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H. M. Christensen

Abstract

A new proper score, the error-spread score (ES), has recently been proposed for evaluation of ensemble forecasts of continuous variables. The ES is formulated with respect to the moments of the ensemble forecast. It is particularly sensitive to evaluating how well an ensemble forecast represents uncertainty: is the probabilistic forecast well calibrated? In this paper, it is shown that the ES can be decomposed into its reliability, resolution, and uncertainty components in a similar way to the Brier score. The first term evaluates the reliability of the forecast standard deviation and skewness, rewarding systems where the forecast moments reliably indicate the properties of the verification. The second term evaluates the resolution of the forecast standard deviation and skewness, and rewards systems where the forecast moments vary from the climatological moments according to the predictability of the atmospheric flow. The uncertainty term depends only on the observed error distribution and is independent of the forecast standard deviation or skewness. The decomposition was demonstrated using forecasts made with the European Centre for Medium-Range Weather Forecasts ensemble prediction system, and was able to identify the source of the skill in the forecasts at different latitudes.

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H. M. Christensen, J. Berner, and S. Yeager

Abstract

Information in decadal climate prediction arises from a well-initialized ocean state and from the predicted response to an external forcing. The length of time over which the initial conditions benefit the decadal forecast depends on the start date of the forecast. We characterize this state-dependent predictability for decadal forecasts of upper ocean heat content in the Community Earth System Model. We find regionally dependent initial condition predictability, with extended predictability generally observed in the extratropics. We also detect state-dependent predictability, with the year of loss of information from the initialization varying between start dates. The decadal forecasts in the North Atlantic show substantial information from the initial conditions beyond the 10-yr forecast window, and a high degree of state-dependent predictability. We find some evidence for state-dependent predictability in the ensemble spread in this region, similar to that seen in weather and subseasonal-to-seasonal forecasts. For some start dates, an increase of information with lead time is observed, for which the initialized forecasts predict a growing phase of the Atlantic multidecadal oscillation. Finally we consider the information in the forecast from the initial conditions relative to the forced response, and quantify the crossover time scale after which the forcing provides more information. We demonstrate that the climate change signal projects onto different patterns than the signal from the initial conditions. This means that even after the crossover time scale has been reached in a basin-averaged sense, the benefits of initialization can be felt locally on longer time scales.

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H. M. Christensen, I. M. Moroz, and T. N. Palmer

Abstract

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and a number of different techniques have been proposed for this purpose. This paper presents new perturbed parameter schemes for use in the European Centre for Medium-Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parameterization scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are varied between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, stochastically perturbed parameterization tendencies (SPPT), and to a model that does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parameterization in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skillful representations of model uncertainty owing to convection parameterization.

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Kerstin Stahl, Lena M. Tallaksen, Lukas Gudmundsson, and Jens H. Christensen

Abstract

Land surface models and large-scale hydrological models provide the basis for studying impacts of climate and anthropogenic changes on continental- to regional-scale hydrology. Hence, there is a need for comparison and validation of simulated characteristics of spatial and temporal dynamics with independent observations. This study introduces a novel validation framework that relates to common hydrological design measures. The framework is tested by comparing anomalies of runoff from a high-resolution climate-model simulation for Europe with a large number of streamflow observations from small near-natural basins. The regional climate simulation was performed as a “poor man’s reanalysis,” involving a dynamical downscaling of the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) with the Danish “HIRHAM5” model. For 19 different anomaly levels, two indices evaluate the temporal agreement (i.e., the occurrence and frequency of dry and wet events based on daily anomalies), whereas two other indices compare the interannual variability and trends based on annual anomalies. Benchmarks on each index facilitated a comparison across indices, anomaly levels, and basins. The lowest agreement of observed and simulated anomalies was found for dry anomalies. Weak to moderately wet anomalies agreed best, but agreement dropped again for the wettest anomalies. The results could guide the decision on thresholds if this regional climate model were used for the assessment of climate change scenario impacts on flood and drought statistics. Indices vary across Europe, but a gradient with decreasing correspondence between observed and simulated runoff characteristics from west to east, from lower to higher elevations, and from fast to slowly responding basins can be distinguished. The suggested indices can easily be adapted to other study areas and model types to assist in assessing the reliability of predictions of hydrological change.

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Judith Berner, Hannah M. Christensen, and Prashant D. Sardeshmukh

Abstract

The impact of a warming climate on El Niño–Southern Oscillation (ENSO) is investigated in large-ensemble simulations of the Community Earth System Model (CESM1). These simulations are forced by historical emissions for the past and the RCP8.5-scenario emissions for future projections. The simulated variance of the Niño-3.4 ENSO index increases from 1.4°C2 in 1921–80 to 1.9°C2 in 1981–2040 and 2.2°C2 in 2041–2100. The autocorrelation time scale of the index also increases, consistent with a narrowing of its spectral peak in the 3–7-yr ENSO band, raising the possibility of greater seasonal to interannual predictability in the future. Low-order linear inverse models (LIMs) fitted separately to the three 60-yr periods capture the CESM1 increase in ENSO variance and regularity. Remarkably, most of the increase can be attributed to the increase in the 23-month damping time scale of a single damped oscillatory ENSO eigenmode of these LIMs by 5 months in 1981–2040 and 6 months in 2041–2100. These apparently robust projected increases may, however, be compromised by CESM1 biases in ENSO amplitude and damping time scale. An LIM fitted to the 1921–80 observations has an ENSO eigenmode with a much shorter 8-month damping time scale, similar to that of several other eigenmodes. When the mode’s damping time scale is increased by 5 and 6 months in this observational LIM, a much smaller increase of ENSO variance is obtained than in the CESM1 projections. This may be because ENSO is not as dominated by a single ENSO eigenmode in reality as it is in the CESM1.

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Judith Berner, Prashant D. Sardeshmukh, and Hannah M. Christensen

Abstract

This study investigates the mechanisms by which short time-scale perturbations to atmospheric processes can affect El Niño–Southern Oscillation (ENSO) in climate models. To this end a control simulation of NCAR’s Community Climate System Model is compared to a simulation in which the model’s atmospheric diabatic tendencies are perturbed every time step using a Stochastically Perturbed Parameterized Tendencies (SPPT) scheme. The SPPT simulation compares better with ECMWF’s twentieth-century reanalysis in having lower interannual sea surface temperature (SST) variability and more irregular transitions between El Niño and La Niña states, as expressed by a broader, less peaked spectrum. Reduced-order linear inverse models (LIMs) derived from the 1-month lag covariances of selected tropical variables yield good representations of tropical interannual variability in the two simulations. In particular, the basic features of ENSO are captured by the LIM’s least damped oscillatory eigenmode. SPPT reduces the damping time scale of this eigenmode from 17 to 11 months, which is in better agreement with the 8 months obtained from reanalyses. This noise-induced stabilization is consistent with perturbations to the frequency of the ENSO eigenmode and explains the broadening of the SST spectrum (i.e., the greater ENSO irregularity). Although the improvement in ENSO shown here was achieved through stochastic physics parameterizations, it is possible that similar improvements could be realized through changes in deterministic parameterizations or higher numerical resolution. It is suggested that LIMs could provide useful insight into model sensitivities, uncertainties, and biases also in those cases.

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Peter A. G. Watson, H. M. Christensen, and T. N. Palmer

Abstract

Important questions concerning parameterization of tropical convection are how should subgrid-scale variability be represented and which large-scale variables should be used in the parameterizations? Here the statistics of observational data in Darwin, Australia, are compared with those of short-term forecasts of convection made by the European Centre for Medium-Range Weather Forecasts Integrated Forecast System. The forecasts use multiplicative-noise stochastic physics (MNSP) that has led to many improvements in weather forecast skill. However, doubts have recently been raised about whether MNSP is consistent with observations of tropical convection. It is shown that the model can reproduce the variability of convection intensity for a given large-scale state, both with and without MNSP. Therefore MNSP is not inconsistent with observations, and much of the modeled variability arises from nonlinearity of the deterministic part of the convection scheme. It is also shown that the model can reproduce the lack of correlation between convection intensity and large-scale CAPE and an entraining CAPE, even though the convection parameterization assumes that deep convection is more intense when the vertical temperature profile is more unstable, with entrainment taken into account. Relationships between convection and large-scale convective inhibition and vertical velocity are also correctly captured.

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Julie Bessac, Adam H. Monahan, Hannah M. Christensen, and Nils Weitzel

Abstract

Subgrid-scale (SGS) velocity variations result in gridscale sea surface flux enhancements that must be parameterized in weather and climate models. Traditional parameterizations are deterministic in that they assign a unique value of the SGS velocity flux enhancement to any given configuration of the resolved state. In this study, we assess the statistics of SGS velocity flux enhancement over a range of averaging scales (as a proxy for varying model resolution) through systematic coarse-graining of a convection-permitting atmospheric model simulation over the Indian Ocean and west Pacific warm pool. Conditioning the statistics of the SGS velocity flux enhancement on 1) the fluxes associated with the resolved winds and 2) the precipitation rate, we find that the lack of a separation between “resolved” and “unresolved” scales results in a distribution of flux enhancements for each configuration of the resolved state. That is, the SGS velocity flux enhancement should be represented stochastically rather than deterministically. The spatial and temporal statistics of the SGS velocity flux enhancement are investigated by using basic descriptive statistics and through a fit to an anisotropic space–time covariance structure. Potential spatial inhomogeneities of the statistics of the SGS velocity flux enhancement are investigated through regional analysis, although because of the relatively short duration of the simulation (9 days) distinguishing true inhomogeneity from sampling variability is difficult. Perspectives for the implementation of such a stochastic parameterization in weather and climate models are discussed.

Open access
G. Vali, M. Christensen, R. W. Fresh, E. L. Galyan, L. R. Maki, and R. C. Schnell

Abstract

Transient appearance of ice nuclei active at temperatures of −2 to −5°C has been noted to accompany the natural decay of plant leaf materials. It was shown that the development of these nuclei results from the presence of a bacterium which was identified as Pseudomonas syringae. These bacteria produce highly active nuclei in a variety of growth media. Evidence points to the fact that the bacterial cells themselves are the nuclei, but that nucleating capacity is a rare and changeable property of the cells. The findings raise the possibility that bacteria may play a role in atmospheric precipitation processes.

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H. M. Christensen, Judith Berner, Danielle R. B. Coleman, and T. N. Palmer

Abstract

El Niño–Southern Oscillation (ENSO) is the dominant mode of interannual variability in the tropical Pacific. However, the models in the ensemble from phase 5 of the Coupled Model Intercomparison Project (CMIP5) have large deficiencies in ENSO amplitude, spatial structure, and temporal variability. The use of stochastic parameterizations as a technique to address these pervasive errors is considered. The multiplicative stochastically perturbed parameterization tendencies (SPPT) scheme is included in coupled integrations of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 4 (CAM4). The SPPT scheme results in a significant improvement to the representation of ENSO in CAM4, improving the power spectrum and reducing the magnitude of ENSO toward that observed. To understand the observed impact, additive and multiplicative noise in a simple delayed oscillator (DO) model of ENSO is considered. Additive noise results in an increase in ENSO amplitude, but multiplicative noise can reduce the magnitude of ENSO, as was observed for SPPT in CAM4. In light of these results, two complementary mechanisms are proposed by which the improvement occurs in CAM. Comparison of the coupled runs with a set of atmosphere-only runs indicates that SPPT first improve the variability in the zonal winds through perturbing the convective heating tendencies, which improves the variability of ENSO. In addition, SPPT improve the distribution of westerly wind bursts (WWBs), important for initiation of El Niño events, by increasing the stochastic component of WWB and reducing the overly strong dependency on SST compared to the control integration.

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