Evaluation of delta change and bias correction methods for future daily precipitation: intermodel cross-validation using ENSEMBLES simulations

Due to inherent limitations in climate models, their output is biased in relation to observed climate and as such does not provide reliable climate projections. In this study, nine methods used to account for biases in daily precipitation are tested. First, cross-validation tests were made using a set of ENSEMBLES regional model simulations to gain insights in the potential performance of the methods in the future climate. The results show that quantile mapping type methods, being able to modify the shape of the precipitation distribution, often outperform other types of methods. Yet, as the performance depends on time of the year, location and part of the distribution considered, it is not possible to distinguish one universally best performing method. In addition, the improvement relative to the projections that would have been obtained assuming unchanged climate is relatively modest, particularly in the early twentyfirst century conditions. Further tests with different method combinations show that the projections could be potentially improved by using several well performing methods in parallel. In the second part of the study, contributions of method and model differences to the overall variation of precipitation projections are assessed. It is shown that although intermodel differences play an important role, uncertainties related to intermethod differences are substantial, particularly in the tails of the distribution. This suggests that method uncertainty should be taken into account when constructing daily precipitation projections, possibly by using several methods in parallel.     

Observation-based blended projections from ensembles of regional climate models

We consider the problem of projecting future climate from ensembles of regional climate model (RCM) simulations using results from the North American Regional Climate Change Assessment Program (NARCCAP). To this end, we develop a hierarchical Bayesian space-time model that quantifies the discrepancies between different members of an ensemble of RCMs corresponding to present day conditions, and observational records. Discrepancies are then propagated into the future to obtain high resolution blended projections of 21st century climate. In addition to blended projections, the proposed method provides location-dependent comparisons between the different simulations by estimating the different modes of spatial variability, and using the climate model-specific coefficients of the spatial factors for comparisons. The approach has the flexibility to provide projections at customizable scales of potential interest to stakeholders while accounting for the uncertainties associated with projections at these scales based on a comprehensive statistical framework. We demonstrate the methodology with simulations from the Weather Research & Forecasting regional model (WRF) using three different boundary conditions. We use simulations for two time periods: current climate conditions, covering 1971 to 2000, and future climate conditions under the Special Report on Emissions Scenarios (SRES) A2 emissions scenario, covering 2041 to 2070. We investigate and project yearly mean summer and winter temperatures for a domain in the South West of the United States.     

Extended regional climate model projections for Europe until the mid-twentyfirst century: combining ENSEMBLES and CMIP3

This study aims at sharpening the existing knowledge of expected seasonal mean climate change and its uncertainty over Europe for the two key climate variables air temperature and precipitation amount until the mid-twentyfirst century. For this purpose, we assess and compensate the global climate model (GCM) sampling bias of the ENSEMBLES regional climate model (RCM) projections by combining them with the full set of the CMIP3 GCM ensemble. We first apply a cross-validation in order to assess the skill of different statistical data reconstruction methods in reproducing ensemble mean and standard deviation. We then select the most appropriate reconstruction method in order to fill the missing values of the ENSEMBLES simulation matrix and further extend the matrix by all available CMIP3 GCM simulations forced by the A1B emission scenario. Cross-validation identifies a randomized scaling approach as superior in reconstructing the ensemble spread. Errors in ensemble mean and standard deviation are mostly less than 0.1 K and 1.0 % for air temperature and precipitation amount, respectively. Reconstruction of the missing values reveals that expected seasonal mean climate change of the ENSEMBLES RCM projections is not significantly biased and that the associated uncertainty is not underestimated due to sampling of only a few driving GCMs. In contrast, the spread of the extended simulation matrix is partly significantly lower, sharpening our knowledge about future climate change over Europe by reducing uncertainty in some regions. Furthermore, this study gives substantial weight to recent climate change impact studies based on the ENSEMBLES projections, since it confirms the robustness of the climate forcing of these studies concerning GCM sampling.     

Climate model errors, feedbacks and forcings: a comparison of perturbed physics and multi-model ensembles

Ensembles of climate model simulations are required for input into probabilistic assessments of the risk of future climate change in which uncertainties are quantified. Here we document and compare aspects of climate model ensembles from the multi-model archive and from perturbed physics ensembles generated using the third version of the Hadley Centre climate model (HadCM3). Model-error characteristics derived from time-averaged two-dimensional fields of observed climate variables indicate that the perturbed physics approach is capable of sampling a relatively wide range of different mean climate states, consistent with simple estimates of observational uncertainty and comparable to the range of mean states sampled by the multi-model ensemble. The perturbed physics approach is also capable of sampling a relatively wide range of climate forcings and climate feedbacks under enhanced levels of greenhouse gases, again comparable with the multi-model ensemble. By examining correlations between global time-averaged measures of model error and global measures of climate change feedback strengths, we conclude that there are no simple emergent relationships between climate model errors and the magnitude of future global temperature change. Algorithms for quantifying uncertainty require the use of complex multivariate metrics for constraining projections.     

中国地区极端事件预估研究

简要介绍了极端气候事件预估的基本方法,概述了东亚和中国地区关于气候和极端气候事件预估研究的进展。针对极端事件变化预估研究中的重要问题,如高分辨率、长时间尺度的区域气候变化模拟和预估,高时空分辨率的网格化观测资料,除温室效应外的土地利用和气溶胶的作用,使用合理方法进行多模式结果的集合,以及统计降尺度方法的应用等,进行了讨论。     

Creating regional climate change scenarios over southern South America for the 2020’s and 2050’s using the pattern scaling technique: validity and limitations

Dynamical downscaling of global climate simulations is the most adequate tool to generate regional projections of climate change. This technique involves at least a present climate simulation and a simulation of a future scenario, usually at the end of the twenty first century. However, regional projections for a variety of scenarios and periods, the 2020s or the 2050s, are often required by the impact community. The pattern scaling technique is used to estimate information on climate change for periods and scenarios not simulated by the regional model. We based our study on regional simulations performed over southern South America for present climate conditions and two emission scenarios at the end of the twenty first century. We used the pattern scaling technique to estimate mean seasonal changes of temperature and precipitation for the 2020s and the 2050s. The validity of the scalability assumptions underlying the pattern scaling technique for estimating near future regional climate change scenarios over southern South America is assessed. The results show that the pattern scaling works well for estimating mean temperature changes for which the regional changes are linearly related to the global mean temperature changes. For precipitation changes, the validity of the scalability assumption is weaker. The errors of estimating precipitation changes are comparable to those inherent to the regional model and to the projected changes themselves.     

A sensitivity-based approach to evaluating future changes in Colorado River discharge

Projections of a drier, warmer climate in the U.S. Southwest would complicate management of the Colorado River system—yet these projections, often based on coarse resolution global climate models, are quite uncertain. We present an approach to understanding future Colorado River discharge based on land surface characterizations that map the Colorado River basin’s hydrologic sensitivities (e.g., changes in streamflow magnitude) to annual and seasonal temperature and precipitation changes. The approach uses a process-based macroscale land surface model (LSM; in this case, the Variable Infiltration Capacity hydrologic model, although methods are applicable to any LSM) to develop sensitivity maps (equivalent to a simple empirical model), and uses these maps to evaluate long-term annual streamflow responses to future precipitation and temperature change. We show that global climate model projections combined with estimates of hydrologic sensitivities, estimated for different seasons and at different change increments, can provide a basis for approximating cumulative distribution functions of streamflow changes similar to more common, computationally intensive full-simulation approaches that force the hydrologic model with downscaled future climate scenarios. For purposes of assessing risk, we argue that the sensitivity-based approach produces viable first-order estimates that can be easily applied to newly released climate information to assess underlying drivers of change and bound, at least approximately, the range of future streamflow uncertainties for water resource planners.     

Influence of SST biases on future climate change projections

We use a quantile-based bias correction technique and a multi-member ensemble of the atmospheric component of NCAR CCSM3 (CAM3) simulations to investigate the influence of sea surface temperature (SST) biases on future climate change projections. The simulations, which cover 1977?C1999 in the historical period and 2077?C2099 in the future (A1B) period, use the CCSM3-generated SSTs as prescribed boundary conditions. Bias correction is applied to the monthly time-series of SSTs so that the simulated changes in SST mean and variability are preserved. Our comparison of CAM3 simulations with and without SST correction shows that the SST biases affect the precipitation distribution in CAM3 over many regions by introducing errors in atmospheric moisture content and upper-level (lower-level) divergence (convergence). Also, bias correction leads to significantly different precipitation and surface temperature changes over many oceanic and terrestrial regions (predominantly in the tropics) in response to the future anthropogenic increases in greenhouse forcing. The differences in the precipitation response from SST bias correction occur both in the mean and the percent change, and are independent of the ocean?Catmosphere coupling. Many of these differences are comparable to or larger than the spread of future precipitation changes across the CMIP3 ensemble. Such biases can affect the simulated terrestrial feedbacks and thermohaline circulations in coupled climate model integrations through changes in the hydrological cycle and ocean salinity. Moreover, biases in CCSM3-generated SSTs are generally similar to the biases in CMIP3 ensemble mean SSTs, suggesting that other GCMs may display a similar sensitivity of projected climate change to SST errors. These results help to quantify the influence of climate model biases on the simulated climate change, and therefore should inform the effort to further develop approaches for reliable climate change projection.     

统计降尺度法对华北地区未来区域气温变化情景的预估

迄今为止,大部分海气耦合气候模式（AOGCM）的空间分辨率还较低,很难对区域尺度的气候变化情景做合理的预测。降尺度法已广泛用于弥补AOGCM在这方面的不足。作者采用统计降尺度方法对1月和7月华北地区49个气象观测站的未来月平均温度变化情景进行预估。采用的统计降尺度方法是主分量分析与逐步回归分析相结合的多元线性回归模型。首先,采用1961～2000年的 NCEP再分析资料和49个台站的观测资料建立月平均温度的统计降尺度模型,然后把建立的统计降尺度模型应用于HadCM3 SRES A2 和 B2 两种排放情景, 从而生成各个台站1950～2099年1月份和7月份温度变化情景。结果表明:在当前气候条件下,无论1月还是7月,统计降尺度方法模拟的温度与观测的温度有很好的一致性,而且在大多数台站,统计降尺度模拟气温与观测值相比略微偏低。对于未来气候情景的预估方面,无论1月还是7月,也无论是HadCM3 SRES A2 还是B2排放情景驱动统计模型,结果表明大多数的站点都存在温度的明显上升趋势,同时7月的上升趋势与1月相比偏低。     

River discharge to the Baltic Sea in a future climate

This study reports on new projections of discharge to the Baltic Sea given possible realisations of future climate and uncertainties regarding these projections. A high-resolution, pan-Baltic application of the Hydrological Predictions for the Environment (HYPE) model was used to make transient simulations of discharge to the Baltic Sea for a mini-ensemble of climate projections representing two high emissions scenarios. The biases in precipitation and temperature adherent to climate models were adjusted using a Distribution Based Scaling (DBS) approach. As well as the climate projection uncertainty, this study considers uncertainties in the bias-correction and hydrological modelling. While the results indicate that the cumulative discharge to the Baltic Sea for 2071 to 2100, as compared to 1971 to 2000, is likely to increase, the uncertainties quantified from the hydrological model and the bias-correction method show that even with a state-of-the-art methodology, the combined uncertainties from the climate model, bias-correction and impact model make it difficult to draw conclusions about the magnitude of change. It is therefore urged that as well as climate model and scenario uncertainty, the uncertainties in the bias-correction methodology and the impact model are also taken into account when conducting climate change impact studies.     

Projections of climate change impacts on central America tropical rainforest

Tropical rainforest plays an important role in the global carbon cycle, accounting for a large part of global net primary productivity and contributing to CO₂ sequestration. The objective of this work is to simulate potential changes in the rainforest biome in Central America subject to anthropogenic climate change under two emissions scenarios, RCP4.5 and RCP8.5. The use of a dynamic vegetation model and climate change scenarios is an approach to investigate, assess or anticipate how biomes respond to climate change. In this work, the Inland dynamic vegetation model was driven by the Eta regional climate model simulations. These simulations accept boundary conditions from HadGEM2-ES runs in the two emissions scenarios. The possible consequences of regional climate change on vegetation properties, such as biomass, net primary production and changes in forest extent and distribution, were investigated. The Inland model projections show reductions in tropical forest cover in both scenarios. The reduction of tropical forest cover is greater in RCP8.5. The Inland model projects biomass increases where tropical forest remains due to the CO₂ fertilization effect. The future distribution of predominant vegetation shows that some areas of tropical rainforest in Central America are replaced by savannah and grassland in RCP4.5. Inland projections under both RCP4.5 and RCP8.5 show a net primary productivity reduction trend due to significant tropical forest reduction, temperature increase, precipitation reduction and dry spell increments, despite the biomass increases in some areas of Costa Rica and Panama. This study may provide guidance to adaptation studies of climate change impacts on the tropical rainforests in Central America.     

A multi-model ensemble of downscaled spatial climate change scenarios for the Dommel catchment, Western Europe

Regional or local scale hydrological impact studies require high resolution climate change scenarios which should incorporate some assessment of uncertainties in future climate projections. This paper describes a method used to produce a multi-model ensemble of multivariate weather simulations including spatial–temporal rainfall scenarios and single-site temperature and potential evapotranspiration scenarios for hydrological impact assessment in the Dommel catchment (1,350 km²) in The Netherlands and Belgium. A multi-site stochastic rainfall model combined with a rainfall conditioned weather generator have been used for the first time with the change factor approach to downscale projections of change derived from eight Regional Climate Model (RCM) experiments for the SRES A2 emission scenario for the period 2071–2100. For winter, all downscaled scenarios show an increase in mean daily precipitation (catchment average change of +9% to +40%) and typically an increase in the proportion of wet days, while for summer a decrease in mean daily precipitation (−16% to −57%) and proportion of wet days is projected. The range of projected mean temperature is 7.7°C to 9.1°C for winter and 19.9°C to 23.3°C for summer, relative to means for the control period (1961–1990) of 3.8°C and 16.8°C, respectively. Mean annual potential evapotranspiration is projected to increase by between +17% and +36%. The magnitude and seasonal distribution of changes in the downscaled climate change projections are strongly influenced by the General Circulation Model (GCM) providing boundary conditions for the RCM experiments. Therefore, a multi-model ensemble of climate change scenarios based on different RCMs and GCMs provides more robust estimates of precipitation, temperature and evapotranspiration for hydrological impact assessments, at both regional and local scale.     

Projecting long-term armed conflict risk: An underappreciated field of inquiry?

Little research has been done on projecting long-term conflict risks. Such projections are currently neither included in the development of socioeconomic scenarios or climate change impact assessments nor part of global agenda-setting policy processes. In contrast, in other fields of inquiry, long-term projections and scenario studies are established and relevant for both strategical agenda-setting and applied policies. Although making projections of armed conflict risk in response to climate change is surrounded by uncertainty, there are good reasons to further develop such scenario-based projections. In this perspective article we discuss why quantifying implications of climate change for future armed conflict risk is inherently uncertain, but necessary for shaping sustainable future policy agendas. We argue that both quantitative and qualitative projections can have a purpose in future climate change impact assessments and put out the challenges this poses for future research.     

分位数映射法在RegCM4中国气温模拟订正中的应用

将一种分位数映射法RQUANT,应用到一个区域气候模式（RegCM4）所模拟中国气温的误差订正中。从气候平均态、年际变率、极端气候及农业气候等多方面,评估了该方法对日平均气温、日最高气温和日最低气温模拟的订正效果。结果表明,该订正方法对模式模拟的日平均、日最高和最低气温气候平均态的订正效果都非常明显,中国大部分地区的订正结果与观测的偏差在±0.5℃之间。在降低极端气温指数和农业气候相关指数的模拟误差方面也有显著的效果,但对气温年际变率的订正效果有限。结合以往对降水订正的评估分析,该方法对模式模拟结果有较好的订正效果,可以应用于区域气候模式的气候变化模拟预估中,为气候变化及相关影响评估研究提供更适用和可靠的数据。     

Projection of future climate change conditions using IPCC simulations, neural networks and Bayesian statistics. Part 2: Precipitation mean state and seasonal cycle in South America

Evaluating the response of climate to greenhouse gas forcing is a major objective of the climate community, and the use of large ensemble of simulations is considered as a significant step toward that goal. The present paper thus discusses a new methodology based on neural network to mix ensemble of climate model simulations. Our analysis consists of one simulation of seven Atmosphere–Ocean Global Climate Models, which participated in the IPCC Project and provided at least one simulation for the twentieth century (20c3m) and one simulation for each of three SRES scenarios: A2, A1B and B1. Our statistical method based on neural networks and Bayesian statistics computes a transfer function between models and observations. Such a transfer function was then used to project future conditions and to derive what we would call the optimal ensemble combination for twenty-first century climate change projections. Our approach is therefore based on one statement and one hypothesis. The statement is that an optimal ensemble projection should be built by giving larger weights to models, which have more skill in representing present climate conditions. The hypothesis is that our method based on neural network is actually weighting the models that way. While the statement is actually an open question, which answer may vary according to the region or climate signal under study, our results demonstrate that the neural network approach indeed allows to weighting models according to their skills. As such, our method is an improvement of existing Bayesian methods developed to mix ensembles of simulations. However, the general low skill of climate models in simulating precipitation mean climatology implies that the final projection maps (whatever the method used to compute them) may significantly change in the future as models improve. Therefore, the projection results for late twenty-first century conditions are presented as possible projections based on the “state-of-the-art” of present climate modeling. First, various criteria were computed making it possible to evaluate the models’ skills in simulating late twentieth century precipitation over continental areas as well as their divergence in projecting climate change conditions. Despite the relatively poor skill of most of the climate models in simulating present-day large scale precipitation patterns, we identified two types of models: the climate models with moderate-to-normal (i.e., close to observations) precipitation amplitudes over the Amazonian basin; and the climate models with a low precipitation in that region and too high a precipitation on the equatorial Pacific coast. Under SRES A2 greenhouse gas forcing, the neural network simulates an increase in precipitation over the La Plata basin coherent with the mean model ensemble projection. Over the Amazonian basin, a decrease in precipitation is projected. However, the models strongly diverge, and the neural network was found to give more weight to models, which better simulate present-day climate conditions. In the southern tip of the continent, the models poorly simulate present-day climate. However, they display a fairly good convergence when simulating climate change response with a weak increase south of 45°S and a decrease in Chile between 30 and 45°S. Other scenarios (A1B and B1) strongly resemble the SRES A2 trends but with weaker amplitudes.     

Consistency of observed winter precipitation trends in northern Europe with regional climate change projections

Often it is claimed that the recent changes in northern European climate are at least partly anthropogenic even though a human influence has not yet been successfully detected. Hence we investigate whether the recent changes are consistent with regional climate change projections. Therefore, trends in winter (DJF) mean precipitation in northern Europe are compared to human induced changes as predicted by a set of four regional climate model simulations. The patterns of recent trends and predicted changes match reasonably well as indicated by pattern correlation and the similarity is very likely not random. However, the model projections generally underestimate the recent change in winter precipitation. That is, the signal-to-noise ratio of the anthropogenic precipitation change is either rather low or the presently used simulations are significantly flawed in their ability to project changes into the future. European trends contain large signals related to the North Atlantic Oscillation (NAO), of which a major unknown part may be unrelated to the anthropogenic signal. Therefore, we also examine the consistency of recent and projected changes after subtracting the NAO signal in both the observations and in the projections. It turns out that even after the removal of the NAO signal, the pattern of trends in the observations is similar to those projected by the models. At the same time, the magnitude of the trends is considerably reduced and closer to the magnitude of the change in the projections.     

Characterizing climate change risks by linking robust decision frameworks and uncertain probabilistic projections

There is increasing concern that avoiding climate change impacts will require proactive adaptation, particularly for infrastructure systems with long lifespans. However, one challenge in adaptation is the uncertainty surrounding climate change projections generated by general circulation models (GCMs). This uncertainty has been addressed in different ways. For example, some researchers use ensembles of GCMs to generate probabilistic climate change projections, but these projections can be highly sensitive to assumptions about model independence and weighting schemes. Because of these issues, others argue that robustness-based approaches to climate adaptation are more appropriate, since they do not rely on a precise probabilistic representation of uncertainty. In this research, we present a new approach for characterizing climate change risks that leverages robust decision frameworks and probabilistic GCM ensembles. The scenario discovery process is used to search across a multi-dimensional space and identify climate scenarios most associated with system failure, and a Bayesian statistical model informed by GCM projections is then developed to estimate the probability of those scenarios. This provides an important advancement in that it can incorporate decision-relevant climate variables beyond mean temperature and precipitation and account for uncertainty in probabilistic estimates in a straightforward way. We also suggest several advancements building on prior approaches to Bayesian modeling of climate change projections to make them more broadly applicable. We demonstrate the methodology using proposed water resources infrastructure in Lake Tana, Ethiopia, where GCM disagreement on changes in future rainfall presents a major challenge for infrastructure planning.     

On the simulation of Laurentian Great Lakes water levels under projections of global climate change

A new method is proposed to estimate future net basin supplies and lake levels for the Laurentian Great Lakes based on GCM projections of global climate change. The method first dynamically downscales the GCM simulation with a regional climate model, and then bias—corrects the simulated net basin supply in order to be used directly in a river—routing/lake level scheme. This technique addresses two weaknesses in the traditional approach, whereby observed sequences of climate variables are perturbed with fixed ratios or differences derived directly from GCMs in order to run evaporation and runoff models. Specifically, (1) land surface—atmosphere feedback processes are represented, and (2) changes in variability can be analyzed with the new approach. The method is demonstrated with a single, high resolution simulation, where small changes in future mean lake levels for all the upper Great Lakes are found, and an increase in seasonal range—especially for Lake Superior—is indicated. Analysis of a small ensemble of eight lower resolution regional climate model simulations supports these findings. In addition, a direct comparison with the traditional approach based on the same GCM projections used as the driving simulations in this ensemble shows that the new method indicates smaller declines in level for all the upper Great Lakes than has been reported previously based on the traditional method, though median differences are only a few centimetres in each case.     

GCM-based regional temperature and precipitation change estimates for Europe under four SRES scenarios applying a super-ensemble pattern-scaling method

Seasonal GCM-based temperature and precipitation projections for the end of the 21st century are presented for five European regions; projections are compared with corresponding estimates given by the PRUDENCE RCMs. For most of the six global GCMs studied, only responses to the SRES A2 and B2 forcing scenarios are available. To formulate projections for the A1FI and B1 forcing scenarios, a super-ensemble pattern-scaling technique has been developed. This method uses linear regression to represent the relationship between the local GCM-simulated response and the global mean temperature change simulated by a simple climate model. The method has several advantages: e.g., the noise caused by internal variability is reduced, and the information provided by GCM runs performed with various forcing scenarios is utilized effectively. The super-ensemble method proved especially useful when only one A2 and one B2 simulation is available for an individual GCM. Next, 95% probability intervals were constructed for regional temperature and precipitation change, separately for the four forcing scenarios, by fitting a normal distribution to the set of projections calculated by the GCMs. For the high-end of the A1FI uncertainty interval, temperature increases close to 10°C could be expected in the southern European summer and northern European winter. Conversely, the low-end warming estimates for the B1 scenario are ~ 1°C. The uncertainty intervals of precipitation change are quite broad, but the mean estimate is one of a marked increase in the north in winter and a drastic reduction in the south in summer. In the RCM simulations driven by a single global model, the spread of the temperature and precipitation projections tends to be smaller than that in the GCM simulations, but it is possible to reduce this disparity by employing several driving models for all RCMs. In the present suite of simulations, the difference between the mean GCM and RCM projections is fairly small, regardless of the number or driving models applied.     

QM和QDM方法对中国极端气候的高分辨率气候变化模拟的误差订正对比

采用分位数映射（Quantile Mapping, QM）和delta分位数映射（Quantile Delta Mapping, QDM）两种误差订正方法对区域气候模式RegCM4在中国区域内模拟的逐日气温和降水数据进行订正。模式数据是5种不同全球气候模式驱动下的区域模式气候变化模拟结果。计算订正前后的极端气候指数进行对比分析,包括日最高气温极大值（TXx）、日最低气温极小值（TNn）、连续干旱日数（CDD）和最大日降水量（RX1day）。结果表明,5组模拟结果和其集合平均（ensR）都显示气温指数的模拟效果高于降水指数,其中对TXx模拟最好,对CDD的模拟最差;经过订正后,针对不同模式的两种订正结果都能够有效地减小模式与观测的偏差并提高了空间相关系数,且两种方法的订正效果无明显差别。对RCP4.5情景下未来变化的分析中,QM在一定程度上改变了模式模拟的未来变化幅度和空间分布特征,QDM则能够有效地保留所有极端指数的气候变化信号。从全国平均来看,除CDD外,所有指数未来都呈现增加趋势,且QDM订正结果与订正前模式模拟的变化趋势更为接近。建议在气候变化模拟的误差订正中采用QDM方法。