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1.
Summary This paper presents a study of the sensibility of the Penman-Monteith evapotranspiration model to climatic (available energy and vapour pressure deficit) and parametric (aerodynamic and canopy resistances, r a and r c respectively) factors in a semi-arid climate, for crops in contrasting water status (well irrigated and under water stress) and of different heights. Three experiments were carried out in southern Italy on reference grass (≈ 0.1 m), grain sorghum (≈ 1 m) and sweet sorghum (≈ 3 m). For this analysis the sensitivity coefficients, taken as hourly means, were evaluated during the growth season when the crops completely covered the soil. The relative errors on evapotranspiration were also evaluated for r a and r c . The results showed that, for reference grass, available energy and aerodynamic resistance play a major role. For crops under water stress the most important term to evaluate is canopy resistance. For a tall crop, as sweet sorghum, the role of the vapour pressure deficit is fundamental, both when the crop is in good water status and under water stress. Received July 14, 1997 Revised February 5, 1998  相似文献   

2.
Energy balance comparison of sorghum and sunflower   总被引：3，自引：0，他引：3  
Summary An understanding of the energy exchange processes at the surface of the earth is necessary for studies of global climate change. If the climate becomes drier, as is predicted for northern mid-latitudes, it is important to know how major agricultural crops will play a role in the budget of heat and moisture. Thus, the energy balance components of sorghum [Sorghum bicolor (L.) Moench.] and sunflower (Helianthus annuus L.), two drought-resistant crops grown in the areas where summertime drying is forecasted, were compared. Soil water content and evapotranspiration (ET) rates also were determined. Net radiation was measured with net radiometers. Soil heat flux was analyzed with heat flux plates and thermocouples. The Bowen ratio method was used to determine sensible and latent heat fluxes. Sunflower had a higher evapotranspiration rate and depleted more water from the soil than sorghum. Soil heat flux into the soil during the daytime was greater for sorghum than sunflower, which was probably the result of the more erect leaves of sorghum. Nocturnal net radiation loss from the sorghum crop was greater than that from the sunflower crop, perhaps because more heat was stored in the soil under the sorghum crop. But daytime net radiation values were similar for the two crops. The data indicated that models of climate change must differentiate nighttime net radiation of agricultural crops. Sensible heat flux was not always less (or greater) for sorghum compared to sunflower. Sunflower had greater daytime values for latent heat flux, reflecting its greater depletion of water from the soil. Evapotranspiration rates determined by the energy balance method agreed relatively well with those found by the water balance method. For example, on 8 July (43 days after planting), the ET rates found by the energy-balance and water-balance methods were 4.6 vs. 5.5 mm/day for sunflower, respectively; for sorghum, these values were 4.0 vs. 3.5 mm/day, respectively. If the climate does become drier, the lower soil water use and lower latent heat flux of sorghum compared to sunflower suggest that sorghum will be better adapted to the climate change.Contribution from the Kansas Agricultural Experiment Station. F. Rachidi is now with the Département d'Écologie Végétale et Pastoralisme, École Nationale d'Agriculture, Meknès, Morocco, and E. T. Kanemasu is now with the Department of Agronomy, University of Georgia, Griffin, Georgia, U.S.A.With 5 Figures  相似文献   

3.
Summary The evaporation of deep crops such as forests is usually considered in terms of the two-resistance Penman-Monteith model, though this conflates two of the three resistances actually involved, i.e. the canopy resistancer c between the transpiring leaves and the top of the canopy, and the resistancer s due to the stomates of the leaves. A review of the literature on these and the aerodynamic resistancer a (between the crop and the atmosphere) shows how distinctly different they are, and therefore how inappropriate it is to lump any two together.Once the soil has dried substantially,r s depends approximately onM –2, whereM is the fractional available soil moisture.As regards grassed surfaces,r a is 300/u s m–1, whereu is the wind speed at 2 m.With 2 Figures  相似文献   

4.
The present study evaluates firstly the ability of the FAO-56 methodology, based on the two-step approach “reference evapotranspiration (ET0)—crop coefficient (K c),” to accurately determine the actual evapotranspiration (ET) of irrigated crops and proposes, secondly, the alternative approaches for improving this determination. The FAO-56 methodology is supported by two hypotheses: (1) ET0 represents all effects of weather and (2) K c varies predominately with specific crop characteristics and only marginally with climate, which enables the transfer of K c standard values among locations and climates. On the base of the theoretical analysis and experimental observations, a critical examination of the previous hypotheses demonstrates that they are not verified by reality. The first hypothesis is not verified for two reasons: (a) The formulation adapted by the Penman–Monteith equation and proposed in FAO-56 methodology for calculating ET0 uses climatic variables determined at a 24-h average scale. However, in principle it is only valid in permanent regime, in other words at least on an hourly scale. (b) The FAO-56-proposed formulation attributes a constant value to the canopy resistance of the reference surface; but in reality, this resistance is variable in relation to the climatic variables. The second hypothesis, concerning the two-step approach, is also not verified because the values of K c largely vary in relation to climatic variables (radiation, air vapour pressure deficit and wind speed). This fact does not support the possibility of the transferability of K c values into locations where the local conditions deviate from the conditions where the adjusted values of K c were determined. The weakness of the ET estimation, observed on several crops cultivated in the Mediterranean region, through the application of the FAO-56 methodology, is the result of errors accumulation, associated with that affects the determination of either ET0 or K c. The present study underlines the advantage of using a one-step approach in the calculation of ET, since it is based on fewer computation steps and, consequently, on fewer error sources than the two-step model. Two models adopting this approach are proposed and validated, one of which can be considered as operational, i.e. it only needs standard meteorological data as input. The use of these models enables an improvement of the ET estimation. This objective is a key component of any strategy to improve agricultural water management in Mediterranean region.  相似文献   

5.
Direct calculation of actual evapotranspiration ETc based on Penman-Monteith type models gives more accurate values than indirect models, which need the determination of reference evapotranspiration and crop coefficient. However, the direct models need the measurement of weather variables above the crop, which is limiting and not easily feasible in practice. An operational version of a known ETc direct model is described and tested. This new version is based on the determination of the weather variables collected in a standard agro-meteorological station. The original and the operational versions of the ETc model were validated on two crops with contrasting height: soybean (0.8 m) and sweet sorghum (3 m). For soybean, ETc calculated with the two versions gave results very similar at both hourly and daily scales. For sweet sorghum, ETc calculated with the operational version is good at daily scale and not as good, although acceptable, at the hourly scale.  相似文献   

6.
This paper analyzes the impact of climate, crop production technology, and atmospheric carbon dioxide (CO2) on current and future crop yields. The analysis of crop yields endeavors to advance the literature by estimating the effect of atmospheric CO2 on observed crop yields. This is done using an econometric model estimated over pooled historical data for 1950–2009 and data from the free air CO2 enrichment experiments. The main econometric findings are: 1) Yields of C3 crops (soybeans, cotton, and wheat) directly respond to the elevated CO2, while yields of C4 crops (corn and sorghum) do not, but they are found to indirectly benefit from elevated CO2 in times and places of drought stress; 2) The effect of technological progress on mean yields is non-linear; 3) Ignoring atmospheric CO2 in an econometric model of crop yield likely leads to overestimates of the pure effects of technological progress on crop yields of about 51, 15, 17, 9, and 1 % of observed yield gain for cotton, soybeans, wheat, corn and sorghum, respectively; 4) Average climate conditions and climate variability contribute in a statistically significant way to average crop yields and their variability; and 5) The effect of CO2 fertilization generally outweighs the effect of climate change on mean crop yields in many regions resulting in an increase of 7–22, 4–47, 5–26, 65–96, and 3–35 % for yields of corn, sorghum, soybeans, cotton, and wheat, respectively.  相似文献   

7.
Evapotranspiration is a major component of both the energy and water balances of wetland tundra environments during the thaw season. Reliable estimates of evapotranspiration are required in the analysis of climatological and hydrological processes occurring within a wetland and in interfacing the surface climate with atmospheric processes. Where direct measurements are unavailable, models designed to accurately predict evapotranspiration for a particular wetland are used.This paper evaluates the performance, sensitivity and limitations of three physically-based, one-dimensional models in the simulation of evaporation from a wetland sedge tundra in the Hudson Bay Lowland near Churchill, Manitoba. The surface of the study site consists of near-saturated peat soil with a sparse sedge canopy and a constantly varying coverage of standing water. Measured evaporation used the Bowen ratio energy balance approach, to which the model results were compared. The comparisons were conducted with hourly and daily simulations.The three models are the Penman-Monteith model, the Shuttleworth-Wallace sparse canopy model and a modified Penman-Monteith model which is weighted for surface area of the evaporation sources.Results from the study suggest that the weighted Penman-Monteith model has the highest potential for use as a predictive tool. In all three cases, the importance of accurately measuring the surface area of each evaporation source is recognized. The difficulty in determining a representative surface resistance for each source and the associated problems in modelling without it are discussed.

List of Symbols

Models BREB Bowen ratio energy balance - P-M Penman-Monteith combination - S-W Shuttleworth-Wallace combination - W-P-M Weighted Penman-Monteith combination Other AE Available energy-all surfaces - AE c Available energy-canopy (S-W, W-P-M) - AE s Available energy-bare soil (S-W, W-P-M) - AE w Available energy-open water (W-P-M) - C p Specific heat of air - D Vapor pressure deficit - DAI Dead area index - FAI Foliage area index - LAI Leaf area index - Q * Net radiation - Q e Latent heat flux-total - Q ec Latent heat flux-canopy (S-W, W-P-M) - Q es Latent heat flux-bare soil (S-W, W-P-M) - Q ew Latent heat flux-open water (W-P-M) - Q g ground heat flux - Q h Sensible heat flux - S Proportion of area in bare soil - W Proportion of surface in open water - r a Aerodynamic resistance (P-M, W-P-M) - r c Canopy resistance - r s Generalized optimized surface resistance - r st Stomatal resistance - r c a Bulk boundary layer resistance (S-W) - r s a Aerodynamic resistance below mean canopy level (S-W) - r s s Soil surface resistance (S-W, W-P-M) Greek Bowen ratio - Psychrometer constant - Air density - Slope of saturation vapour pressure vs temperature curve  相似文献   

8.
黄淮海平原冬小麦最大可能蒸散的估算   总被引：1，自引：1，他引：0       下载免费PDF全文
作物最大可能蒸散考虑了作物及当地地表状况,为当地地表实际覆盖情况下实际蒸散的理论上限值,能客观分析作物对水分的需求程度和农业干旱状况。基于遥感（叶面积指数和地表反照率）数据和逐日气象数据,利用Penman-Monteith公式,计算黄淮海平原小麦种植区27个气象站冬小麦生育期2000-2015年逐日蒸散,提取得到冬小麦生育期逐日最大可能蒸散数据集,并分析其时空变化特征及成因。结果表明:与联合国粮农组织（FAO）单作物系数法计算的最大可能蒸散Ek对比,区域平均最大可能蒸散Ec的时间变化趋势与Ek一致,空间分布上Ec符合客观实际。黄淮海平原冬小麦全生育期、越冬期和返青-拔节期Ec均呈北低南高的分布特征,日平均值分别为1.99 mm,0.44 mm和2.75 mm;其余3个生育期（越冬前、抽穗期、乳熟-成熟期）在空间分布上差异不大,日平均值分别为1.23 mm,4.71 mm和3.74 mm。冬小麦不同生育期（含全生育期）Ec的空间分布主要受叶面积指数分布特征的影响,二者呈显著正相关关系。  相似文献   

9.
Influence of drizzle on Z–M relationships in warm clouds   总被引：1，自引：0，他引：1  
This paper addresses the sensitivity of the relationships between radar reflectivity (Z) and liquid water content (M) for liquid water clouds to microphysical drizzle parameters by means of simulated radar observation at a frequency of 3 GHz of modeled cumulus clouds. A power law relationship for non drizzling clouds with water content as high as 3 gm− 3: Zc = 0.026 Mc1.61 is numerically derived and agreed with previous empirical relationships relative to cumulus and stratocumulus. This relationship is then used to explore the influence of drizzle on the correlation between radar reflectively and water content. Due to their large diameters with respect to cloud droplets, drizzle sized drops dominate radar reflectivity but do not carry the cloud water content so that reflectivity and liquid water content are expected to be not correlated in clouds containing drizzle. It is shown that for congestus or extreme congestus cumuli, microphysical conditions for which the Zc–Mc relationship can be used with a tolerance of 5 and 10% are provided whereas for humilis or mediocris cumuli, the presence of drizzle breaks down the Zc–Mc relationship whatever the situations.  相似文献   

10.
We use the CERES family of crop models to assess the effect of different spatial scales of climate change scenarios on the simulated yield changes of maize (Zea mays L.), winter wheat (Triticum aestivum L.),and rice (Oryza sativa L.) in the Southeastern United States. The climate change scenarios were produced with the control and doubled CO2 runs of a high resolution regional climate model anda coarse resolution general circulation model, which provided the initial and lateral boundary conditions for the regional model. Three different cases were considered for each scenario: climate change alone, climate change plus elevated CO2, and the latter with adaptations. On the state level,for most cases, significant differences in the climate changed yields for corn were found, the coarse scale scenario usually producing larger modeled yield decreases or smaller increases. For wheat, however, which suffered large decreases in yields for all cases, very little contrast in yield based on scale of scenario was found. Scenario scale resulted in significantly different rice yields, but mainly because of low variability in yields. For maize the primary climate variable that explained the contrast in the yields calculated from the two scenarios is the precipitation during grain fill leading to different water stress levels. Temperature during vernalization explains some contrasts in winter wheat yields. With adaptation, the contrasts in the yields of all crops produced by the scenarios were reduced but not entirely removed. Our results indicate that spatial resolution of climate change scenarios can be an important uncertainty in climate change impact assessments, depending on the crop and management conditions.  相似文献   

11.
In unstable conditions, the set of equations defining the aerodynamic resistance to sensible heat transfer, r a , cannot be solved analytically. An iterative technique must be used to obtain r a exactly, but this is cumbersome and time consuming. In this paper, a new, empirical equation is presented relating the ratio, Q, of the aerodynamic resistances in neutral and unstable conditions, to the bulk Richardson number, Ri B . The equation takes the form Q = a + b(–Ri) c , where a, b and c are empirical functions of (z – d)/z om . This model is shown to predict r awith a mean absolute error of 0.06 s m–1 over the ranges -15 < Ri B < 0 and 10 < (z – d)/z om < 2300. Statistical comparison with other equations that have been proposed for r a in unstable conditions indicates the superior precision of the model presented here.  相似文献   

12.
To investigate the alfalfa crop response to environmental factors, a Bowen ratio-energy balance method was used to evaluate short-term alfalfa canopy resistance. Continuous evapotranspiration (ET a ) and the aerodynamic resistance (r a ) for an alfalfa crop in each 20-min interval were calculated. Using the calculated ET a and r a and the Penman-Monteith approach, the bulk stomatal or actual canopy resistance (r c ) was evaluated. The continuous 20-min resistances were computed for clear and partially cloudy sky conditions, and different average crop heights. The results show that this technique can satisfactorily be used to study the manner in which the aerodynamic and canopy resistances respond to short-term variations in weather elements such as photosynthetically active radiation (PAR), wind speed and atmospheric saturation vapor deficit.Research Assistant Professor and Assistant Utah State Climatologist, Research Associate Professor and Research Assistant, respectively.  相似文献   

13.
An integrated canopy micrometeorological model is described for calculating CO2, water vapor and sensible heat exchange rates and scalar concentration profiles over and within a crop canopy. The integrated model employs a Lagrangian random walk algorithm to calculate turbulent diffusion. The integrated model extends previous Lagrangian modelling efforts by employing biochemical, physiological and micrometeorological principles to evaluate vegetative sources and sinks. Model simulations of water vapor, CO2 and sensible heat flux densities are tested against measurements made over a soybean canopy, while calculations of scalar profiles are tested against measurements made above and within the canopy. The model simulates energy and mass fluxes and scalar profiles above the canopy successfully. On the other hand, model calculations of scalar profiles inside the canopy do not match measurements.The tested Lagrangian model is also used to evaluate simpler modelling schemes, as needed for regional and global applications. Simple, half-order closure modelling schemes (which assume a constant scalar profile in the canopy) do not yield large errors in the computation of latent heat (LE) and CO2 (F c ) flux densities. Small errors occur because the source-sink formulation of LE andF c are relatively insensitive to changes in scalar concentrations and the scalar gradients are small. On the other hand, complicated modelling frames may be needed to calculate sensible heat flux densities; the source-sink formulation of sensible heat is closely coupled to the within-canopy air temperature profile.  相似文献   

14.
The present study involves using the Canadian Climate Centre (CCC) climate change scenario to evaluate the impacts of a CO2-induced climate change on agriculture in Québec and vicinity. Climate change using the CCC General Circulation Model (GCM) data are fed into a crop model (FAO) so as to gauge the changes in agroclimatic factors such as growing season length and growing degree days, and subsequently potential yield changes for a variety of cereal (C3 and C4), leguminous, oleaginous, vegetable and special crops, for twelve major agricultural regions in southern Québec. Our results show that depending upon the agricultural zone and crop type, yields may increase (ex. corn and sorghum by 20%) or decrease (ex. wheat and soybean by 20 to 30%). Also, these crop yield changes appear to be related to acceleration in maturation rates, mainly to change in moisture stress and to shifts in optimal thermal growth conditions. These possible shifts in agricultural production potentials would solicit the formulation of appropriate adaptation strategies.  相似文献   

15.
Summary ?The performance of the Penman-Monteith (PM) equation to estimate daily reference evapotranspiration (ETO) was investigated by attributing three distinct features to the canopy resistance (r c): (i) r c constant at 70 s m−1 (Allen et al., 1998; FAO Irrigation and Drainage Paper n. 56), (ii) r c variable as linear function of a critical resistance r c, depending on weather variables and empirical parameters relating r c to r * (Katerji and Perrier, 1983; Agronomie, 3[6]: 513–521) and (iii) r c variable as a mechanistic function of weather variables only (Todorovic, 1999; J. Irrig. Drainage Eng., ASCE, 125[5]: 235–245). Daily weather and grass lysimeter data, measured for a period of seven years at Policoro (Southern Italy), were used. The results confirmed the relative robustness of the PM method with constant r c while better estimates were obtained only when variable r c was used. The mechanistic approach of Todorovic (1999) provided the best estimates, while the approach of Katerji and Perrier (1983), with empirically derived parameters, has shown to be not conservative enough to be extended to different locations without calibration. Received January 2, 2002; revised October 31, 2002; accepted December 7, 2002  相似文献   

16.
In this paper warm cloud microphysical parameters including cloud droplet number concentration (Nc), liquid water content (ql) and effective radius (re) from 75 flights around the Beijing area during 2005 and 2006 are summarized. Average Nc (cm− 3) for Cu, Sc, Ac, As and Ns are 376 ± 290, 257 ± 226, 147 ± 112, 60 ± 35 and 60 ± 84, respectively. Many records of high Nc above 1000 cm− 3 are observed. The large standard deviations indicate a large variation of Nc and ql in this region. The maxima of ql reach 1.4 g m− 3 in Cu and 1.0 g m− 3 in Sc, respectively. Different parameterizations of effective radius are examined with the in-situ data in this area. There are different ways to obtain the prefactor representing the relationship between effective radius and mean volume radius. Significant systematic errors are found to be at the large sizes when the prefactor is expressed with relative dispersion under the Gamma Distribution. Fixed prefactor of 1, which was widely used, even produces much larger error. A prefactor of 1.22 is found to be better than the former two methods by fitting with the observed data. The effective radius is further parameterized as functions of mean volume radius, liquid water content and cloud droplet number concentration. We suggest that the effective radius can be parameterized as re,p ≈ 1.20rv + 0.22–1.28/rv2, which is a practical and more accurate scheme without too much computation complexity.  相似文献   

17.
Summary In regions such as west Texas where water is scarce, changes in the water balance may have a significant impact on agricultural production and management of water resources. We used the mechanistic soil-plant-atmosphere simulation model ENWATBAL to evaluate changes in soil water evaporation (E) and transpiration (T) in cotton and grain sorghum that may occur due to climate change and elevated CO2 in west Texas. Climatic and plant factors were varied individually, and in combination, to determine their impact onE andT. Of the climatic factors,E was most sensitive to changes in vapor pressure, andT to changes in irradiance. Simulations suggest that if warming is accompanied by higher humidity, the impact of climate change may be minimal. However, if the climate becomes warmer and less humid,ET may increase substantially. Simulations also suggest that enhanced growth due to elevated CO2 may have a greater impact onET than climatic change.With 9 Figures  相似文献   

18.
Summary Simultaneous measurements of xylem sap flow and water vapour flux over a Scots pine (Pinus sylvestris) forest (Hartheim, Germany), were carried out during the Hartheim Experiment (HartX), an intensive observation campaign of the international programme REKLIP. Sap flow was measured every 30 min using both radial constant heating (Granier, 1985) and two types of Cermak sap flowmeters installed on 24 trees selected to cover a wide range of the diameter classes of the stand (min 8 cm; max 17.5 cm). Available energy was high during the observation period (5.5 to 6.9 mm.day–1), and daily cumulated sap flow on a ground area basis varied between 2.0 and 2.7 mm day–1 depending on climate conditions. Maximum hourly values of sap flow reached 0.33 mm h–1, i.e., 230 W m–2.Comparisons of sap flow with water vapour flux as measured with two OPEC (One Propeller Eddy Correlation, University of Arizona) systems showed a time lag between the two methods, sap flow lagging about 90 min behind vapour flux. After taking into account this time lag in the sap flow data set, a good agreement was found between both methods: sap flow = 0.745* vapour flux,r 2 = 0.86. The difference between the two estimates was due to understory transpiration.Canopy conductance (g c ) was calculated from sap flow measurements using the reverse form of Penman-Monteith equation and climatic data measured 4 m above the canopy. Variations ofg c were well correlated (r 2 = 0.85) with global radiation (R) and vapour pressure deficit (vpd). The quantitative expression forg c =f (R, vpd) was very similar to that previously found with maritime pine (Pinus pinaster) in the forest of Les Landes, South Western France.With 6 Figures  相似文献   

19.
As one of the key grain-producing regions in China, the agricultural system in the North China Plain (NCP) is vulnerable to climate change due to its limited water resources and strong dependence on irrigation for crop production. Exploring the impacts of climate change on crop evapotranspiration (ET) is of importance for water management and agricultural sustainability. The VIP (Vegetation Interface Processes) process-based ecosystem model and WRF (Weather Research and Forecasting) modeling system are applied to quantify ET responses of a wheat-maize cropping system to climate change. The ensemble projections of six General Circulation Models (GCMs) under the B2 and A2 scenarios in the 2050s over the NCP are used to account for the uncertainty of the projections. The thermal time requirements (TTR) of crops are assumed to remain constant under air warming conditions. It is found that in this case the length of the crop growth period will be shortened, which will result in the reduction of crop water consumption and possible crop productivity loss. Spatially, the changes of ET during the growth periods (ETg) for wheat range from ?7 to 0 % with the average being ?1.5?±?1.2 % under the B2 scenario, and from ?8 to 2 % with the average being ?2.7?±?1.3 % under the A2 scenario/consistently, changes of ETg for maize are from ?10 to 8 %, with the average being ?0.4?±?4.9 %, under the B2 scenario and from ?8 to 8 %, with the average being ?1.2?±?4.1 %, under the A2 scenario. Numerical analysis is also done on the condition that the length of the crop growth periods remains stable under the warming condition via breeding new crop varieties. In this case, TTR will be higher and the crop water requirements will increase, with the enhancement of the productivity. It is suggested that the options for adaptation to climate change include no action and accepting crop loss associated with the reduction in ETg, or breeding new cultivars that would maintain or increase crop productivity and result in an increase in ETg. In the latter case, attention should be paid to developing improved water conservation techniques to help compensate for the increased ETg.  相似文献   

20.
《Atmospheric Research》2008,87(3-4):297-314
This paper addresses the sensitivity of the relationships between radar reflectivity (Z) and liquid water content (M) for liquid water clouds to microphysical drizzle parameters by means of simulated radar observation at a frequency of 3 GHz of modeled cumulus clouds. A power law relationship for non drizzling clouds with water content as high as 3 gm− 3: Zc = 0.026 Mc1.61 is numerically derived and agreed with previous empirical relationships relative to cumulus and stratocumulus. This relationship is then used to explore the influence of drizzle on the correlation between radar reflectively and water content. Due to their large diameters with respect to cloud droplets, drizzle sized drops dominate radar reflectivity but do not carry the cloud water content so that reflectivity and liquid water content are expected to be not correlated in clouds containing drizzle. It is shown that for congestus or extreme congestus cumuli, microphysical conditions for which the Zc–Mc relationship can be used with a tolerance of 5 and 10% are provided whereas for humilis or mediocris cumuli, the presence of drizzle breaks down the Zc–Mc relationship whatever the situations.  相似文献   

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