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\"A comprehensive introduction to the most commonly used statistical methods relevant in atmospheric, oceanic and climate sciences. Each method is described step-by-step using plain language, and illustrated with concrete examples, with relevant statistical and scientific concepts explained as needed. Particular attention is paid to nuances and pitfalls, with sufficient detail to enable the reader to write relevant code. Topics covered include hypothesis testing, time series analysis, linear regression, data assimilation, extreme value analysis, Principal Component Analysis, Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. The specific statistical challenges that arise in climate applications are also discussed, including model selection problems associated with Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. Requiring no previous background in statistics, this is a highly accessible textbook and reference for students and early-career researchers in the climate sciences\"-- Provided by publisher.

Scientific descriptions of the climate have traditionally been based on the study of average meteorological values taken from different positions around the world.In recent years however it has become apparent that these averages should be considered with other statistics that ultimately characterize spatial and temporal variability.

This comprehensive book describes the powerful tools of mathematical statistics which find wide application in climatological research. Suitable for graduate courses on statistics for climatic, atmospheric and oceanic science, this book will also be valuable as a reference source for researchers in climatology, meteorology, atmospheric science, and oceanography.

Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also valuable for graduate students in atmospheric dynamics and physics, meteorology, oceanography and climatology.

New precipitation (P) datasets are released regularly, following innovations in weather forecasting models, satellite retrieval methods, and multi-source merging techniques. Using the conterminous US as a case study, we evaluated the performance of 26 gridded (sub-)daily P datasets to obtain insight into the merit of these innovations. The evaluation was performed at a daily timescale for the period 2008–2017 using the Kling–Gupta efficiency (KGE), a performance metric combining correlation, bias, and variability. As a reference, we used the high-resolution (4 km) Stage-IV gauge-radar P dataset. Among the three KGE components, the P datasets performed worst overall in terms of correlation (related to event identification). In terms of improving KGE scores for these datasets, improved P totals (affecting the bias score) and improved distribution of P intensity (affecting the variability score) are of secondary importance. Among the 11 gauge-corrected P datasets, the best overall performance was obtained by MSWEP V2.2, underscoring the importance of applying daily gauge corrections and accounting for gauge reporting times. Several uncorrected P datasets outperformed gauge-corrected ones. Among the 15 uncorrected P datasets, the best performance was obtained by the ERA5-HRES fourth-generation reanalysis, reflecting the significant advances in earth system modeling during the last decade. The (re)analyses generally performed better in winter than in summer, while the opposite was the case for the satellite-based datasets. IMERGHH V05 performed substantially better than TMPA-3B42RT V7, attributable to the many improvements implemented in the IMERG satellite P retrieval algorithm. IMERGHH V05 outperformed ERA5-HRES in regions dominated by convective storms, while the opposite was observed in regions of complex terrain. The ERA5-EDA ensemble average exhibited higher correlations than the ERA5-HRES deterministic run, highlighting the value of ensemble modeling. The WRF regional convection-permitting climate model showed considerably more accurate P totals over the mountainous west and performed best among the uncorrected datasets in terms of variability, suggesting there is merit in using high-resolution models to obtain climatological P statistics. Our findings provide some guidance to choose the most suitable P dataset for a particular application.

The objective of this paper is to review statistical methods, dynamics, modeling efforts, and trends related to temperature extremes, with a focus upon extreme events of short duration that affect parts of North America. These events are associated with large scale meteorological patterns (LSMPs). The statistics, dynamics, and modeling sections of this paper are written to be autonomous and so can be read separately. Methods to define extreme events statistics and to identify and connect LSMPs to extreme temperature events are presented. Recent advances in statistical techniques connect LSMPs to extreme temperatures through appropriately defined covariates that supplement more straightforward analyses. Various LSMPs, ranging from synoptic to planetary scale structures, are associated with extreme temperature events. Current knowledge about the synoptics and the dynamical mechanisms leading to the associated LSMPs is incomplete. Systematic studies of: the physics of LSMP life cycles, comprehensive model assessment of LSMP-extreme temperature event linkages, and LSMP properties are needed. Generally, climate models capture observed properties of heat waves and cold air outbreaks with some fidelity. However they overestimate warm wave frequency and underestimate cold air outbreak frequency, and underestimate the collective influence of low-frequency modes on temperature extremes. Modeling studies have identified the impact of large-scale circulation anomalies and land–atmosphere interactions on changes in extreme temperatures. However, few studies have examined changes in LSMPs to more specifically understand the role of LSMPs on past and future extreme temperature changes. Even though LSMPs are resolvable by global and regional climate models, they are not necessarily well simulated. The paper concludes with unresolved issues and research questions.

This paper surveys the current state of knowledge regarding large-scale meteorological patterns (LSMPs) associated with short-duration (less than 1 week) extreme precipitation events over North America. In contrast to teleconnections, which are typically defined based on the characteristic spatial variations of a meteorological field or on the remote circulation response to a known forcing, LSMPs are defined relative to the occurrence of a specific phenomenon—here, extreme precipitation—and with an emphasis on the synoptic scales that have a primary influence in individual events, have medium-range weather predictability, and are well-resolved in both weather and climate models. For the LSMP relationship with extreme precipitation, we consider the previous literature with respect to definitions and data, dynamical mechanisms, model representation, and climate change trends. There is considerable uncertainty in identifying extremes based on existing observational precipitation data and some limitations in analyzing the associated LSMPs in reanalysis data. Many different definitions of “extreme” are in use, making it difficult to directly compare different studies. Dynamically, several types of meteorological systems—extratropical cyclones, tropical cyclones, mesoscale convective systems, and mesohighs—and several mechanisms—fronts, atmospheric rivers, and orographic ascent—have been shown to be important aspects of extreme precipitation LSMPs. The extreme precipitation is often realized through mesoscale processes organized, enhanced, or triggered by the LSMP. Understanding of model representation, trends, and projections for LSMPs is at an early stage, although some promising analysis techniques have been identified and the LSMP perspective is useful for evaluating the model dynamics associated with extremes.

Accurate measurement of rainfall is vital to analyze the spatial and temporal patterns of precipitation at various scales. However, the conventional rain gauge observations in many parts of the world such as Ethiopia are sparse and unevenly distributed. An alternative to traditional rain gauge observations could be satellite-based rainfall estimates. Satellite rainfall estimates could be used as a sole product (e.g., in areas with no (or poor) ground observations) or through integrating with rain gauge measurements. In this study, the potential of a newly available Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) rainfall product has been evaluated in comparison to rain gauge data over the Upper Blue Nile basin in Ethiopia for the period of 2000 to 2015. In addition, the Tropical Applications of Meteorology using SATellite and ground-based observations (TAMSAT 3) and the African Rainfall Climatology (ARC 2) products have been used as a benchmark and compared with CHIRPS. From the overall analysis at dekadal (10 days) and monthly temporal scale, CHIRPS exhibited better performance in comparison to TAMSAT 3 and ARC 2 products. An evaluation based on categorical/volumetric and continuous statistics indicated that CHIRPS has the greatest skills in detecting rainfall events (POD = 0.99, 1.00) and measure of volumetric rainfall (VHI = 1.00, 1.00), the highest correlation coefficients (r= 0.81, 0.88), better bias values (0.96, 0.96), and the lowest RMSE (28.45 mm dekad−1, 59.03 mm month−1) than TAMSAT 3 and ARC 2 products at dekadal and monthly analysis, respectively. CHIRPS overestimates the frequency of rainfall occurrence (up to 31 % at dekadal scale), although the volume of rainfall recorded during those events was very small. Indeed, TAMSAT 3 has shown a comparable performance with that of the CHIRPS product, mainly with regard to bias. The ARC 2 product was found to have the weakest performance underestimating rain gauge observed rainfall by about 24 %. In addition, the skill of CHIRPS is less affected by variation in elevation in comparison to TAMSAT 3 and ARC 2 products. CHIRPS resulted in average biases of 1.11, 0.99, and 1.00 at lower (< 1000 m a.s.l.), medium (1000 to 2000 m a.s.l.), and higher elevation (> 2000 m a.s.l.), respectively. Overall, the finding of this validation study shows the potentials of the CHIRPS product to be used for various operational applications such as rainfall pattern and variability study in the Upper Blue Nile basin in Ethiopia.

The planetary boundary layer (PBL) governs the vertical transport of mass, momentum, and moisture between the surface and the free atmosphere, and thus the determination of PBL height (BLH) is recognized as crucial for air quality, weather, and climate analysis. Although reanalysis products can provide important insight into the global view of BLH in a seamless way, the BLH observed in situ on a global scale remains poorly understood due to the lack of high-resolution (1 or 2 s) radiosonde measurements. The present study attempts to establish a near-global BLH climatology at synoptic times (00:00 and 12:00 UTC) and in the daytime using high-resolution radiosonde measurements over 300 radiosonde sites worldwide for the period 2012 to 2019, which is then compared against the BLHs obtained from four reanalysis datasets, including ERA5, MERRA-2, JRA-55, and NCEP-2. The variations in daytime BLH exhibit large spatial and temporal dependence, and as a result the BLH maxima are generally discerned over the regions such as the western United States and western China, in which the balloon launch times mostly correspond to the afternoon. The diurnal variations in BLH are revealed with a peak at 17:00 local solar time (LST). The most promising reanalysis product is ERA5, which underestimates BLH by around 130 m as compared to radiosondes released during daytime. In addition, MERRA-2 is a well-established product and has an underestimation of around 160 m. JRA-55 and NCEP-2 might produce considerable additional uncertainties, with a much larger underestimation of up to 400 m. The largest bias in the reanalysis data appears over the western United States and western China, and it might be attributed to the maximal BLH in the afternoon when the PBL has risen. Statistical analyses further indicate that the biases of reanalysis BLH products are positively associated with orographic complexity, as well as the occurrence of static instability. To our best knowledge, this study presents the first near-global view of high-resolution radiosonde-derived boundary layer height and provides a quantitative assessment of the four frequently used reanalysis products.

Based on four reanalyses or gridded data sets (ERA5, 20CR, APHRODITE and REGEN), we provide an overview of 23 Historical and 7 HighResMIP experiments’ performance from the Coupled Model Intercomparison Project Phase 6 (CMIP6) (for short, 6-Hist, HighRes) in simulating seven extreme precipitation indices over Asia defined by the Expert Team on Climate Change Detection and Indices (ETCCDI). We compare them with 28 Historical experiments in CMIP5 (5-Hist). CMIP5 and CMIP6 models are generally able to reproduce extreme precipitation’s spatial distribution and their trend patterns in comparison to the benchmark data set (APHRODITE). The overall performance of individual model is summarized by a “portrait” diagram based on four statistics for each index. We divide all 58 models into three groups (A, the top 20%; B, the median 60% and C group, the last 20%) according to MR rankings (the comprehensive ranking measure). Based on the “portrait” diagram and MR rankings, models that perform relatively well for all seven extreme precipitation indices include HadCM3, HadGEM2-AO, HadGEM2-CC and HadGEM2-ES from 5-Hist, EC-Earth3, EC-Earth3-Veg from 6-Hist and ECMWF-IFS-HR, ECMWF-IFS-LR, ECMWF-IFS-MR from HighRes. The simulated performance of CMIP6 is polarized, for the top four and the last five ranking models are both from CMIP6. Compared with the counterpart models in CMIP6 and CMIP5, the improvement of PCC (pattern correlation coefficient) is more obvious. Furthermore, the dry biases of CMIP6 (both 6-Hist and HighRes) in Southern China and India and the wet biases of CMIP6 in Tibet are reduced compared to CMIP5. This may benefit from the improvement that CMIP6 models can capture the characteristics of meridional moisture flux convergence, and improve the overestimation or underestimation of meridional and zonal specific humidity eddies compared to CMIP5.