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Di Qi and Andrew J. Majda

Abstract

Accurate uncertainty quantification for the mean and variance about forced responses to general external perturbations in the climate system is an important subject in understanding Earth’s atmosphere and ocean in climate change science. A low-dimensional reduced-order method is developed for uncertainty quantification and capturing the statistical sensitivity in the principal model directions with largest variability and in various regimes in two-layer quasigeostrophic turbulence. Typical dynamical regimes tested here include the homogeneous flow in the high latitudes and the anisotropic meandering jets in the low latitudes and/or midlatitudes. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. Here a statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. The reduced-order model displays uniformly high prediction skill for the mean and variance response to general forcing for both homogeneous flow and anisotropic zonal jets in the first 102 dominant low-wavenumber modes, where only about 0.15% of the total spectral modes are resolved, compared with the full model resolution of 2562 horizontal modes.

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Andrew J. Grundstein, Qi Qi Lu, and Robert Lund

Abstract

This paper estimates return levels of extreme snow water equivalents (SWE) in the northern Great Plains region, containing North and South Dakota, Iowa, Minnesota, and Nebraska. The return levels are estimated from extreme-value methods using a new hybrid SWE dataset that improves the spatial resolution of existing data in the area. A novel aspect of the methods is the use of standard error margins to spatially smooth the estimated SWE return levels computed on individual grid cells. The end product is a reliable return-level estimate that controls for uncertainties in the raw observations. The methods should prove useful in analyses of other geographical regions.

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Yoonsang Lee, Andrew J. Majda, and Di Qi

Abstract

Ensemble-based filtering or data assimilation methods have proved to be indispensable tools in atmosphere and ocean science as they allow computationally cheap, low-dimensional ensemble state approximation for extremely high-dimensional turbulent dynamical systems. For sparse, accurate, and infrequent observations, which are typical in data assimilation of geophysical systems, ensemble filtering methods can suffer from catastrophic filter divergence, which frequently drives the filter predictions to machine infinity. A two-layer quasigeostrophic equation, which is a classical idealized model for geophysical turbulence, is used to demonstrate catastrophic filter divergence. The mathematical theory of adaptive covariance inflation by Tong et al. and covariance localization are investigated to stabilize the ensemble methods and prevent catastrophic filter divergence. Two forecast models—a coarse-grained ocean code, which ignores the small-scale parameterization, and stochastic superparameterization (SP), which is a seamless multiscale method developed for large-scale models without scale gap between the resolved and unresolved scales—are applied to generate large-scale forecasts with a coarse spatial resolution compared to the full resolution . The methods are tested in various dynamical regimes in ocean with jets and vorticities, and catastrophic filter divergence is documented for the standard filter without inflation. Using the two forecast models, various kinds of covariance inflation with or without localization are compared. It shows that proper adaptive additive inflation can effectively stabilize the ensemble methods without catastrophic filter divergence in all regimes. Furthermore, stochastic SP achieves accurate filtering skill with localization while the ocean code performs poorly even with localization.

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Qi Hu, Song Feng, and Robert J. Oglesby

Abstract

Understanding the development and variation of the atmospheric circulation regimes driven by the Atlantic multidecadal oscillation (AMO) is essential because these circulations interact with other forcings on decadal and interannual time scales. Collectively, they determine the summer (June, July, and August) precipitation variations for North America. In this study, a general circulation model (GCM) is used to obtain such understanding, with a focus on physical processes connecting the AMO and the summertime precipitation regime change in North America. Two experimental runs are conducted with sea surface temperature (SST) anomalies imposed in the North Atlantic Ocean that represent the warm and cold phases of the AMO. Climatological SSTs are used elsewhere in the oceans. Model results yield summertime precipitation anomalies in North America closely matching the observed anomaly patterns in North America, suggesting that the AMO provides a fundamental control on summertime precipitation in North America at decadal time scales. The impacts of the AMO are achieved by a chain of events arising from different circulation anomalies during warm and cold phases of the AMO. During the warm phase, the North Atlantic subtropical high pressure system (NASH) weakens, and the North American continent is much less influenced by it. A massive body of warm air develops over the heated land in North America from June–August, associated with high temperature and low pressure anomalies in the lower troposphere and high pressure anomalies in the upper troposphere. In contrast, during the cold phase of the AMO, the North American continent, particularly to the west, is much more influenced by an enhanced NASH. Cooler temperatures and high pressure anomalies prevail in the lower troposphere, and a frontal zone forms in the upper troposphere. These different circulation anomalies further induce a three-cell circulation anomaly pattern over North America in the warm and cold phases of the AMO. In particular, during the cold phase, the three-cell circulation anomaly pattern features a broad region of anomalous low-level southerly flow from the Gulf of Mexico into the U.S. Great Plains. Superimposed with an upper-troposphere front, more frequent summertime storms develop and excess precipitation occurs over most of North America. A nearly reversed condition occurs during the warm phase of the AMO, yielding drier conditions in North America. This new understanding provides a foundation for further study and better prediction of the variations of North American summer precipitation, especially when modulated by other multidecadal variations—for example, the Pacific decadal oscillation and interannual variations associated with the ENSO and the Arctic Oscillation.

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Qing Cao, Yang Hong, Jonathan J. Gourley, Youcun Qi, Jian Zhang, Yixin Wen, and Pierre-Emmanuel Kirstetter

Abstract

This study presents a statistical analysis of the vertical structure of precipitation measured by NASA–Japan Aerospace Exploration Agency’s (JAXA) Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) in the region of southern California, Arizona, and western New Mexico, where the ground-based Next-Generation Radar (NEXRAD) network finds difficulties in accurately measuring surface precipitation because of beam blockages by complex terrain. This study has applied TRMM PR version-7 products 2A23 and 2A25 from 1 January 2000 to 26 October 2011. The seasonal, spatial, intensity-related, and type-related variabilities are characterized for the PR vertical profile of reflectivity (VPR) as well as the heights of storm, freezing level, and bright band. The intensification and weakening of reflectivity at low levels in the VPR are studied through fitting physically based VPR slopes. Major findings include the following: precipitation type is the most significant factor determining the characteristics of VPRs, the shape of VPRs also influences the intensity of surface rainfall rates, the characteristics of VPRs have a seasonal dependence with strong similarities between the spring and autumn months, and the spatial variation of VPR characteristics suggests that the underlying terrain has an impact on the vertical structure. The comprehensive statistical and physical analysis strengthens the understanding of the vertical structure of precipitation and advocates for the approach of VPR correction to improve surface precipitation estimation in complex terrain.

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Andrew J. Dowdy, Lixin Qi, David Jones, Hamish Ramsay, Robert Fawcett, and Yuri Kuleshov

Abstract

Climatological features of tropical cyclones in the South Pacific Ocean have been analyzed based on a new archive for the Southern Hemisphere. A vortex tracking and statistics package is used to examine features such as climatological maps of system intensity and the change in intensity with time, average tropical cyclone system movement, and system density. An examination is presented of the spatial variability of these features, as well as changes in relation to phase changes of the El Niño–Southern Oscillation phenomenon. A critical line is defined in this study based on maps of cyclone intensity to describe the statistical geographic boundary for cyclone intensification. During El Niño events, the critical line shifts equatorward, while during La Niña events the critical line is generally displaced poleward. Regional variability in tropical cyclone activity associated with El Niño–Southern Oscillation phases is examined in relation to the variability of large-scale atmospheric or oceanic variables associated with tropical cyclone activity. Maps of the difference fields between different phases of El Niño–Southern Oscillation are examined for sea surface temperature, vertical wind shear, lower-tropospheric vorticity, and midtropospheric relative humidity. Results are also examined in relation to the South Pacific convergence zone. The common region where each of the large-scale variables showed favorable conditions for cyclogenesis coincided with the location of maximum observed cyclogenesis for El Niño events as well as for La Niña years.

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S. Chen, P. E. Kirstetter, Y. Hong, J. J. Gourley, Y. D. Tian, Y. C. Qi, Q. Cao, J. Zhang, K. Howard, J. J. Hu, and X. W. Xue

Abstract

In this paper, the authors estimate the uncertainty of the rainfall products from NASA and Japan Aerospace Exploration Agency's (JAXA) Tropical Rainfall Measurement Mission (TRMM) Precipitation Radar (PR) so that they may be used in a quantitative manner for applications like hydrologic modeling or merging with other rainfall products. The spatial error structure of TRMM PR surface rain rates and types was systematically studied by comparing them with NOAA/National Severe Storms Laboratory's (NSSL) next generation, high-resolution (1 km/5 min) National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE; NMQ/Q2) over the TRMM-covered continental United States (CONUS). Data pairs are first matched at the PR footprint scale (5 km/instantaneous) and then grouped into 0.25° grid cells to yield spatially distributed error maps and statistics using data from December 2009 through November 2010. Careful quality control steps (including bias correction with rain gauges and quality filtering) are applied to the ground radar measurements prior to considering them as reference data. The results show that PR captures well the spatial pattern of total rainfall amounts with a high correlation coefficient (CC; 0.91) with Q2, but this decreases to 0.56 for instantaneous rain rates. In terms of precipitation types, Q2 and PR convective echoes are spatially correlated with a CC of 0.63. Despite this correlation, PR's total annual precipitation from convection is 48.82% less than that by Q2, which points to potential issues in the PR algorithm's attenuation correction, nonuniform beam filling, and/or reflectivity-to-rainfall relation. Finally, the spatial analysis identifies regime-dependent errors, in particular in the mountainous west. It is likely that the surface reference technique is triggered over complex terrain, resulting in high-amplitude biases.

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Ikrom Artikov, Stacey J. Hoffman, Gary D. Lynne, Lisa M. Pytlik Zillig, Qi Hu, Alan J. Tomkins, Kenneth G. Hubbard, Michael J. Hayes, and William Waltman

Abstract

Results of a set of four regression models applied to recent survey data of farmers in eastern Nebraska suggest the causes that drive farmer intentions of using weather and climate information and forecasts in farming decisions. The model results quantify the relative importance of attitude, social norm, perceived behavioral control, and financial capability in explaining the influence of climate-conditions information and short-term and long-term forecasts on agronomic, crop insurance, and crop marketing decisions. Attitude, serving as a proxy for the utility gained from the use of such information, had the most profound positive influence on the outcome of all the decisions, followed by norms. The norms in the community, as a proxy for the utility gained from allowing oneself to be influenced by others, played a larger role in agronomic decisions than in insurance or marketing decisions. In addition, the interaction of controllability (accuracy, availability, reliability, timeliness of weather and climate information), self-efficacy (farmer ability and understanding), and general preference for control was shown to be a substantive cause. Yet control variables also have an economic side: The farm-sales variable as a measure of financial ability and motivation intensified and clarified the role of control while also enhancing the statistical robustness of the attitude and norms variables in better clarifying how they drive the influence. Overall, the integrated model of planned behavior from social psychology and derived demand from economics, that is, the “planned demand model,” is more powerful than models based on either of these approaches alone. Taken together, these results suggest that the “human dimension” needs to be better recognized so as to improve effective use of climate and weather forecasts and information for farming decision making.

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Bo Dong, John D. Lenters, Qi Hu, Christopher J. Kucharik, Tiejun Wang, Mehmet E. Soylu, and Phillip M. Mykleby

Abstract

Variations in climate have important influences on the hydrologic cycle. Observations over the continental United States in recent decades show substantial changes in hydrologically significant variables, such as decreases in cloud cover and increases in solar radiation (i.e., solar brightening), as well as increases in air temperature, changes in wind speed, and seasonal shifts in precipitation rate and rain/snow ratio. Impacts of these changes on the regional water cycle from 1984 to 2007 are evaluated using a terrestrial ecosystem/land surface hydrologic model (Agro-IBIS). Results show an acceleration of various components of the surface water balance in the Upper Mississippi, Missouri, Ohio, and Great Lakes basins over the 24-yr period, but with significant seasonal and spatial complexity. Evapotranspiration (ET) has increased across most of our study domain and seasons. The largest increase is found in fall, when solar brightening trends are also particularly significant. Changes in runoff are characterized by distinct spatial and seasonal variations, with the impact of precipitation often being muted by changes in ET and soil-water storage rate. In snow-dominated regions, such as the northern Great Lakes basin, spring runoff has declined significantly due to warmer air temperatures and an associated decreasing ratio of snow in total precipitation during the cold season. In the northern Missouri basin, runoff shows large increases in all seasons, primarily due to increases in precipitation. The responses to these changes in the regional hydrologic cycle depend on the underlying land cover type—maize, soybean, and natural vegetation. Comparisons are also made with other hydroclimatic time series to place the decadal-scale variability in a longer-term context.

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Qi Hu, Lisa M. Pytlik Zillig, Gary D. Lynne, Alan J. Tomkins, William J. Waltman, Michael J. Hayes, Kenneth G. Hubbard, Ikrom Artikov, Stacey J. Hoffman, and Donald A. Wilhite

Abstract

Although the accuracy of weather and climate forecasts is continuously improving and new information retrieved from climate data is adding to the understanding of climate variation, use of the forecasts and climate information by farmers in farming decisions has changed little. This lack of change may result from knowledge barriers and psychological, social, and economic factors that undermine farmer motivation to use forecasts and climate information. According to the theory of planned behavior (TPB), the motivation to use forecasts may arise from personal attitudes, social norms, and perceived control or ability to use forecasts in specific decisions. These attributes are examined using data from a survey designed around the TPB and conducted among farming communities in the region of eastern Nebraska and the western U.S. Corn Belt. There were three major findings: 1) the utility and value of the forecasts for farming decisions as perceived by farmers are, on average, around 3.0 on a 0–7 scale, indicating much room to improve attitudes toward the forecast value. 2) The use of forecasts by farmers to influence decisions is likely affected by several social groups that can provide “expert viewpoints” on forecast use. 3) A major obstacle, next to forecast accuracy, is the perceived identity and reliability of the forecast makers. Given the rapidly increasing number of forecasts in this growing service business, the ambiguous identity of forecast providers may have left farmers confused and may have prevented them from developing both trust in forecasts and skills to use them. These findings shed light on productive avenues for increasing the influence of forecasts, which may lead to greater farming productivity. In addition, this study establishes a set of reference points that can be used for comparisons with future studies to quantify changes in forecast use and influence.

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