一种大气污染物干沉积速率的计算方法及其应用

介绍了一种计算大气污染物干沉积速率的方法。这种方法详细地考虑了植物生理特征和冠层内湍流结构对干沉积的影响，考虑了3层覆盖物对表面阻抗的影响，通过计算7个不同的阻抗因子获得干沉积速率。利用该方法计算了农田下垫面上7种不同大气污染物沉积的表面阻抗和江西(鹰洋)红壤典型地区农田下垫面上的二氧化硫(SO2)和硫酸盐(SO4^2—)的干沉积速率，估算了大气硫输入农田生态系统的干沉积通量，并与其他方法作了定量比较。结果表明：农田下垫面上SO2与SO4^2—的干沉积速率平均值分别为0．31cm／s，0．20cm／s；干沉积速率具有明显的日变化特征，一般白天大于夜间，中午时分出现最大值；月际变化也较明显，在冬季有大值；大气硫输入农田生态系统的全年干沉积通量为7．35g/m^2。     

Dry deposition of particles to a pine plantation

There has been some controversy concerning the rate of deposition of particles having diameters near 1.0 m to vegetated surfaces. In this size range, the processes of Brownian diffusion and inertial impaction are not effective and deposition to smooth surfaces reaches a minimum. However, most measurements of deposition of micrometer diameter particles to vegetated surfaces indicate a greater deposition than extrapolation of the results from less rough surfaces would suggest. In this study, the aerodynamic profile method was used to estimate deposition to a pine plantation. The deposition velocities were found to be sensitive to the displacement height and the form of the profile stability correction used in the calculations. An analysis of a limited set of Bowen ratio data, collected over the same forest, suggests that the data are reasonably described by using a displacement height of 7.9 m and the stability correction proposed by Raupach (1979).The average deposition velocities, measured over a 9-month period were 0.0043, 0.0078, and 0.0092 m/s for the three diameter classes 0.5\2-1.0, 1.0\2-2.0 and 2.0\2-5.0 \gmm. These deposition velocities are lower than the corresponding aerodynamic conductance for the same periods, indicating that the deposition rate is limited by surface phenomena. Average surface conductances calculated for the three size classes of particles were 0.0060, 0.0141, and 0.0276 m/s, respectively. A multiple regression analysis showed high correlation between deposition velocity and wind speed. No other measured environmental factor or linear combination of factors was significantly correlated with deposition velocity.This paper was prepared in connection with work done under Contract No. DE-AC09-76R00001 with the U.S. Department of Energy. By acceptance of this paper, the publisher and/or recipient acknowledges the U.S. Government's right to retain a nonexclusive, royalty-free license in and to any copyright covering this paper, along with the right to produce and to authorize others to reproduce all or part of the copyrighted paper.     

中国东部地区SO2, SO4=和HNO3(g)干沉降速度的季节变化

使用中国东部及其邻近地区各主要台站１９９２年全年００点和１２点（ＧＭＴ）地面及探空资料，由中尺度气象预报模式ＭＭ４产生中国东部地区地面以上大约４０ｍ高度（最低模式层）处二维温度、湿度和风场，使用污染物干沉降模块及该地区下垫面类型资料，计算出了该地区ＳＯ２，ＳＯ＝４和ＨＮＯ３（ｇ）全年干沉降速度的区域分布和季节变化。结果表明，由于受气象条件和下垫面类型的综合影响，３种污染物的干沉降速度有明显的变化。对ＳＯ２，全年区域平均极小值为０．０８８ｃｍ／ｓ，极大值为１．２７５ｃｍ／ｓ，平均值为０．４３０ｃｍ／ｓ；对ＳＯ＝４，分别为０．０１４ｃｍ／ｓ，０．２８７ｃｍ／ｓ和０．１１８ｃｍ／ｓ；对ＨＮＯ３（ｇ），分别为０．０６０ｃｍ／ｓ，５．２５０ｃｍ／ｓ和１．１２３ｃｍ／ｓ。ＳＯ２干沉降速度极大值分布在巴丹吉林沙漠和腾格里沙漠一带，对ＳＯ＝４和ＨＮＯ３（ｇ），除在上述沙漠地带有一极大值区域外，在靠近四川的云贵高原尚有另一极大区。对１９９２年全年来说，ＳＯ２和ＨＮＯ３（ｇ）干沉降速度极大值均出现在七月份，分别为０．５５２ｃｍ／ｓ和１．５１８ｃｍ／ｓ；而对ＳＯ＝４，干沉降速度极大值出现在九月份，其值为０．０９６ｃｍ／ｓ。这些值     

利用次网格技术模拟华东地区大气硫氮沉降

采用数值模拟方法,在区域酸性沉降模式系统中引入次网格处理技术。通过4种次网格方案模拟结果的相互比较,选择最优方案,然后利用最优次网格方案,选取华东地区为例,进一步模拟研究大气硫氮沉降的空间分布。结果表明,就干沉积速率而言,以细网格方案(水平分辨率25 km)为参照,采用次网格方案比粗网格方案(水平分辨率75 km)有明显改进,其中“次网格风速与摩擦速度之积为常数”为最优次网格方案。华东地区硫的年总沉降量是1.92 mt(1 mt=106ton),氮的年总沉降量是0.65mt。华东地区硫化物(SO2、硫酸盐SO42-)干沉降量占总沉降量的49%,氮化物(NO、NO2、硝酸盐NO3-)干沉降量占总沉降量的80%,可见干沉降在大气沉降中具有重要地位。华东地区总的大气硫、氮沉降量中,70%以上到达有植被覆盖的土壤生态系统,这将对农田、草地和森林的硫素和氮素平衡有重要影响。此外,华东部分地区的硫沉降已经超过了临界负荷,而氮沉降尚未出现超临界负荷的现象。     

Size distributions of ambient air particles and enrichment factor analyses of metallic elements at Taichung Harbor near the Taiwan Strait

This work attempts to characterize metallic elements associated with atmospheric particulate matter on a dry deposition plate, a TE-PUF high-volume air sampler and a universal air sampler. Dry deposition fluxes of particulates and concentrations of total suspended particulate, fine (PM_2.5) and coarse (PM_2.5–10) particulate matters were collected at Taichung harbor sampling sites from August 2004 to January 2005. Chemical analyses of metallic elements were made using a flame atomic absorption spectrophotometer coupled with hollow cathode lamps. Concentrations of metal elements in the forms of coarse particles and fine particles as well as the coarse/fine particulate ratios were presented. Statistical methods such as correlation analysis, principal component analysis and enrichment factor analysis were performed to compare the chemical components and identify possible emission sources at the sampling sites. Metallic elements of Cu, Zn, Pb, Cr, Ni and Mg had higher EF_crust ratios in winter and spring than in summer and autumn. Diurnal and nocturnal variations of metallic element concentrations in fine and coarse particles were also discussed.     

Combining biology,chemistry, and meteorology in modeling and measuring dry deposition

The range of chemical, biological, and meteorological processes contributing to the net exchange of trace chemical species between the atmosphere and the underlying surface is examined, in the context of a multiple-resistance exchange model. For those chemical species known to be always depositing, the resistance model provides a means to formulate appropriate deposition velocities in a convenient manner; however, extension to other situations is not straightforward. Field data indicate that the multiple-resistance approach is appropriate for application to assess the dry deposition of ozone and sulfur dioxide, but is not as appropriate for nitrogen dioxide. Data obtained over agricultural crops suggest that canopy factors frequently dominate the overall exchange process. A trial program of dry deposition measurement based on application of parameterized deposition velocities was initiated late in 1984, and has demonstrated shortcomings in under-standing concerning several factors, most importantly the roles of surface emissions and wetness, and the scaling-up of laboratory results to describe vegetative canopies.     

Evaluate dry deposition velocity of the nitrogen oxides using Noah-MP physics ensemble simulations for the Dinghushan Forest,Southern China

There has been a rapid growth of reactive nitrogen (Nr) deposition over the world in the past decades. The Pearl River Delta region is one of the areas with high loading of nitrogen deposition. But there are still large uncertainties in the study of dry deposition because of its complex processes of physical chemistry and vegetation physiology. At present, the forest canopy parameterization scheme used in WRF-Chem model is a single-layer “big leaf” model, and the simulation of radiation transmission and energy balance in forest canopy is not detailed and accurate. Noah-MP land surface model (Noah-MP) is based on the Noah land surface model (Noah LSM) and has multiple parametric options to simulate the energy, momentum, and material interactions of the vegetation-soil-atmosphere system. Therefore, to investigate the improvement of the simulation results of WRF-Chem on the nitrogen deposition in forest area after coupled with Noah-MP model and to reduce the influence of meteorological simulation biases on the dry deposition velocity simulation, a dry deposition single-point model coupled by Noah- MP and the WRF-Chem dry deposition module (WDDM) was used to simulate the deposition velocity (V_d). The model was driven by the micro-meteorological observation of the Dinghushan Forest Ecosystem Location Station. And a series of numerical experiments were carried out to identify the key processes influencing the calculation of dry deposition velocity, and the effects of various surface physical and plant physiological processes on dry deposition were discussed. The model captured the observed V_d well, but still underestimated the V_d. The self-defect of Wesely scheme applied by WDDM, and the inaccuracy of built-in parameters in WDDM and input data for Noah-MP (e.g. LAI) were the key factors that cause the underestimation of V_d. Therefore, future work is needed to improve model mechanisms and parameterization.     

Effects of a Remotely Sensed Land Cover Dataset with High Spatial Resolution on the Simulation of Secondary Air Pollutants over China Using the Nested-grid GEOS-Chem Chemical Transport Model简

A number of remotely sensed land cover datasets with spatial resolutions ~〈 1 km have recently become available or are in the process of being mapped. The application of these higher resolution and more up-to-date land cover datasets in chemical transport models （CTMs） is expected to improve the simulation of dry deposition and biogenic emissions of non-methane volatile organic compounds （NMVOCs）, which affect ozone and other secondary air pollutants. In the present study, we updated the land cover dataset in the nested-grid GEOS-Chem CTM with the 1 km resolution GLC2000 land cover map and examined the resulting changes in the simulation of surface ozone and sulfate over China in July 2007. Through affecting the dry deposition velocities of ozone and its precursors, using GLC2000 in the dry deposition module can decrease the simulated surface ozone by 3% （up to 6 ppb） over China. Simulated surface sulfate shows an increase of 3% in northwestern China and a decrease of 1% in northern China. Applying GLC2000 in the biogenic emissions of the NMVOC module can lead to a 0.5--4.5 ppb increase in simulated surface ozone over East China, mainly driven by the larger cove~：age of broadleaf trees in East China in the GLC2000 dataset. Our study quantifies the large sensitivity to land cover dataset~ with different spatial resolutions and time periods of simulated secondary air pollutants over China, supporting ongoing research efforts to produce high resolution and dynamically updated land cover datasets over China, as well as for the globe.     

Observations on the use of analytical and numerical models for the description of transfer to porous surface vegetation such as lichen

Convective deposition of submicron-size aerosol to porous surface vegetation was studied by electrochemical simulation, under Reynolds and Schmidt similarity, to a rectangular array of closely-packed lichen and artificial wire roughness layers. Results, showing an approximate tenfold increase in deposition velocity over that of a flat plate placed at the same position, were compared with predictions made on the basis of various rough-surface transfer models, including those based on statistical eddy renewal, as well as with numerical solutions of the diffusion equation in statistically-renewed surface cavities. Most analytical models could be made to fit the observed data, at least for a limited range of flow velocities, but poorly known and poorly defined parameters limit their usefulness for predictive purposes; and their validity across a large variation in molecular diffusivity (or Schmidt number Sc) is generally not assured. Numerical models also depend on poorly substantiated physical assumptions but the effect of such assumptions on transfer can be calculated for a wider range of conditions than those permitting an analytical solution. This allows more direct feedback between model assumptions and calculated or observed transfer. Numerically calculated values for deposition velocity in air for Sc from 0.7 to 7000 and flow velocities from 0.2 to 5 m s^-1 are presented for different model assumptions, with values ranging from < 0.01 to > 1 cms^-1.     

On equilibrium profiles of suspended particles

A power law is often used to represent the vertical profile of uniform suspended particles above a horizontally homogeneous surface. It serves as an analytical solution representing an equilibrium between vertical turbulent diffusion and gravitational settling, andcan be used to extract settling velocity information from observed particle number density profiles. In this note, we analyse this situation and use a numerical model to investigate the temporal change of particle number density and of the net vertical flux due to turbulent diffusion and gravitational settling. The results show that the net flux approaches zero very slowly for small particles (w_s/ u_* < 1), and show that the power law does not hold for small particles. If the power law is used to extract settling velocities from observed vertical distributions of particle number density in these cases, the estimated settling velocity may be unrealistically large.     

华东典型地区大气硫沉降通量的观测和模拟研究

本文使用中国科学院常熟和鹰潭生态实验站和气象站的观测资料，应用区域酸沉降模式系统（RegADMS）和大叶阻力相似模型来研究华东地区不同下垫面条件上的大气硫沉降问题，定量估计了农田下垫面上大气硫化物的沉降通量。SO2和硫酸盐的干沉降速率使用大叶阻力相似模型来估计，使用与降水量有关的参数化方案来确定湿沉降系数。结果表明，常熟地区农田下垫面的大气硫沉降通量为19．0gm^-2 a^-1，其中干沉降占42％；而位于江西红壤地区的鹰潭站的大气硫沉降通量为10．4gm^-2a^-1，其中干沉降占83％。比较发现，两地硫干沉降通量绝对值相差不大，但其在总沉降通量中所占的份额有较大差异；常熟站的硫湿沉降通量比鹰潭站要大9．23gm^-2a^-1，该差异是由两地污染状况和气象条件的不同造成。华东地区的年硫沉降总量为1．88Mt（1Mt=10^6t），其中72．8％沉降在农田下垫面上。硫沉降中43％是干沉降，57％是湿沉降。     

Model analysis of the influence of gas diffusivity in soil on CO and H2 uptake

CO and H₂ uptake by soil was studied as a diffusion process. A diffusion model was used to determine how the surface fluxes (net deposition velocities) were controlled by in‐situ microbial uptake rates and soil gas diffusivity calculated from the 3‐phase system (solid, liquid, gas) in the soil. Analytical solutions of the diffusion model assuming vertical uniformity of soil properties showed that physical properties such as air‐filled porosity and soil gas diffusivity were more important in the uptake process than in the emission process. To incorporate the distribution of in‐situ microbial uptake, we used a 2‐layer model incorporating "a microbiologically inactive layer and an active layer" as suggested from experimental results. By numerical simulation using the 2‐layer model, we estimated the effect of several factors on deposition velocities. The variations in soil gas diffusivity due to physical properties, i.e., soil moisture and air‐filled porosity, as well as to the depth of the inactive layer and in‐situ microbial uptake, were found to be important in controlling deposition velocities. This result shows that the diffusion process in soil is critically important for CO and H₂ uptake by soil, at least in soils with higher in‐situ uptake rates and/or with large variation in soil moisture. Similar uptake rates and the difference in deposition velocity between CO and H₂ may be attributable to differences in CO and H₂ molecular diffusivity. The inactive layer is resistant to diffusion and creates uptake limits in CO and H₂ by soil. The coupling of high temperature and a thick inactive layer, common in arid soils, markedly lowers net CO deposition velocity. The temperature for maximum uptake of CO changes with depth of the inactive layer.     

沙尘传输路径上气溶胶浓度与干沉降通量的粒径分布特征

利用2002年春季中国北京、青岛和日本福冈3个地区的分级气溶胶浓度资料,结合改进的Wil-liams模型,分析了沙尘传输路径上空气动力学直径≤11μm气溶胶(PM11)浓度和干沉降通量的粒径分布特征,并估算了黄海海域春季PM11的干沉降通量及不同粒径气溶胶的贡献。结果表明:3个地区PM11浓度粒径分布在非沙尘时期呈双峰分布,两个峰值分别出现在细颗粒(<2.1μm)部分和粗颗粒(2.1～11μm)部分;沙尘时期,3个地区PM11浓度粒径分布均趋于单峰分布,峰值位于粗颗粒部分,并且越靠近沙尘源地,这种趋势越明显。较强沙尘天气时期,粗颗粒部分的浓度峰值粒径从沙尘源地附近到黄海西岸、东岸呈降低趋势,但在一般沙尘天气时期,这种现象并不明显。沙尘时期和非沙尘时期,3个地区粗颗粒的干沉降通量均随粒径增加而增大,细颗粒的干沉降通量随粒径的变化不明显。虽然沙尘时期粗颗粒沉降通量较非沙尘时期有明显增加,但粗颗粒对PM11干沉降通量的贡献与非沙尘时期相比,并没有明显的变化。较强沙尘天气时期,3个地区粗颗粒的干沉降通量明显高于一般沙尘天气时期;细颗粒的干沉降通量较一般沙尘天气时期略有增加。黄海海域春季沙尘时期PM11的干沉降通量约为31.70～58.59mg.m-2.d-1,非沙尘时期约为8.33～15.94mg.m-2.d-1。粗颗粒是黄海海域春季PM11干沉降通量的主要贡献者,约占PM11干沉降通量的94.2%以上。     

北京冬季降水粒子谱及其下落速度的分布特征

为了深入探讨北京冬季云降水的微物理特征,提高雷达反演冬季固态降水的精度和冬季降水的预报水平,利用PARSIVEL（Particle Size and Velocity）降水粒子谱仪所观测的冬季降水粒子谱,结合地面显微镜粒子图像和云雷达数据,对比分析了北京海坨山地区冬季过冷雨滴、霰粒、雪花、混合态降水的粒子谱和下落速度特征,得到主要结论如下:（1）霰粒降水过程的云顶最高,整层的含水量最大,低层的退偏振比（LDR）最小,粒子更接近于球形;降雪过程的云顶最低,云中含水量最少,低层的退偏振比较大;混合态降水过程的雷达回波强度和高度特征介于两者之间,但低层的退偏振比最大;（2）在云中上升或下沉气流及湍流的影响下,过冷雨滴、霰粒和雪的下落速度均对称分布于各自理论下落末速度曲线的两侧。因此可根据粒子浓度相对于其直径和速度分布的中轴线位置,判断出该段降水过程中的主要粒子形态;（3）冬季雪花、霰粒和混合态降水粒子下落速度分布的散度较雨滴更大,其原因是由于冷云降水过程的粒子形态复杂,且固态粒子下落过程中更容易受破碎、聚并和凇附等微物理过程影响;（4）在4种降水类型中,雪的平均直径和离散度最大,雨滴最小;混合态降水粒子的总数浓度最大,雨滴的总数浓度最低,并且4种降水类型的粒子数浓度、平均直径和离散度均随降水强度的增大而增大。      

白鹤滩水电站峡谷地形区的风特征研究

位居世界第二大的白鹤滩水电站地处金沙江下游峡谷区,频繁的大风给水电站建设和运行带来了严重影响。掌握水电站坝区大风变化规律,评估峡谷地形对风速的作用,有利于基于周围风场监测和预警峡谷区大风。根据水电站及周边观测资料,对坝区风的变化特征和峡谷地形作用进行了分析。(1)峡谷区最高频率的风向和最大平均风速的风向均为顺着峡谷的偏南风或偏北风,且偏北风频率达55%以上,峡谷锁定了流经气流。(2)坝区大风多发生在干季11月—次年5月,且夜间至清晨大风频率比日间高。干季峡谷风效应强,尤其在19时—次日08时。雨季峡谷风效应降低,局地山谷风增强,表现为山风比谷风持续时间长,08时和18时是山风和谷风交替时间。对应干季和夜晚大风频繁,说明峡谷风效应是影响大风的关键因子。(3)通过狭管效应分析马脖子和葫芦口大桥两个站之间的风速关系,表明峡谷地形使马脖子站风速加强为葫芦口大桥站的1.27倍。利用多种拟合方法建立的两站风速关系表明,当葫芦口大桥站为5m·s-1以下低风速,各方法都难以拟合峡谷区的风速,当风速在5.0～11.5m·s-1时,狭管效应对风速拟合最优,准确率超过70%,对11.5m·s-1以上强风速,多项式拟合效果较优,准确率接近65%。     

二氧化硫干沉降的测量

通过在成都市郊对二氧化硫气体浓度和气象要素进行同步梯度观测,得到二氧化硫的干沉降速度.总结了影响二氧化硫干沉降速度的主要因子及日变化规律,发现其干沉降速度白天大于夜间,并在白天午后15时前后出现极大值,夜间2时前后出现极小值,平均沉降速度为1—1.5cm/s,且随稳定度的增加干沉降速度减小.     

Flow distortion errors caused by rigid obstacles in dry deposition measurement systems

Flow distortion errors on wind and friction velocity induced by a box simulating the housing of a gas analyzer used in dry deposition eddy correlation measurements were determined in a field experiment. ‘Undisturbed’ and ‘disturbed’ wind and friction velocities, measured with two dry deposition monitoring systems run simultaneously, were compared, one to the other. In the ‘disturbed’ case the box was mounted below the 3-component probe of the sonic anemometer of one of these systems, while in the ‘undisturbed’ case the box was removed. When the probe was located on the upstream side of the box, the results showed satisfactory agreement with theoretical estimates using Wyngaard’s potential-flow approach and a spherical model for the box. This model can be applied to obtain first-order corrections for flow distortion errors induced by cubic-like (or spherical) obstacles such as a gas analyzer housing used in dry deposition research systems, or to determine the optimal location of this housing relative to the sonic probe in such systems. When the probe was located halfway downstream and halfway to the side of the box, the experimental flow distortion errors did not exceed those for the upstream case. This implies that to keep flow distortion errors in dry deposition systems as small as possible the sonic probe can be placed upstream but also to the side of the gas analyzer housing. The results of our experiments also confirmed that correcting for flow distortion with the commonly used tilt equations yields underestimated values.     

颗粒物干沉降对AERMOD模型预测大气污染的影响

AERMOD模型是《环境影响评价技术导则—大气环境》中的推荐模式。为了更好地验证颗粒物干沉降作用对该模型预测结果的影响,选取福州市的煤堆场作为面源污染源,对预测范围内所有网格点PM10、TSP最大地面浓度进行预测。结果表明：所有网格点TSP地面浓度考虑干沉降时,约为不考虑干沉降时的0.13;PM10地面浓度考虑干沉降时,约为不考虑干沉降时的0.70,干沉降对TSP的影响大于PM10。同一粒径分布下,密度对颗粒物干沉降的影响较大,密度增加对可吸入颗粒物干沉降的影响大于总悬浮颗粒物,当密度大于3 g.cm-3时,所有网格点PM10与TSP地面浓度比值的平均值接近于0.98,认为粒径大于10μm的颗粒物基本完全沉降。此后,随着密度增加网格点处地面浓度的减小主要由PM10的沉降引起。AERMOD考虑干沉降时,距离污染源中心500 m外的网格点处地面浓度,PM10/TSP〉0.98,大于10μm的粗颗粒几乎完全沉降。     

A NEW DRY DEPOSITION VELOCITY PATTERN AND ITS PRACTICAL APPLICATION IN HIGH RESOLUTION REGIONAL ACID DEPOSITION MODEL*

A new dry deposition velocity pattern (NDDVP) for the study of region-scale dry deposition processes is developed. The mean ratio between NDDVP and 1022 experimental data of dry deposition velocity V_d is 1.06±0.82. The result shows that NDDVP is well consistent with experimental data. Practical cases are forecasted by the high resolution regional acid deposition model (EM3) with both NDDVP and old V_d pattern. The maximum ratio between the central concentrations for SO₄^- can reach 2.4 only due to different V_d patterns. 3-D distributions of species concentrations and dry depositions forecasted by NDDVP are better than those by the old V_d pattern.     

Fluxes of gases and particles above a deciduous forest in wintertime

Eddy-correlation measurements of the vertical fluxes of ozone, carbon dioxide, fine particles with diameter near 0.1 m, and particulate sulfur, as well as of momentum, heat and water vapor, have been taken above a tall leafless deciduous forest in wintertime. During the experimental period of one week, ozone deposition velocities varied from about 0.1 cm s^–1 at night to more than 0.4 cm s^-1 during the daytime, with the largest variations associated primarily with changes in solar irradiation. Most of the ozone removal took place in the upper canopy. Carbon dioxide fluxes were directed upward due to respiration and exhibited a strong dependence on air temperature and solar heating. The fluxes were approximately zero at air temperatures less than 5 °C and approached 0.8 mg m^–2 s^–1 when temperatures exceeded 15 °C during the daytime. Fine-particle deposition rates were large at times, with deposition velocities near 0.8 cm s^–1 when turbulence levels were high, but fluxes directed upward were found above the canopy when the surface beneath was covered with snow. Diffusional processes seemed to dominate fine-particle transfer across quasilaminar layers and subsequent deposition to the upper canopy. Deposition velocities for particulate sulfur were highly variable and averaged to a value small in magnitude as compared to similar measurements taken previously over a pine forest in summer.