A Broadband Microwave Radiometer Technique

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A Broadband Microwave Radiometer Technique at X-band for Rain and Drop Size Distribution Estimation
Robert Meneghini, Senior Member, IEEE
Abstract—Radiometric brightness temperatures below about 12 GHz provide accurate estimates of path attenuation through precipitation and cloud water. Multiple brightness temperature measurements at X-band frequencies can be used to estimate rainfall rate and parameters of the drop size distribution once correction for cloud water attenuation is made. Employing a stratiform storm model, calculations of the brightness temperatures at 9.5, 10, and 12 GHz are used to simulate estimates of pathaveraged median mass diameter, number concentration, and rainfall rate. The results indicate that reasonably accurate estimates of rainfall rate and information on the drop size distribution can be derived over ocean under low to moderate wind speed conditions. Index Terms—Airborne radiometer, drop size distribution, microwave radiometry, rain rate estimation, spaceborne radiometer.
I. INTRODUCTION OR FREQUENCIES up to about 12 GHz, the radiometric brightness temperature from rain over ocean is closely related to the path integrated attenuation (PIA) for low to moderate surface wind speeds. Multifrequency measurements of brightness temperature at X-band (8.2–12.4 GHz) over a bandwidth of 2–3 GHz, in principle, provide sufcient information to estimate parameters of the drop size distribution and rainfall rate. The purpose of this paper is to derive equations for and investigate the feasibility of this type of parameter estimation. The instrument concept is similar to that used in the steppedfrequency microwave radiometer (SFMR). In the SFMR, multiple bands in the frequency range from 4.6–7.2 GHz are used to estimate rainfall rate and near-surface wind speed over the ocean [1], [2]. Here, the emphasis is different in the sense that the objective is to estimate parameters of the path-averaged drop size distribution (DSD) and rain rate using X-band frequencies. The approach considered here is also related to that used for estimation of DSD parameters from multifrequency transmission measurements along a microwave link [3]–[5]. In essence, two path-attenuation measurements yield two parameters of the exponential form of the DSD or, equivalently, two parameters of the gamma DSD with the shape parameter, , xed or expressed as a function of one of the variable parameters [6]. There are, however, several complicating factors in the application of this technique to microwave radiometry. The rst is that con-
F
to path-integrated attenuversion of brightness temperature ation is not one-to-one: changes in the characteristics of the mixed-phase particles and scattering contributions from the ice to and water introduce uncertainty in the conversion of that translate into estimation errors. Cloud liquid water presents a somewhat different problem. Cloud droplets are Rayleigh scatterers/absorbers within the frequency band of interest so that the functional dependence of the specic attenuation on frequency is known. This contribution can be eliminated in part by considering the difference of path attenuations with suitable normalizations. Once the rain parameters are estimated from differential quantities, the cloud liquid water, in principle, can be recovered from the equation for total path attenuation. For operation below or above X-band, the error sources become larger. Below X-band, the differential attenuation is typically small and the relative errors in the estimate render the estimates inaccurate. While the differential attenuation is relatively strong above 12 GHz, greater scattering contributions from ice and snow, as well as the rain itself, introduce to – relationship, an increasing amount of variability into the making the estimation of DSD parameters impractical. The use of closely spaced frequencies has also been considered for airborne and spaceborne weather radars [7], [8]. For radar, the differential reectivity factor serves as an estimator of , of rain as well as snow. For the the median mass diameter, X-band radiometer, a ratio of normalized differential path attenuations, derived from brightness temperatures, provides an estimator for the path-averaged median mass diameter of the rain. In a sense, the radiometer-based algorithm is more straightforward: for the radar application, correction for attenuation must be made before the differential reectivity can be used whereas for the radiometer algorithm, a function of the differential attenuation serves as a direct estimator of the path-averaged in rain. As in most applications of air- or spaceborne radar and radiometer to precipitation, the primary advantage of the radar is its range-proling capability while the attractions of the microwave radiometer are higher reliability, lower cost, and, typically, more rapid scanning capabilities. II. ALGORITHM CONSIDERATIONS The rst objective is to express parameters of the DSD and rain rate as functions of the PIA or differential PIA. In the following section, these quantities are related to the brightness temperatures so that a connection is made between the measurements and the quantities to be estimated.
Manuscript received April 5, 2004; revised September 3, 2004. The author is with NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA (e-mail: Robert.Meneghini-1@https://www.wendangku.net/doc/565249795.html,). Digital Object Identier 10.1109/TGRS.2004.839590
U.S. Government work not protected by U.S. copyright.

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Let be the PIA (decibels) at frequency (hertz) from ) to the surface ( ), and let the storm top (range be the specic attenuation (dB km ) at . The and are related by quantities (1) The specic attenuation consists of terms corresponding to contributions from rain, snow, mixed-phase precipitation, as well as cloud liquid and cloud ice and various atmospheric gases such as water vapor and oxygen. Although the effects of atmospheric gases will be assessed in the error analysis given later, for the purpose of constructing estimators of the DSD parameters, we assume that the contributions from rain and mixed-phase preand that from cloud liquid water dominate so cipitation that (2) As the cloud water droplets much smaller than the wavelengths of interest, can be related to the cloud water content (grams per cubic meter) by [9] Im (3)
If brightness temperature measurements are available at fre) then the difference of the normalized quencies , ( path attenuations can be written (9) Assuming for either value of that (10) then an approximation for the normalized differential path attenuation, independent of cloud liquid water, is
(11) To understand how information on the raindrop size distribution can be obtained from the measurements, we write the drop di(per cubic meter per millimeter) at ameter distribution as (12) where is the number concentration (per cubic meter). For the can be expressed as [10] log-normal distribution (13) and for the Gamma distribution as [11] (14) where, in general, , for the log-normal distribution and , for the Gamma distribution are functions of height. In the numerical results presented later, we use the median mass diameter where [10], [11] (15) for the Gamma distribution and (16) for the log-normal distribution. In the following equations, we assume the Gamma parameterization; equations for the log-normal parameterization can with . The be obtained by replacing can be expressed in specic attenuation from precipitation terms of the drop diameter distribution and the extincby tion cross section (17) is in decibels per kilometer and taking Noting that to be in square meters and in units per cubic meter, . Substituting (17) into (11) gives then
where is the speed of light (centimeters per second) and is the dielectric factor related to the complex index of refraction of water by (4) is a function The imaginary part of the dielectric factor Im or height. To remove, in an of frequency and temperature approximate sense, the inuence of cloud water on the DSD and rain rate estimates, consider the following two normalization factors: (5a) Im (5b)
where in (5b) is the estimated mean temperature of the cloud gives droplets. Normalizing (3) by (6) where or and where Im Im Im (7a) (7b)
by and letting then, on Dividing using (1)–(3), the normalized path attenuation can be written (8)
(18)

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where
An estimate of the path-averaged rain rate (millimeters per hour) follows from the denition of this quantity along with and obtained from the previous equations (19) (25)
Although not written as such, varies with height because of the temperature dependence of . Just as it at some mean cloud droplet temis necessary to evaluate perature, a mean raindrop temperature must be used to evaluate in the estimates. Implicit in the equations below is is independent of height and the assumption that that, for the estimation procedure, the extinction cross sections must be computed at a xed temperature. Errors that arise from this will be discussed in Section V. An interchange in the order of integration in (18) gives
where the velocity distribution of raindrops second) is approximated by [12]
(meters per
(26) where is in millimeters in (25) and (26) so that (27) As shown by the equations above, measurements of path attenuation are needed at a minimum of three frequencies to estimate and of the the path-averaged rain rate and the parameters drop size distribution. Although (23), which provides an esti, is independent of the effective range, , through mate of and . In the case the precipitation, this is not the case for of stratiform rain, the effective range would include the melting layer and rain but not the dry snow above the melting layer, an estimate of which would require either the detection of the melting layer by radar or an estimate of the surface temperature and lapse rate.
(20) Replacing the inner integral with the approximation (21) allows (18) to be written (22) Although and yield the path-averaged number concentration and slope parameter only for range-independent drop size distributions, these will be taken to be the estimated values of these quantities. If we have access to brightness temperatures measured at three frequencies, then, using the approximation (22), the ratio (or ) yields a quantity independent of the mean number concentration and approximately independent of cloud water (23) If is a constant or a function of , then (23) can be solved nu. Once has been found, follows from merically for or (22). Next, can be estimated from and : this determines from and using esthe rst term of (8). Estimating and from (22) and (23), respectively, provides timates of . Specically, from (8), the integrated cloud water content, with in (7) taken to be unity, an estimator of is
III. CONVERSION OF BRIGHTNESS TEMPERATURE TO PATH ATTENUATION To use the equations given in the previous section, the brightness temperatures must be related to the PIA or differential PIA. to the We begin by relating the brightness temperature PIA by [13], [14] (28) where is a constant brightness temperature. Recalling that is dened by (9), the differential normalized PIA and letting (29) then (28) implies that can be expressed in the following form: (30) where (31) (32)
(24) where can be any of the frequencies at which the brightness temperature is measured.
Although the coefcients in (30) can be expressed in terms and in (28), a more accurate procedure is to generate of , ; from model storms and determine the and coefcients by linear regressions.

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TABLE I COEFFICIENTS c (f ), c (f ) IN A(f ) = c (f ) + c (f ) ln[T T = 280 K
0T
(f )];
TABLE II
COEFFICIENTS, WITH T = 280 K A (f ; f ) = + ln(T T (f ) + ln(T
0
0T
(f ))
Fig. 1.
(Top) Vertical proles of measured radar reectivity factor,
Z (9:5 GHz), (second from top) Proles of differential radar reectivity factor, Z (12 GHz; 9:5 GHz), (third from top) brightness temperature, T (9:5 GHz), and (bottom) differential brightness temperature, T (12 GHz) T (9:5 GHz),
for the baseline storm and surface model.
0
IV. STORM MODEL AND BRIGHTNESS TEMPERATURE CALCULATIONS We construct a simple model of stratiform rain by the following procedure [6]. From ground-based disdrometer-measured drop size distributions the number concentration and are calculated. Next, a best t median mass drop diameter is computed either for each DSD or for the ensemble. For . As can be seen from (14) and the results here, we use (15), this information species a gamma distribution of drop diameters which is then used to characterize the distribution along an entire vertical column of precipitation. The procedure is repeated for a series of measured drop size distributions so that a set of such gamma distributions (and the corresponding vertical columns) are generated. The height of the rain layer is xed at 4 km; above this, a melting layer and snow layer are appended. In the melting region, the model of Yokoyama and Tanaka [15] is used along with the effective medium or Bruggeman approximation [16] for the effective dielectric constant of mixed-phase hydrometeors. Above the 0 isotherm, a 1-km layer of snow is added where the particle mass density is taken to be either 0.05 or 0.2 g cm . Throughout the vertical column the mass ux, or equivalent rain rate, is taken to be constant. Added to the precipitation-sized particles is cloud liquid water which is specied by the liquid water content (grams per cubic meter) as a function of height. For the results presented here, a uniform distribution of cloud water of 1-km is allowed to take on depth is located above the 0 isotherm. values from 0–2 g m so that the integrated cloud water can
Fig. 2. PIA (unnormalized) (in decibels) at three frequencies versus corresponding brightness temperature T using the baseline stratiform storm model.
range from 0–2 kg m . The relative humidity is allowed to take on values between 70% and 100%. In the radiative transfer model of Kummerow [17], the surface emissivity is computed

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Fig. 3. A (12; 9:5 GHz) versus T (12 GHz) and T (9:5 GHz) where values are derived from model data shown in Fig. 1. The solid line represents a tted curve through the data.
Fig. 4. (Top) Ratio of frequency-normalized differential path-attenuations and (bottom) corresponding estimate of this quantity derived from brightness temperatures. Results are plotted as a function of the median mass diameter D . The solid line represents the best t curve of D as a function of the ratio plotted along the ordinate.
as a function of wind speed and frequency using the models of Hollinger et al. [18] and Stogyrn [19]. In the baseline model, we take the wind speed to be 7 m s ; the effects of changes from this value are discussed later. From the storm and surface scattering models, brightness temperatures and total path attenuations at various frequencies are calculated over each vertical column. The brightness temperatures are calculated using the Eddington approximation for the radiative transfer equation [17]. Although arbitrary incidence angles can be used, we restrict the calculations to nadir incidence. V. RESULTS Using the storm model just described, we calculate the apparent radar reectivity factor proles at 9.5 GHz for nadir incidence above the storm where the apand actual radar reectivity factor are related at parent radar range by (33) A sequence of 379 proles is shown in the top panel of Fig. 1. In this case, the integrated cloud water is taken to be 0.5 kg m with snow density of 0.2 g cm and 80% relative humidity.
The radar brightband, corresponding to mixed-phase hydrometeors in the melting layer, is evident in the region just below 4 km. In the second panel from the top, the reectivity factor difference GHz GHz GHz (34)
is shown. The characteristics of the reectivity and differential reectivity proles are discussed in [6]. The corresponding brightness temperature results are shown in the lower two GHz and GHz GHz panels: GHz GHz . Notice that is bounded below at approximately 6 K. The bulk of this difference is caused by the differential path attenuation from cloud liquid water, water vapor and molecular oxygen. If the integrated cloud water is set to zero the minimum brightness temperature difference is about 4 K; if it is set to 1 kg m , the minimum is about 8 K. In other words, at light rain rates, an increase in the integrated cloud water of 1 kg m results in an increase in the differential brightness temperature between 9.5 and 12 GHz of about 4 K. , and from (22), (23), and (25) it is rst To estimate , to and using the functional necessary to convert the forms given by (28) and (30) for the storm model data shown

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Fig. 5. (Top) Estimated median mass diameter ( ) versus the true value using the tting curve shown in Fig. 4. (Bottom) Logarithm of estimated number concentration .
N
D
Fig. 6. (Top) Estimated and true rain rates versus sequence number. (Bottom) Scatter plot of estimated and true rain rates from data in the top panels.
in Fig. 1. For all ts, we assume that K. Tables I and II provide the coefcients , , and , , and , respectively for several frequencies and frequency pairs. Plots of path attenuation versus brightness temperature are shown in Fig. 2 for the frequencies 9.5, 10, and 12 GHz along with the ts (solid lines) using the coefcients from Table I. It should be pointed out that the solution set of (30) denes a plane in - - space: the solid curve shown in Fig. 3 is obtained by rst expressing GHz as a linear function of GHz and then plotting in (30) as a function of GHz . It should also be noted that in Fig. 3 and for the coefcients in Table II we have chosen the rst normalization factor so that . This is also the normalization used for the estimates. The coefcients given in Tables I and II are xed for all calculations. Although these are the best t coefcients for the baseline model results, they are not the best t coefcients for models with changes in cloud water, water vapor, snow density or surface wind speed. Clearly, the feasibility of the method depends not only on the quality of estimates using data from a particular model but the accuracy of estimates from storm models that differ from the baseline. Using (23), we compute and plot in Fig. 4 the ratio versus where GHz. For the scatter plot in the top panel, the true differential normalized path integrated attenuation is used to
compute the ratio while for the bottom panel and are estimated from the brightness temperatures using (30) with the coefcients listed in Table II. Differences between the upper and lower scatter plots are largely due to . errors incurred in converting brightness temperatures to , (typically light rain rates), the Notice also that at small true value of is determined primarily by the differential attenuations of the cloud and atmospheric gases and is nearly independent of the characteristics of the precipitation. Taking the data in the bottom panel of Fig. 4 as the basis of estimating from , then on using a quadratic t to the data, we obtain (35) where (35) is plotted as a solid line in the lower panel of Fig. 4. The results shown in Figs. 1–4 address the forward problem where the brightness temperature and path-integrated attenuation is computed for a given frequency and storm model. The remainder of the paper is focused on the inverse problem where estimates of rain rate and parameters of the drop size distribution are obtained from brightness temperatures at several frequencies. , we rst convert the to To obtain an estimate of and using (30) and the coefcients in then follows Table II. From these quantities is computed. from (35). The results of the procedure are shown in Fig. 5

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Fig. 7. Effects of a change in temperature from 24 C to 12 C at which N . estimates are evaluated. (Top) Estimated versus true values of (Bottom) Estimated versus true values of rain rate.
log( )
Fig. 8. Estimated versus true values of stratiform storm model: snow density : kg 1 m , RH .
0 25
= 90%
, log( ), and for a modied = 0 2 g cm , integrated cloud water =
D : N R 1
(top). Once is obtained, is determined from (22). A scatter plot of the logarithm (base 10) of the estimated values versus the “true” values (i.e., those values used in the and ) is shown in the bottom forward calculations of estimates is achieved by panel of Fig. 5. Less scatter in the using rather than so that the normalization in (22) has been used. It worth emphasizing that although (35) is versus for the data generated from the best t curve of the baseline model only, the coefcients of the t are used for all subsequent estimates despite changes in the storm model . parameters and wind speed used in the calculations of and , shown in Fig. 5, the From the estimated values of rain rate estimates are calculated from (25). Plots of the results versus sequence number are shown in the top panel of Fig. 6; below this are plotted the true rain rates. A scatter plot of the estimated versus true rain rates is given in the bottom panel of Fig. 6. As mentioned in Section III, evaluation of the integrals in and (22)–(25) requires computations of at a xed temperature. For the results in Figs. 4 and 5, the near-surface temperature of 24 C was used. If we change this to the temperature of the midpoint of the rain layer (12 C), but signicantly difwe obtain almost identical results for and . Plots of the estimated versus true ferent values for values of these latter two variables are shown in Fig. 7; it can be
seen that a change in the assumed temperature of raindrops from 24 C. to 12 C increases the estimates of number concentration and produces positively biased rain rates. For subsequent plots and are evaluated at and computations, 24 C. Before discussing changes to the baseline model, we note that estimates of integrated cloud water using (24) are generally unreliable. The reason for this can be understood by recognizing , that (24) expresses the cloud water attenuation, as a difference between the total attenuation and the attenuation from precipitation alone. The estimate is positively biased because attenuation contributions from water vapor and O have not been subtracted from the total. This problem can be partly circumvented by modifying the estimate to include this subtraction using nominal values for these contributions. However, a more serious problem with (24) is that for moderate and heavy rain rates, the cloud water attenuation, for the models considered here, is a small fraction of the total. As a consequence, variations in the estimate of the second term on the right-hand because of the subtracside of (24) introduce large errors in tion of quantities of roughly equal magnitude. The remaining examples focus on results from modications of the baseline stratiform storm model. Shown in Figs. 8–10 (top), are scatter plots of the estimated versus true values of

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Fig. 9. Estimated versus true values of stratiform storm model: snow density : kg 1 m , RH . water
= 0 75
= 90%
, log( ), and for a modied = 0 05 g cm , integrated cloud
D N R : 1
Fig. 10. Estimated versus true values of D , stratiform storm model: snow density : g 1 cm . kg 1 m , RH
2
= 80%
=02
log( ), and
N
R for a modied , integrated cloud water
=
(center), and (bottom) for the sets of model parameters in Table III. (It is worth noting that a replacement of the effective medium with the Maxwell Garnet formulation, water matrix with ice inclusions, for melting snow particles produces a signicant increase in brightness temperatures which leads to and positive biases in the rain rate. The results increases in are somewhat similar to those shown in Fig. 7. A detailed study of the effects of the mixed-phase region is beyond the scope of the paper, however.) and in these exDespite the fairly large variability in amples, the rain rates tend to have a small amount of scatter relative to the true values with generally negative biases for cases shown in Figs. 8 and 9 and a positive bias for the case in Fig. 10. As noted earlier, the bias is also affected by the assumed temperand are evaluated and the ature at which type of normalization used to form the estimates. The reason for the relatively accurate rain rate estimates appears to arise from and are inversely correlated so that an overthe fact that estimate in one is compensated by an underestimate in the other. This compensation works well for the rainfall estimate because of the underlying path attenuation constraint; that is, the brightness temperatures at the various frequencies are highly correlated with attenuation. Moreover, because rain rate and attenuation are approximately equal to the same moment of the drop
TABLE III PARAMETERS USED IN THE CALCULATION OF BRIGHTNESS TEMPERATURE
size distribution [20], this constraint extends, in an approximate sense, to the rain rate estimates. For similar reasons, a direct conversion of a brightness temperature measurement at X-band to path-averaged rainfall rate is fairly accurate. The primary advantage of the use of multiple frequencies is the added information provided on path-averaged number concentration and median mass diameter. Although the rainfall estimates appear to be reasonably accurate, the improvement over a straightforward rain rate estimator using a single brightness temperature needs to be explored. were calculated under the asIn previous examples, the sumption of an ocean wind speed of 7 m s . In the baseline model, the assumed wind speed was also taken to be 7 m s .

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atures at three X-band frequencies, provides an estimate of the of the rain. The equations also lead median mass diameter to estimates of the mean number concentration, , and rainfall rate. A simple simulation using a stratiform storm model suggests that reasonably accurate rain rates are possible even and can be high. On the other though the variability in hand, estimates of integrated cloud water content appear to be unreliable. Although the approach appears to be feasible for low to moderate wind speeds over ocean, more detailed studies are needed on variations in the shape parameter, , changes in the drop size distribution with height and the effects of the melting layer. The error budget must also include the measurement error of the brightness temperatures in the context of the system design, measurement requirements and scanning strategy. ACKNOWLEDGMENT The author wishes to thank C. Kummerow for the use of his radiative transfer code and J. Weinman for helpful discussions and suggestions. REFERENCES
[1] P. G. Black and C. L. Swift, “Airborne stepped frequency microwave radiometer measurements of rainfall rate and surface wind speed in hurricanes,” in Proc. 22nd Conf. Radar Meteorology, Boston, MA, Sep. 1984, pp. 433–438. [2] E. W. Uhlhorn and P. G. Black, “Verication of remotely sensed sea surface winds in hurricanes,” J. Atmos. Oceanic Technol., vol. 20, pp. 99–116, Jan. 2003. [3] Y. T. Furuhama and T. Ihara, “Remote sensing of path-average raindrop size distributions from microwave scattering measurements,” IEEE Trans. Antennas Propagat., vol. AP-29, no. 3, pp. 275–281, Mar. 1981. [4] T. Ihara, Y. Furuhama, and T. Manabe, “Inference of raindrop size distribution from rain attenuation statistics at 12, 35, and 82 GHz,” Trans. IECE Japan, vol. E67, pp. 211–217, Apr. 1984. [5] R. F. Rincon and R. H. Lang, “Microwave link dual-wavelength measurements of path-average attenuation for the estimation of drop size distribution and rainfall,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 4, pp. 760–770, Apr. 2002. [6] G. Zhang, J. Vivekanandan, and E. Brandes, “A method for estimating rain rate and drop size distribution from polarimetric radar measurements,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 4, pp. 830–841, Apr. 2001. [7] R. Meneghini, L. Liao, S. W. Bidwell, and G. M. Heymseld, “On the feasibility of a Doppler weather radar for estimates of drop size distribution using two closely-spaced frequencies,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 10, pp. 2203–2216, Oct. 2001. [8] R. Meneghini, S. W. Bidwell, L. Liao, R. Rincon, and G. M. Heymseld, “Differential-frequency Doppler weather radar: Theory and experiment,” Radio Sci., vol. 38, pp. 5.1–5.10, Mar. 2003. [9] L. J. Battan, Radar Observations of the Atmosphere. Chicago, IL: Univ. Chicago Press, 1973, p. 324. [10] G. Feingold and Z. Levin, “The log-normal t to raindrop spectra from frontal convective clouds in Israel,” J. Clim. Appl. Meteorol., vol. 25, pp. 1346–1363, 1986. [11] C. W. Ulbrich, “Natural variations in the analytical form of the raindrop size distribution,” J. Clim. Appl. Meteorol., vol. 22, pp. 1764–1775, 1983. [12] R. Lhermitte, “Cloud and precipitation sensing at 94 GHz,” IEEE Geosci. Remote Sens., vol. 26, no. 1, pp. 207–216, Jan. 1988. [13] J. A. Weinman, R. Meneghini, and K. Nakamura, “Retrieval of precipitation proles from airborne radar and passive radiometer measurements: Comparison with dual-frequency radar measurements,” J. Appl. Meteorol., vol. 29, pp. 981–993, Oct. 1990. [14] Durden et al., “Measurement of rainfall path attenuation near nadir: A comparison of radar and radiometer methods at 13.8 GHz,” Radio Sci., vol. 30, pp. 943–947, Jul.-Aug. 1994. [15] T. Yokoyama and H. Tanaka, “Microphysical processes of melting snowakes detected by two-wavelength radar,” J. Meteorol. Soc. Japan, vol. 62, pp. 650–666, 1984.
Fig. 11.
Estimated versus true rain rates for an ocean wind speed of 15 m 1 s
.
If the are calculated at a higher wind speed than the assumed is positively biased and value of 7 m s , we nd that is negatively biased. Fig. 11 shows the effect on the rain rate estimates for a wind speed of 15 m s , where, as always, a 7-m s speed is assumed in the retrieval. Note that the relative error is particularly large at light rain rates. For low winds, the errors in the estimated quantities are much smaller. In general, the results suggest that errors are acceptable up to wind speeds of about 10–15 m s although accuracy depends on the magnitude of the rain rate and cloud liquid water as well as other error sources. Some improvement in the retrieval should be possible by estimating wind speed in nearby rain-free areas. However, in high-wind environments such as hurricanes, the algorithms are unstable and the technique devised for the SFMR becomes applicable [1], [2]. VI. SUMMARY AND CONCLUSION Brightness temperature measurements at multiple frequencies within X-band, over a span of 2–3 GHz, may provide information on the path-averaged rainfall rate and parameters of the raindrop size distribution. The potential for this type of estimation arises from the fact that at X-band, brightness temperature is well correlated with path-integrated attenuation and that a difference of path attenuations normalized by frequency is nearly independent of cloud liquid water attenuation. Moreover, a ratio of such differences, derived from brightness temper-

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[16] D. A. G. Bruggeman, “Berechnung vershiedener physikalischer Konstanten von heteorogenen Substanzen. I. Dielectrizittskonstanten und Leitfhigkeiten der Mischkrper aus isotropen Substanzen,” Ann. Phys., vol. 24, pp. 636–679, 1935. [17] C. Kummerow, “On the accuracy of the Eddington approximation for radiative transfer in the microwave frequencies,” J. Geophys. Res., vol. 98, pp. 2757–2765, Feb. 1993. [18] J. Hollinger, R. Lo, G. Poe, R. Savage, and J. Pierce, Special Sensor Microwave Imager User’s Guide. Washington, DC: Naval Res. Lab., 1987. [19] A. Stogyrn, “The emissivity of sea foam at microwave frequencies,” J. Geophys. Res., vol. 77, pp. 1658–1666, 1972.
[20] D. Atlas and C. W. Ulbrich, “Path- and area-integrated rainfall measurement by microwave attenuation in the 1–3 cm band,” J. Appl. Meteorol., vol. 16, pp. 1322–1331, 1977.
Robert Meneghini (M’80–SM’96) is a member of the Microwave Sensors Branch, NASA Goddard Space Flight Center, Greenbelt, MD. His work focuses on algorithm and instrument development related to microwave remote sensing of the atmosphere.

图表与口诀记忆when、as、while的区别

图表与口诀记忆when、as、while的区别 1.图表与口诀前知识 关键是比较主从句子的动词，看其动词的持续性。瞬间的理解成点，持续的理解成线。主从关系有：点（点点、点线），线线，线点。 点：为瞬间动词，准确地称为“终止性动词”，指动词具有某种内在界限的含义，一旦达到这个界限，该动作就完成了。如come（来），一旦“到来”，该动作就不再继续下去了。 瞬间动词：arrive, begin, borrow, become, buy, catch, come, die, find, go，give, graduate, join, kill, lose, leave, marry, realize… 线：为非瞬间动词，准确地称为叫“延续性动词”。包括动态动词静态动词。 动态动词：live, sit, stand, study, talk, work, write… 静态动词（状态动词）：情感、看法、愿望等。Be, belong, consist, exist, feel, hate, have, hope, love, want… 兼有瞬时和非瞬时的动词：feel，look，move，run，work，write…，需要根据不同的语境判断。 2. when、as、while的区别一览表 【表格说明】：第一个点或者线表示从句谓语动词的持续性特征，黑点表示从句所表示的动作持续短，为瞬间动词，线表示持续长，为非瞬间动词。1~7为主句与从句所表示的动作时间有重合，第8为主句与从句所表示的动作不是同时发生，而是有先后顺序。 线线重相并发生， 长线” 【主句谓语为非瞬间动词中的 动态动词】 【记忆：等线动， 相并发生，但： 【主句谓语为非瞬间动词中的 静态动词】 【记忆：等线动，

when,while,as的区别

一、根据从句动作的持续性来区分 1.“主短从长”型：即主句是一个短暂性的动作，而从句是一个持续性动作，此时三者都可用。如： Jim hurt his arm while [when, as] he was playing tennis. 吉姆打网球时把手臂扭了。 As [When, While] she was waiting for the train, she became very impatient. 她在等火车时，变得很不耐烦。 注意：as用于引出一个持续性动词表示“在……期间”时，其谓语通常只能是那些含有动作和发展意味的动词，一般不能是那些不用于进行时态的动词(如be, seem, love, want, agree, see, know, have 等)，所以下面一句中的while不能换为as： A：I’m going to the post office. 我要去邮局。 B：While you are there, can you get me some stamps? 当你在邮局时，能帮我买几张邮票吗? 若主句与从句表示的是两个几乎同时发生的动作，含有类似汉语“刚要……就”“正要……却”的意思，英语一般要用as(也可用when)，且此时通常连用副词just。且此时，从句一般用进行时，主句用短暂性动词的一般时态。【注意与六区别】 I caught him just when [as] he was leaving the building. 他正要离开大楼的时候，我把他截住了。 Just as [when] the two men were leaving, a message arrived. 就在这两个人要离开的时候，突然有了消息。 2.“主长从长”型：即主句和从句为两个同时进行的动作或存在的状态，且强调主句动作或状态延续到从句所指的整个时间，此时通常要用while。如： I always listen to the radio while I’m driving. 我总是一边开车一边听收音机。 He didn’t ask me in; he kept me standing at the door while he read the me ssage. 他没有让我进去，他只顾看那张条子，让我站在门口等着。 但是，若主句和从句所表示的两个同时进行的动作含有“一边……一边”之意时，则习惯上要用as。如： He swung his arms as he walked. 他走路时摆动着手臂。 I couldn’t remember a story to tell the children, so I made one up as I went along. 我想不出有什么故事可给孩子讲了，只好现编现讲。 3.“主长从短”型：即主句是一个持续性动作，而从句是一个短暂性动作，此时可以用a s或when，但不能用while。如：

while、when和as的用法区别

as when while 的区别和用法 as when while的用法 一、as的意思是“正当……时候”,它既可表示一个具体的时间点，也可以表示一段时间。as可表示主句和从句的动作同时发生或同时持续，即“点点重合”“线线重合”；又可表示一个动作发生在另一个动作的持续过程中，即“点线重合”， 但不能表示两个动作一前一后发生。如果主句和从句的谓语动词都表示持续性的动作，二者均可用进行时，也可以一个用进行时，一个用一般时或者都用一般时。 1、As I got on the bus，he got off. 我上车，他下车。（点点重合）两个动作都是非延续性的 2、He was writing as I was reading. 我看书时，他在写字。（线线重合）两个动作都是延续性的 3、The students were talking as the teacher came in. 老师进来时，学生们正在讲话。（点线重合）前一个动作是延续性的，而后一个动作时非延续性的 二、while的意思是“在……同时（at the same time that )”“在……期间(for as long as, during the time that）”。从while的本身词义来看，它只能表示一段时间，不能表示具体的时间点。在时间上可以是“线线重合”或“点线重合”，但不能表示“点点重合”。例如： 1、He was watching TV while she was cooking. 她做饭时，他在看电视。（线线重合） 2、He was waiting for me while I was working. 我工作的时候，他正等着我。（线线重合） 3、He asked me a question while I was speaking. 我在讲话时，他问了我一个问题。（点线重合）

第七--when-while-as-区别及练习.

When while as区别 一、根据从句动作的持续性来区分 1、“主短从长”型：即主句是一个短暂性动作，而从句是一个持续性动作，此时三者都可用。如： Jim hurt his arm while［when， as］ he was playing tennis. 吉姆打网球时把手臂扭伤了。 2、“主长从长”型：即主句和从句为两个同时进行的动作或存在的状态，且强调主句动作或状态延续到从句所指的整个时间，此时通常要用while。 I always listen to the radio while I’m driving. 我总是一边开车一边听收音机。 He didn’t ask me in; he kept me standing at the door while he read the message. 他没有让我进去，他只顾看那张条子，让我站在门口等着。 但是，若主句和从句所表示的两个同时进行的动作含有“一边……一边”之意时，则习惯上要用as。如： He swung his arms as he walked. 他走路时摆动着手臂。 3、“主长从短”型：即主句是一个持续性动作，而从句是一个短暂性动作，此时可以用as 或when，但不能用while。如： It was raining hard when [as] we arrived. 我们到达时正下着大雨。 二、根据主句与从句动作是否同时发生来区分 1、若主句与从句表示的是两个同时发生的短暂性动作，含有类似汉语“一……就”的意思，英语一般要用as (也可用when)。如： The ice cracked as [when] I stepped onto it. 我一踩冰就裂了。 2、若主句与从句表示的是两个几乎同时发生的短暂性动作，含有类似汉语“刚要……就”“正要……却”的意思，英语一般要用as(也可用when)，且此时通常连用副词just。如： I caught him just when [as] he was leaving the building. 他正要离开大楼的时候，我把他截住了。 三、根据是否具有伴随变化来区分 若要表示主句动作伴随从句动作同时发展变化，有类似汉语“随着”的意思，英语习惯上要用as，而不用when或while。如： The room grew colder as the fire burnt down. 随着炉火逐渐减弱，房间越来越冷。 注：若不是引导从句，而是引出一个短语，则用with，不用as。如： With winter coming on, it’s time to buy warm clothes. 随着冬天到来，该买暖和衣裳了。 四、根据从句动作的规律性来区分 若暗示一种规律性，表示“每当……的时候”，英语一般要用when。如： It’s cold when it snows. 下雪时天冷。 五、根据主从句动作的先后顺序来区分 若主句与从句所表示的动作不是同时发生，而是有先后顺序时，一般要用when。

When while as的区别和用法(综合整理)

When while as的区别和用法 when的用法 当主句使用持续性动词时. Dave was eating,when the doorbell rang.门铃响时,大卫在吃饭. 2.一个动作紧接着另一个动作发生. When the lights went out, I lit some candles.灯灭了,我赶紧点上一些蜡烛. 3.谈论生命中的某一阶段,或过去的某段时间. His mother called him Robbie when he was a baby. 在他很小时,他妈妈叫他Robbin. 4.指"每一次" When I turn on the TV, smoke comes out the back. 每当我打开电视,就有烟从后面冒出. while/as 的用法 从句多为进行时,而且为持续性动词. I'll look after the children while you are making dinner. 你做饭,我来照顾孩子. 注意事项: (1) “主短从长”型：主句表示的是一个短暂性动作，从句表示的是一个持续性动作，三者都可用： He fell asleep when [while, as] he was reading. 他看书时睡着了。 Jim hurt his arm while［when，as］he was playing tennis. 吉姆打网球时把手臂扭伤了。 As［When，While］she was waiting for the train，she became very impatient. 她在等火车时，变得很不耐烦。 (2) “主长从长”型：若主、从句表示两个同时进行的持续性动作，且强调主句表示的动作延续到从句所指的整个时间，通常要用while： Don’t talk while you’re eating. 吃饭时不要说话。 I kept silent while he was writing. 在他写的时候，我默不做声。 但是，若主从句表示的两个同时进行的动作含有“一边…一边”之意思，通常用as：

精华!-微波办公室MWO仿真详细步骤

Microwave Office LC滤波器设计实例 【微波EDA网】Microwave Office 是一个强大的RF计算机辅助设计及仿真软件。它提供一整套完整的把你的设计思想转换为产品的设计环境和解决方案。使用较方便直观。下面应用它来设计一个滤波器。 其主界面如下图： （图1） 应用Microwave Office的整个设计过程可以主要分为以下几个步骤： 1．创建一个schematic电路原理图； 2．加入图表及物理量测量方法； 3．电路仿真； 4．调整电路； 5．创建变量； 6．最优化电路。 具体操作如下： 一、新建一个新的工程 1．选择下拉菜单的File > New Project; 2．选择File > Save Project As，给工程取个名字保存到本地磁盘。

二、设置工程默认的单位 1．选择下拉菜单中的Options > project options > Global Unit 设置为mm 2．修改其中的单位点击OK完成操作。 三、创建一个schematic原理图 1．选择菜单Project > Add Schematic > New Schematic 2．输入原理图的文件名例如：filter 四、放置元器件 1．按一下左下窗口的Elem，出现元件对话框 2．按一下其中的Lumped Element旁边的“+”号，扩展Lumped Element组 3．选择其下面的Inductor子组，再选中下方窗口显示IND模型，用鼠标左键选中并按住拖到schematic 窗口的合适位置出，释放左键。如需改动元件位置再用左键选择拖动即可。 4．再重复上述操作，在schematic中放置一共四个IND电感。并使他们连起来位置如图1所示。 5．选择Capacitor子组，再选中下方窗口中的CAP模型，拖动至schematic中放置位置如图1与电感连接。在拖动过程中按住左键并单击右键可以旋转器件(为什么我旋转不了？因为要在第3步把元件从左边的窗口往后边的电路图中拖的过程中才能旋转)。 五、连接导线 鼠标移至C1的下端节点此时鼠标形状改变，点中并拖动连接C2、C3的下面节点，完成连线。 六、在节点上放置端口 1．选择下拉菜单Schematic > Add Port； 2．移动鼠标到L1的左端放置端口1，并与L1连接； 3．重复上操作放置端口2连接L4的右端，见图1。 七、放置接地点 1．选择下拉菜单Schematic > Add Ground； 2．鼠标移动放置到C1的下节点。 八、编辑元件参数 双击元器件对应的参数即可修改其参数，修改L1和L4为15nH, L2和L3为30nH, C1和C3为8pF, C2为10pF。 九、确定仿真频率 1． Options > project options > Frequency Values 2．修改单位为MHz，输入100在Start field，1000在Stop field，输入10作为步长Step field。其余默认。单击Apply(一定要点击，否则设置无效！). 4．单击Ok完成仿真频率的设置 十、创建图表 1．右键工程视图中的Graphs组，选择Add Graph 2．输入名字“s21 and s11”选择Rectangular单击Ok。

when,while,as引导时间状语从句的区别

when，while，as引导时间状语从句的区别 when，while，as显然都可以引导时间状语从句，但用法区别非常大。 一、when可以和延续性动词连用，也可以和短暂性动词连用；而while和as只能和延续性动词连用。 ①Why do you want a new job when youve got such a good one already？（get 为短暂性动词）你已经找到如此好的工作，为何还想再找新的？ ②Sorry，I was out when you called me．（call为短暂性动词）对不起，你打电话时我刚好外出了。 ③Strike while the iron is hot．（is为延续性动词，表示一种持续的状态）趁热打铁。 ④The students took notes as they listened．（listen为延续性动词）学生们边听课边做笔记。 二、when从句的谓语动词可以在主句谓语动作之前、之后或同时发生；while 和as从句的谓语动作必须是和主句谓语动作同时发生。 1．从句动作在主句动作前发生，只用when。 ①When he had finished his homework，he took a short rest．（finished先发生）当他完成作业后，他休息了一会儿。 ②When I got to the airport，the guests had left．（got to后发生）当我赶到飞机场时，客人们已经离开了。 2．从句动作和主句动作同时发生，且从句动作为延续性动词时，when，while，as都可使用。 ①When ／While ／As we were dancing，a stranger came in．（dance为延续性动词）当我们跳舞时，一位陌生人走了进来。 ②When ／While ／As she was making a phonecall，I was writing a letter．（make为延续性动词）当她在打电话时，我正在写信。 3．当主句、从句动作同时进行，从句动作的时间概念淡化，而主要表示主句动作发生的背景或条件时，只能用as。这时，as常表示“随着……”；“一边……，一边……”之意。 ①As the time went on，the weather got worse．（as表示“随着……”之意） ②The atmosphere gets thinner and thinner as the height increases．随着高度的增加，大气越来越稀薄。 ③As years go by，China is getting stronger and richer．随着时间一年一年过去，中国变得越来越富强了。 ④The little girls sang as they went．小姑娘们一边走，一边唱。 ⑤The sad mother sat on the roadside，shouting as she was crying．伤心的妈妈坐在路边，边哭边叫。 4．在将来时从句中，常用when，且从句须用一般时代替将来时。 ①You shall borrow the book when I have finished reading it．在我读完这本书后，你可以借阅。 ②When the manager comes here for a visit next week，Ill talk with him about this．下周，经理来这参观时，我会和他谈谈此事。 三、when用于表示“一……就……”的句型中（指过去的事情）。 sb．had hardly（＝scarcely）done sth．when．．．＝Hardly ／Scarcely had sb．done sth．when．．．

When,While,As引导时间状语从句的区别

When，While，As引导时间状语从句的区别 when，while，as显然都可以引导时间状语从句，但用法区别非常大。 一、when可以和延续性动词连用，也可以和短暂性动词连用；而while和as 只能和延续性动词连用。 ① Why do you want a new job when you’ve got such a good one already？（get为短暂性动词）你已经找到如此好的工作，为何还想再找新的？ ②Sorry，I was out when you called me．（call为短暂性动词）对不起，你打电话时我刚好外出了。 ③Strike while the iron is hot．（is为延续性动词，表示一种持续的状态）趁热打铁。 ④ The students took notes as they listened．（listen为延续性动词）学生们边听课边做笔记。 二、when从句的谓语动词可以在主句谓语动作之前、之后或同时发生；while 和as从句的谓语动作必须是和主句谓语动作同时发生。 1．从句动作在主句动作前发生，只用 when。 ①When he had finished his homework，he took a short rest．（finished 先发生）当他完成作业后，他休息了一会儿。 ②When I got to the airport，the guests had left．（got to后发生）当我赶到飞机场时，客人们已经离开了。 2．从句动作和主句动作同时发生，且从句动作为延续性动词时，when，while，as都可使用。 ①When ／While ／As we were dancing，a stranger came in．（dance为延续性动词）当我们跳舞时，一位陌生人走了进来。 ②When ／While ／As she was making a phone call，I was writing a letter．（make为延续性动词）当她在打电话时，我正在写信。 3．当主句、从句动作同时进行，从句动作的时间概念淡化，而主要表示主句动作发生的背景或条件时，只能用 as。这时，as常表示“随着……”；“一边……，一边……”之意。 ① As the time went on，the weather got worse．（as表示“随着……”之意） ② The atmosphere gets thinner and thinner as the height increases．随着高度的增加，大气越来越稀薄。 ③As years go by，China is getting stronger and richer．随着时间一年一年过去，中国变得越来越富强了。 ④The little girls sang as they went．小姑娘们一边走，一边唱。 ⑤The sad mother sat on the roadside，shouting as she was crying．伤心的妈妈坐在路边，边哭边叫。 4．在将来时从句中，常用when，且从句须用一般时代替将来时。 ①You shall borrow the book when I have finished reading it．在我读完这本书后，你可以借阅。 ②When the manager comes here for a visit next week，Ill talk with him about this．下周，经理来这参观时，我会和他谈谈此事。 三、when用于表示“一……就……”的句型中（指过去的事情）。

When, while, as的区别和用法

When, while, as的区别和用法 版本一 (1) 若主句表示的是一个短暂性动作，从句表示的是一个持续性动作，三者都可用： He fell asleep when [while, as] he was reading. 他看书时睡着了。 【注】as 用于引出一个持续性动词表示“在……期间”时，其谓语通常只能是那些含有动作(action)和发展(development) 意味的动词，一般不能是那些不用于进行时态的动词(如be, seem, love, want, agree, see, know, have 等)，所以下面一句中的while 不能换为as： A：I’m going to the post office. 我要去邮局。 B：While you’re there, can you get me some stamps? 当你在邮局时，能帮我买几张邮票吗? (2) 若主、从句表示两个同时进行的持续性动作，且强调主句表示的动作延续到从句所指的整个时间，通常要用while： Don’t talk while you’re eating. 吃饭时不要说话。 I kept silent while he was writing. 在他写的时候，我默不做声。 但是，若主从句表示的两个同时进行的动作含有“一边…一边”之意思，通常用as： She sang as she went along. 她边走边唱。 (3) 若从句是一个短暂性动作，主句是一个持续性动作，可用as / when 但不用while： It was raining hard when [as] we arrived. 我们到达时正下着大雨。 (4) 若主从句表示的是两个同时(或几乎同时)发生的短暂性动作，用as / when： I thought of it just when [as] you opened your mouth. 就在你要说的时候，我也想到了。 (5) 若要表示两个正在发展变化的情况，相当于汉语的“随着”，一般用as： Things are getting better and better as time goes on. 随着时间的推移，情况越来越好。 As it grew darker, it became colder. 天色越晚，天气越冷。 (6) 表示“每当…的时候”(暗示一种规律性)，一般要用when： It’s cold when it snows. 下雪时天冷。 He smiles when you praise him. 你夸奖他时他总是笑笑。 (7) 若主从句所表示的动作不是同时发生，而是有先后顺序时，一般要用when： I will go home when he comes back. 他回来时，我就回家去。 (8) when 可用作并列连词，表示“这时(突然)”；while 也可以用作并列连词，表示“而”、“却”(表示对比)；但as 则没有类似用法： We were about to start when it began to rain. 我们正要出发，这时天开始下雨了。 He likes coffee, while she likes tea. 他喜欢咖啡，而她却喜欢茶。 (9) as 和when 后均可直接跟一个名词，构成省略句，但while 一般不这样用： As [When] a boy, he lived in Japan. 他小时候在日本。

第七whenwhileas区别及练习

When while as 区别 一、根据从句动作的持续性来区分 1、“主短从长”型：即主句是一个短暂性动作，而从句是一个持续性动作，此时三者都可 用。如： Jim hurt his arm while ［ when， as］ he was playing tennis. 吉姆打网球时把手臂扭伤了。 2、“主长从长”型：即主句和从句为两个同时进行的动作或存在的状态， 状态延续到从句所指的整个时间，此时通常要用while 。 且强调主句动作或 I always listen to the radio while I ’ m driving. 我总是一边开车一边听收音机。 He didn ’ t ask me in; he kept me standing at the door while he read the message. 他没有让我进去，他只顾看那张条子，让我站在门口等着。 但是，若主句和从句所表示的两个同时进行的动作含有“一边,, 一边”之意时，则习惯上 要用 as。如： He swung his arms as he walked. 他走路时摆动着手臂。 3、“主长从短”型：即主句是一个持续性动作，而从句是一个短暂性动作，此时可以用as 或when，但不能用 while 。如： It was raining hard when [as] we arrived.我们到达时正下着大雨。 二、根据主句与从句动作是否同时发生来区分 1、若主句与从句表示的是两个同时发生的短暂性动作，含有类似汉语 “一英语一般要用 as (也可用 when)。如： ,, 就的”意思，The ice cracked as [when] I stepped onto it. 我一踩冰就裂了。 2、若主句与从句表示的是两个几乎同时发生的短暂性动作，含有类似汉语“刚要“正要 ,, 却”的意思，英语一般要用 as(也可用 when)，且此时通常连用副词 ,, just。如： 就” I caught him just when [as] he was leaving the building. 他正要离开大楼的时候，我把他截住 了。 三、根据是否具有伴随变化来区分 若要表示主句动作伴随从句动作同时发展变化，有类似汉语“随着”的意思，英语习惯上要 用as，而不用 when 或 while 。如： The room grew colder as the fire burnt down.随着炉火逐渐减弱，房间越来越冷。 注：若不是引导从句，而是引出一个短语，则用with ，不用 as。如： With winter coming on, it ’ s time to buy warm clothes. 随着冬天到来，该买暖和衣裳了。 四、根据从句动作的规律性来区分 若暗示一种规律性，表示“每当,, 的时候”，英语一般要用when 。如：It ’s cold when it snows. 下雪时天冷。 五、根据主从句动作的先后顺序来区分 若主句与从句所表示的动作不是同时发生，而是有先后顺序时，一般要用when 。

when while as区别用法详解

when/while/as区别用法详解 when, while, as都可作"当……的时候"解，但它们之间也有差别。 若主句表示的是一个短暂性动作，从句表示的是一个持续性动作，三者都可用。 He fell asleep when/while/as he was reading. 他看书时睡着了。 when只表示一般的时间关系，它既可指时间的一点，也可指一段时间。用when时，从句的动作可与主句的动作同时发生，也可先于主句的动作，因此when用得最多。如： He was playing basketball when I saw him. 当我看见他的时候，他正在打篮球。 Don't forget to return this book for me, when you go to the library. 你去图书馆时，不要忘记替我还这本书。 while只能指一段时间，而不能指时间的一点。用while时，从句的动作或者与主句的动作同时发生，或者主句的动作是在从句的动作的进展过程中发生的。因此，从句中的谓语必须是表示延续性动作或状态的动词。这是while与when的主要差别。如： When we arrived in Beijing, it was raining. (arrive不是延续性的动词)我们到达北京时，天正在下雨。 Please do not trouble me while I am writing my homework. 我写作业时请不要打扰我。在用when和while连接的从句中，常省略与主句相同的主语和相应的be，而在as连接的从句中一般则不省略。如： He fell asleep while(he was)studying his grammar book.他在阅读语法书的时候睡着了。While in London,he studied music.他在伦敦的时候，研究音乐。 when 可用作并列连词，表示“这时(突然)”；while 也可以用作并列连词，表示“而”、“却”(表示对比)；但as 则没有类似用法： We were about to start when it began to rain. 我们正要出发，这时天开始下雨了。 He likes coffee, while she likes tea. 他喜欢咖啡，而她却喜欢茶。

when,while和as引导时间状语从句的用法

when, while 和 as 引导时间状语从句的用法 这三个词的意思很简单，都有“当……时候”的意思。但学生经常会问三个词的区别在哪儿，特别是在做选择题的时候。别说是学生，就我个人而言，做这样的选择题要保证百分之百的 正确也是不可能的。现根据大量的实例和个人的思考，做一点小结，供大家参考。 一、when 的用法 如果只从现象来看，when 从句用的最多的是一般过去时，而主句的时态没有限制，根据具 体情况而定。 When he was a child he was always trying out new ideas. 他小时候就常常试验一些新的设想。 when she came into my room I was just reading a book. 她走进我房间时，我正在看书。 Were you writing when the teacher came in? 老师进来的时候，你在写信吗？ Sorry，I was out when you called me. 对不起，你打电话来的时候我出去了。 He was on the point of leaving when someone knocked at the door. 他正要走,这时有人敲门。 I thought of it just when you opened your mouth. 就在你要说话的时候,我也想到了。 I had hardly[scarcely] closed my eyes when someone knocked at the door. 我刚一闭上眼，就有人在敲门了。 根据以上的例句，我们可以总结出一点：when 从句的A事件，相当于另一个事件B发生的时间点。也就是说，when 从句的重点不在动作本身发生的状态，而只是把它作为一个时间 点，所以when 多数情况下用的是一般过去时，则不用正在进行时。因为如果用正在进行时，它表示的就是一段时间而不是一个时间点了。根据这一点，有的文章补充说：when 从句的动词大多是瞬时动词。这种说法也可以参照。 实际上，when 从句也可以有其它的时态，但几乎也不用进行时，因为它也只是作为一个时 间参照点。例如： When I got to the airport，the guests had left. 当我赶到飞机场时，客人们已经离开了。 When he had finished his homework，he took a short rest． 当他完成作业后，他休息了一会儿。 Why do you want a new job when you have got such a good one already？ 你已经找到如此好的工作，为何还想再找新的？ You shall borrow the book when I have finished reading it.

状语从句中的when,while ,as用法汇总

状语从句中的when, while和as的用法 一．when，while，as在时间状语从句中的区别： ①三者均可表示“当……的时候”，如果主句表示的是短暂的动作，而从句表示的是一段时间，三者可通用。如： I met Kang Li as／when／while I was walking along the street． 当我沿街散步时碰见了康丽。 ②when可以和延续性动词连用，也可以和短暂性动词连用；而while和as只能和延续性动词连用。如： It was snowing when we got to the airport．当我们到达机场时，天正下着雪。 （不能用while） ③as强调主句与从句表示的动作同时发生，as常表示“随着……”；“一边……， 一边……；while强调主句表示的动作持续于while所指的整个时间内；when 可指主、从句所述动作同时或先后发生。如： As the time went on，the weather got worse．（as表示“随着……”之意） He sang as he went along．他边走边唱。 Please write while I read．我读的时候，请写下来。 When he reached home，he had a little rest．回到家后，他休息了一会儿。 ④when用于表示“一……就……”的句型中（指过去的事情）。 somebody had hardly（＝scarcely）done …when．．． ＝Hardly ／Scarcely had somebody done …when．．． ①I had hardly ／scarcely closed my eyes when someone knocked at the door． ＝Hardly ／Scarcely had I closed my eyes when someone knocked at the door．我刚一闭上眼，就有人在敲门了。 二.when, while和as都可引导让步状语从句： ①when引导让步状语从句，意为“尽管，虽然”相当于though或although: They stopped trying when they might have succeeded next time. ②while引导让步状语从句，相当于although ，是较为正式的书面语: While I am willing to go, I would like it better that you went. ③as引导让步状语从句必须倒装，从句中的表语，状语或动词原形置于句首，若表语为名词，前置时省略冠词。 Child as he is, he knows a lot. Much as I like it, I will not buy it, for it’s too expensive.

AWR_Microwave_Office设计套件的介绍

AWR_Microwave_Office设计套件的介绍随着电磁场和微波电路领域数值计算方法的发展，在最近几年出现了大量的电磁场和微波电路仿真软件。在这些软件中，多数软件都属于准3维或称为维电磁仿真软件。例如，Agilent公司的ADS（Advanced Design System）、AWR公司的Microwave Office、Ansoft 公司的Esemble、Serenade和CST公司的CST Design Studio等。目前，真正意义上的三维电磁场仿真软件只有Ansoft公司的HFSS、CST公司的Mafia、CST Microwave Studio、Zeland 公司的Fidelity和IMST GmbH公司的EMPIRE。从理论上讲，这些软件都能仿真任意三维结构的电磁性能。其中，HFSS （HFSS是英文高频结构仿真器（High Frequency Structure Simulator）的缩写）是一种最早出现在商业市场的电磁场三维仿真软件。因此，这一软件在全世界有比较大的用户群体。由于HFSS进入中国市场较早，所以目前国内的电磁场仿真方面HFSS的使用者众多，特别是在各大通信技术研究单位、公司、高校非常普及。

AWR_Microwave_Office设计套件是专门的微波/射频软件，Microwave Office软件是通过两个模拟器来对微波平面电路进行模拟和仿真的。对于由集总元件构成的电路, 用电路的方法来处理较为简便。该软件设有一个叫“VoltaireXL”的模拟器来处理集总元件构成的微波平面电路问题。而对于由具体的微带几何图形构成的分布参数微波平面电路则采用场的方法较为有效, 该软件采用的是一个叫“EMSight”的模拟器来处理任何多层平面结构的三维电磁场的问题。 由于这里意在着重于电磁场分析，所以仅涉及“EMSight”模拟器。下面是它的具体功能：“EMSight”模拟器是一个完整的三维电磁场模拟程序包, 它可用于平面高频电路和天线结构的分析。模拟器分析的电路都安装在一个矩形的金属包装盒内, 对于电路的层数和端口

微波冶金综述 2015年：Microwave-assisted metallurgy

Microwave-assisted metallurgy Zhiwei Peng1,2and Jiann-Yang Hwang*2,3 Microwave heating has been extensively explored in various fields of materials processing.This technology exhibits unique characteristics including volumetric and selective heating,which eventually lead to many exceptional advantages over conventional processing methods including both energy and cost savings,improved product quality,faster processing and greater eco-friendliness,making microwave heating appropriate for applications in metallurgy.This paper presents a critical review on the use of microwave energy in metallurgy,with emphasis on both fundamentals of microwave heating and recent experimental efforts on extractive metallurgy via pyrometallurgical and/or hydrometallurgical routes.Applications to metallurgical processes for extraction of various metals,including heavy metals(Fe,Ni,Co,Cu,Pb and Zn),light metals(Al and Mg),rare metals(Ti,Mo,W and Re)and precious metals(Au,Ag and Pt),are reviewed and discussed. Keywords:Microwave heating,Permittivity,Permeability,Pyrometallurgy,Hydrometallurgy,Materials pretreatment,Microwave reduction/leaching, Waste remediation Introduction Microwave heating has emerged as a unique and distin-guishing technology used for materials processing.1–4 The rapid advancement of this heating technology has inspired many more encouraging and successful applica-tions to metallurgy.The earliest application of micro-wave energy to metallurgy can be traced back to1960s when a patent for microwave treatment of iron ores was granted.5Around the same time,high-temperature microwave processing of oxide and sul?de minerals was reported.6Subsequent studies demonstrated strong microwave absorption in various metal-bearing minerals such as magnetite and pyrite.7Inspired by these dis-coveries,the direct reduction of metal oxides using microwave energy has been extensively explored since the early1990s.8–10It is largely documented that micro-wave reduction of many metal-bearing minerals could be achieved rapidly,which is attributed to the volumetric and selective heating characteristics of microwave heating. Consequently,there can be a considerable reduction in energy consumption and pollution(e.g.CO2and SO2 emissions)compared with conventional processes.11This cost saving,environmentally friendly feature is also accompanied by enhanced microwave heating character-istics(microwave absorption capabilities)of metal sources. Thus,microwave energy is?nding increasing applications in sub?elds of metallurgy,such as pretreatment of metal-bearing materials and metallurgical waste remediation.12 In many cases,the unique advantages of microwave heating were veri?ed by experimental observations. However,from studies over the past half century,it is recognised that there are still dif?culties that hinder the advancement of microwave-assisted metallurgy and more broad applications of the technology to materials proces-sing.Many challenges are confronted in the commercia-lisation and industrialisation of microwave-assisted metallurgy.13 As microwave energy is being used for the extraction of a variety of metals,this paper presents a critical and comprehensive review of the scienti?c literature on microwave-assisted metallurgy.The authors try to put emphasis on both the principles and applications of microwave heating associated with numerous metallurgi-cal processes for extraction of various metals including heavy metals(Fe,Ni,Co,Cu,Pb and Zn),light metals(Al and Mg),rare metals(Ti,Mo,W and Re)and precious metals(Au,Ag and Pt).Some key fundamentals of microwave heating that relate microwave–material inter-actions will be described by introducing the main microwave heating mechanisms,crucial physical para-meters(e.g.permittivity,permeability,microwave pene-tration depth,re?ection loss and impedance matching degree),and characteristics of microwave heating.This is followed by a brief introduction of features in microwave-assisted metallurgy and a detailed discussion on various applications to extractive metallurgy.Concluding remarks touch on major dif?culties that limit further development of microwave-assisted metallurgy followed by promising measures that address challenges faced with commercia-lisation and industrialisation. Microwave heating fundamentals Introduction to microwave heating Microwaves are electromagnetic waves with wavelengths from1mm to1m with corresponding frequencies 1School of Minerals Processing and Bioengineering,Central South University,Changsha,Hunan410083,China 2Department of Materials Science and Engineering,Michigan Technological University,Houghton,MI49931,USA 3Advanced Materials R&D Centre of WISCO,Beijing102211,China *Corresponding author,email jhwang@https://www.wendangku.net/doc/565249795.html, ?2015Institute of Materials,Minerals and Mining and ASM International Published by Maney for the Institute and ASM International Received13March2014;accepted8August2014 DOI10.1179/1743280414Y.0000000042International Materials Reviews2015VOL60NO1 30