but it remains challenging to determine to what degree prevalent atmospheric and land surface conditions aggravated the intensity of a specific heatwave event. Quantifying the respective contributions is therefore paramount for process understanding but also for attribution and future projection statements conditional on the state of atmospheric circulation or land surface conditions. We here propose and evaluate a statistical framework based on extreme value theory, which enables us to learn the respective statistical relationship between extreme temperature and process variables in initial-condition large ensemble climate model simulations. Elements of statistical learning theory are implemented in order to integrate the effect of the governing regional circulation pattern. The learned statistical models can be applied to reanalysis data to quantify the relevance of physical process variables in observed heatwave events. The method also allows us to make conditional attribution statements and answer "what if" questions. For instance, how much would a heatwave intensify given the same dynamic conditions but at a different warming level? How much additional warming is needed for the same heatwave intensity to occur under average circulation conditions? Changes in the exceedance probability under varying large- and regional-scale conditions can also be assessed. We show that each additional degree of global warming increases the 7 d maximum temperature for the Pacific Northwest area by almost 2 °C, and likewise, we quantify the direct effect of anti-cyclonic conditions on heatwave intensity. Based on this, we find that the combined global warming and circulation effect of at least 2:9 °C accounts for 60 %-80% of the 2021 excess event intensity relative to average pre-industrial heatwave conditions. [ABSTRACT FROM AUTHOR]

General circulation model (GCM) outputs are a primary source of information for climate change impact assessments. However, raw GCM data rarely are used directly for regional-scale impact assessments as they frequently contain systematic error or bias. In this article, we propose a novel extension to standard quantile mapping that allows for a continuous seasonal change in bias magnitude using localized regression. Our primary goal is to examine the efficacy of this tool in the context of larger statistical downscaling efforts on the tropical island of Puerto Rico, where localized downscaling can be particularly challenging. Along the way, we utilize a multivariate infilling algorithm to estimate missing data within an incomplete climate data network spanning Puerto Rico. Next, we apply a combination of multivariate downscaling methods to generate in situ climate projections at 23 locations across Puerto Rico from three general circulation models in two carbon emission scenarios: RCP4.5 and RCP8.5. Finally, our bias-correction methods are applied to these downscaled GCM climate projections. These bias-correction methods allow GCM bias to vary as a function of a user-defined season (here, Julian day). Bias is estimated using a continuous curve rather than a moving window or monthly breaks. Results from the selected ensemble agree that Puerto Rico will continue to warm through the coming century. Under the RCP4.5 forcing scenario, our methods indicate that the dry season will have increased rainfall, while the early and late rainfall seasons will likely have a decline in total rainfall. Our methods applied to the RCP8.5 forcing scenario favor a wetter climate for Puerto Rico, driven by an increase in the frequency of highmagnitude rainfall events during Puerto Rico's early rainfall season (April to July) as well as its late rainfall season (August to November). [ABSTRACT FROM AUTHOR]

A renewed focus on southern Africa's winter rainfall zone (WRZ) following the Day Zero drought and water crisis has not shed much light on the spatial patterns of its rainfall variability and climatological seasonality. However, such understanding remains essential in studying past and potential future climate changes. Using a dense station network covering the region encompassing the WRZ, we study spatial heterogeneity in rainfall seasonality and temporal variability. These spatial patterns are compared to those of rainfall occurring under each ERA5 synoptic-scale wind direction sector. A well-defined "true" WRZ is identified with strong spatial coherence between temporal variability and seasonality not previously reported. The true WRZ is composed of a core and periphery beyond which lies a transition zone to the surrounding year-round rainfall zone (YRZ) and late summer rainfall zone. In places, this transition is highly complex, including where the YRZ extends much further westward along the southern mountains than has previously been reported. The core receives around 80% of its rainfall with westerly or north-westerly flow compared to only 30% in the south-western YRZ incursion, where below-average rainfall occurs on days with (usually pre-frontal) north-westerly winds. This spatial pattern corresponds closely to those of rainfall seasonality and temporal variability. Rainfall time series of the core and surroundings are very weakly correlated (R² < 0:1), also in the winter half-year, implying that the YRZ is not simply the superposition of summer and winter rainfall zones. In addition to rain-bearing winds, latitude and annual rain day climatology appear to influence the spatial structure of rainfall variability but have little effect on seasonality. Mean annual rainfall in the true WRZ exhibits little association with the identified patterns of seasonality and rainfall variability despite the driest core WRZ stations being an order of magnitude drier than the wettest stations. This is consistent with the general pattern of near homogeneity within the true WRZ, in contrast to steep and complex spatial change outside it. [ABSTRACT FROM AUTHOR]

The North Atlantic Oscillation (NAO) is the dominant mode of climate variability over the North Atlantic basin and has a significant impact on seasonal climate and surface weather conditions. This is the result of complex and nonlinear interactions between many spatio-temporal scales. Here, the authors study a number of linear and nonlinear models for a station-based time series of the daily winter NAO index. It is found that nonlinear autoregressive models, including both short and long lags, perform excellently in reproducing the characteristic statistical properties of the NAO, such as skewness and fat tails of the distribution, and the different timescales of the two phases. As a spin-off of the modelling procedure, we can deduce that the interannual dependence of the NAO mostly affects the positive phase, and that timescales of 1 to 3 weeks are more dominant for the negative phase. Furthermore, the statistical properties of the model make it useful for the generation of realistic climate noise. [ABSTRACT FROM AUTHOR]

Reliable estimates of historical effective radiative forcing (ERF) are important for understanding the causes of past climate change and for constraining predictions of future warming. This study proposes a new linear-filtering method for estimating historical radiative forcing from time series of global mean surface temperature (GMST), using energy-balance models (EBMs) fitted to GMST from CO2- quadrupling general circulation model (GCM) experiments. We show that the response of any k-box EBM can be represented as an ARMA(k, k -1) (autoregressive moving-average) filter. We show how, by inverting an EBM's ARMA filter representation, time series of surface temperature may be converted into radiative forcing. The method is illustrated using three-box EBM fits to two recent Earth system models from CMIP5 and CMIP6 (Coupled Model Intercomparison Project). A comparison with published results obtained using the established ERF_trans method, a purely GCM-based approach, shows that our new method gives an ERF time series that closely matches the GCM-based series (correlation of 0.83). Time series of estimated historical ERF are obtained by applying the method to a dataset of historical temperature observations. The results show that there is clear evidence of a significant increase over the historical period with an estimated forcing in 2018 of 1:45±0:504Wm-2 when derived using the two Earth system models. This method could be used in the future to attribute past climate changes to anthropogenic and natural factors and to help constrain estimates of climate sensitivity. [ABSTRACT FROM AUTHOR]

A conventional parameterization of midlatitude warm fog occurrence, based on in situ observations, is employed to estimate marine surface visibility in the Arctic and North Atlantic from three datasets: an ensemble member of the Hadley Earth System (HadGEM2) model and a nested regional WRF simulation that follow historical and future emissions scenarios for 1979-2100, and the ERA-Interim reanalysis for 1979-2004. Over large scales (of an entire year and region), all three gridded datasets agree well in terms of variables like surface air temperature, whose systematic differences seem small by comparison with its predicted change over the course of this century. On the other hand, systematic differences are more apparent in large-scale estimates of relative humidity and visibility. Large differences are attributed to a sensitivity to representation bias that is inherent in the formulation of each individual model and analysis. Two simple linear calibrations are examined, both of which assume that an in situ based parameterization is broadly consistent with the use of marine (ICOADS) observations of air and dew point temperature as an errorfree reference. A single-step calibration is considered that takes the mean and variance of ICOADS frequency distributions as a reference. A two-step calibration is also performed in which ICOADS collocations are taken as a reference for the ERA reanalysis, which in turn is taken as a large-scale reference for the 1979-2004 HadGEM2 and WRF simulations. Both linear calibrations are applied (locally in time and space to air and dew point temperature) to the future climate scenarios of HadGEM2 and WRF. Although ICOADS observations are not error-free and parameterized visibility estimates are unlikely to capture much more than half the variance found in observations, attempts are made to present consistent regional changes in the frequency of high relative humidity, as a proxy for warm fog occurrence. The large-scale decrease in visibility over the 21st century is in the range of 8%-12% in the Arctic and 0%-5% in the North Atlantic. [ABSTRACT FROM AUTHOR]

We present a data-driven approach to assess and compare the behavior of large-scale spatial averages of surface temperature in climate model simulations and in observational products. We rely on univariate and multivariate dynamic linear model (DLM) techniques to estimate both long-term and seasonal changes in temperature. The residuals from the DLM analyses capture the internal variability of the climate system and exhibit complex temporal autocorrelation structure. To characterize this internal variability, we explore the structure of these residuals using univariate and multivariate autoregressive (AR) models. As a proof of concept that can easily be extended to other climate models, we apply our approach to one particular climate model (MIROC5). Our results illustrate model versus data differences in both long-term and seasonal changes in temperature. Despite differences in the underlying factors contributing to variability, the different types of simulation yield very similar spectral estimates of internal temperature variability. In general, we find that there is no evidence that the MIROC5 model systematically underestimates the amplitude of observed surface temperature variability on multi-decadal timescales - a finding that has considerable relevance regarding efforts to identify anthropogenic "fingerprints" in observational surface temperature data. Our methodology and results present a novel approach to obtaining data-driven estimates of climate variability for purposes of model evaluation. [ABSTRACT FROM AUTHOR]

The study of climate change and its impacts depends on generating projections of future temperature and other climate variables. For detailed studies, these projections usually require some combination of numerical simulation and observations, given that simulations of even the current climate do not perfectly reproduce local conditions. We present a methodology for generating future climate projections that takes advantage of the emergence of climate model ensembles, whose large amounts of data allow for detailed modeling of the probability distribution of temperature or other climate variables. The procedure gives us estimated changes in model distributions that are then applied to observations to yield projections that preserve the spatiotemporal dependence in the observations. We use quantile regression to estimate a discrete set of quantiles of daily temperature as a function of seasonality and long-term change, with smooth spline functions of season, long-term trends, and their interactions used as basis functions for the quantile regression. A particular innovation is that more extreme quantiles are modeled as exceedances above less extreme quantiles in a nested fashion, so that the complexity of the model for exceedances decreases the further out into the tail of the distribution one goes. We apply this method to two large ensembles of model runs using the same forcing scenario, both based on versions of the Community Earth System Model (CESM), run at different resolutions. The approach generates observation-based future simulations with no processing or modeling of the observed climate needed other than a simple linear rescaling. The resulting quantile maps illuminate substantial differences between the climate model ensembles, including differences in warming in the Pacific Northwest that are particularly large in the lower quantiles during winter. We show how the availability of two ensembles allows the efficacy of the method to be tested with a "perfect model" approach, in which we estimate transformations using the lower-resolution ensemble and then apply the estimated transformations to single runs from the high-resolution ensemble. Finally, we describe and implement a simple method for adjusting a transformation estimated from a large ensemble of one climate model using only a single run of a second, but hopefully more realistic, climate model. [ABSTRACT FROM AUTHOR]

Instrumental climate records of the last centuries suffer from multiple breaks due to relocations and changes in measurement techniques. These breaks are detected by relative homogenization algorithms using the difference time series between a candidate and a reference. Modern multiple changepoint methods use a decomposition approach where the segmentation explaining most variance defines the breakpoints, while a stop criterion restricts the number of breaks. In this study a pairwise multiple breakpoint algorithm consisting of these two components is tested with simulated data for a range of signal-to-noise ratios (SNRs) found in monthly temperature station datasets. The results for low SNRs obtained by this algorithm do not differ much from random segmentations; simply increasing the stop criterion to reduce the number of breaks is shown to not be helpful. This can be understood by considering that, in case of multiple breakpoints, even a random segmentation can explain about half of the break variance. We derive analytical equations for the explained noise and break variance for random and optimal segmentations. From these we conclude that reliable break detection at low but realistic SNRs needs a new approach. The problem is relevant because the uncertainty of the trends of individual stations is shown to be climatologically significant also for these small SNRs. An important side result is a new method to determine the break variance and the number of breaks in a difference time series by studying the explained variance for random break positions. We further discuss the changes from monthly to annual scale which increase the SNR by more than a factor of 3. [ABSTRACT FROM AUTHOR]

Given uncertainties in physical theory and numerical climate simulations, the historical temperature record is often used as a source of empirical information about climate change. Many historical trend analyses appear to de-emphasize physical and statistical assumptions: examples include regression models that treat time rather than radiative forcing as the relevant covariate, and time series methods that account for internal variability in nonparametric rather than parametric ways. However, given a limited data record and the presence of internal variability, estimating radiatively forced temperature trends in the historical record necessarily requires some assumptions. Ostensibly empirical methods can also involve an inherent conflict in assumptions: they require data records that are short enough for naive trend models to be applicable, but long enough for long-timescale internal variability to be accounted for. In the context of global mean temperatures, empirical methods that appear to de-emphasize assumptions can therefore produce misleading inferences, because the trend over the twentieth century is complex and the scale of temporal correlation is long relative to the length of the data record. We illustrate here how a simple but physically motivated trend model can provide better-fitting and more broadly applicable trend estimates and can allow for a wider array of questions to be addressed. In particular, the model allows one to distinguish, within a single statistical framework, between uncertainties in the shorterterm vs. longer-term response to radiative forcing, with implications not only on historical trends but also on uncertainties in future projections. We also investigate the consequence on inferred uncertainties of the choice of a statistical description of internal variability. While nonparametric methods may seem to avoid making explicit assumptions, we demonstrate how even misspecified parametric statistical methods, if attuned to the important characteristics of internal variability, can result in more accurate uncertainty statements about trends. [ABSTRACT FROM AUTHOR]