Anomalies and fluctuations of near-surface air temperature at Tianhuangping (Zhejiang), China, produced by the longest total solar eclipse of the 21st century under cloudy skies

We analyze the near-surface air temperature response, at three different heights over the ground, recorded by the Williams College expedition under meteorological conditions characterized by cloudy skies during the longest total solar eclipse of the 21st century on 22 July 2009, at Tianhuangping (Zhejiang), China. An analysis of the relationship between solar radiation and air temperature was made by applying a study previously published in which we evaluated the cloudiness contribution in estimating the impact on global solar radiation throughout this phenomenon at that site. The analysis of this response includes linear and absolute negative anomalies as well as fluctuations, which was undertaken through a statistical study to get information on the convection activity produced by the latter. The fluctuations generated by turbulence were studied by analyzing variance and residuals. The results, indicating a steady decrease and recovery of both perturbations, were consistent with those published by other studies for this total solar eclipse.

When the center of the umbra reached the Indian-China border (at 01:05 TCU), the shadow's velocity was 1.8 km/s; at Hubei province's capital Wuhan, just 20 km south of central line, the umbra's velocity was 1.0 km/s (at 01:27 UTC) (Espenak & Anderson, 2008). The instant of greatest eclipse occurred at 02:35:19 UTC at 24° 13' N and 144° 07' E when axis of the Moon's shadow passed closest to the center of Earth.

Meteorological circumstances
At that date, in the morning and during the event, the sky was mostly cloudy over the region of Zhejiang. Morning storms were followed by widespread cirrostratus and variable stratocumulus during the eclipse, followed by afternoon rain showers. Because of its importance in assessing the incident solar radiation on the ground and, therefore in the overall eclipse, this cloudiness, recorded with a wide-field camera, is quantified and analyzed in Peñaloza-Murillo & Pasachoff (2018). Table 2 gives some meteorological circumstances (and also photometric) corresponding to which this event took place, conveying information on variation of different variables throughout and surrounding the eclipse period. Note that NSAT measurements are given for three different heights above the ground: very close to the ground at 2 cm, close to the ground at 10 cm, and above the ground at 2 m. The photometric and relative-humidity information was taken from the measurements made by Stoeva et al. (2009) at the same observation site. These authors Submitted to Journal of Geophysical Research -Atmosphere (March, 2019 gave illumination values for three different directions in the sky (zenith, horizon and solar area).
Total reductions of 6.01 °C, 5.90 °C, and 4.37 °C in air temperature were observed at 2 cm, 10 cm, and 2 m, respectively, in duration intervals of ~ 80 min (1.30 h), ~ 79 min (1.32 h) and ~ 79 min (1.32 h), respectively, between first contact and the instant of minimum temperature (see Table 2). This same feature was observed for the respective time lag: 7.98 min for the lower height and 7.08 min for the rest, measured from the beginning of totality (at second contact) when the direct solar radiation is first completely blocked by the Moon. Recall that thermal response of the air is not in phase with the solar radiation response. The drop in temperature during these lags were, respectively, 0.73 °C, 0.44 °C and 0.34 °C. Other reductions such as the maximum "linear anomaly" DTLIN, were 8.42 °C, 7.07 °C, and 5.27 °C, respectively (see Table 2). By applying a linear regression fit, this anomaly is related to a hypothetical temperature time series over the 2016 (see Fig. 2b)]. This linear time series is assumed to be representative of temperature observations in the absence of an eclipse. Thus, the linear anomaly is obtained by subtracting the value of the interpolated temperature corresponding to that under noeclipse condition (Ti,n-e) at the same time of that corresponding to the observed minimum temperature during the eclipse. The other anomaly, the "absolute anomaly" DTABS, were 6.80 °C, 6.77 °C and 5.17 °C, respectively (see Table 2), which involves calculating the difference between a pre-eclipse maximum temperature (between first and second contacts) and an eclipse period minimum temperature [see Fig. 2a (Clark, 2016)].
Changes in surface temperatures moves the air's water vapor content closer to saturation, increasing its relative humidity (RH). This time RH increased by 12% between 6 09:10:00 and 09:45:00 , corresponding from roughly 23 minutes prior to 6 minutes following totality. The ambient illumination was drastically reduced in all three directions by up to 17 lx, for the zenith; 4 lx for the horizon; and 120 lx, for the solar area . No wind data were available. prior to the event. The temperature sensors were installed at three different heights above the ground (see Table 2), surrounded by green vegetation, and shielded from direct sunlight using small shades. Figure 3 presents a general view of temperature variation from 06:13:00 to 14:44:00. Readings were recorded every 63 seconds. An inspection of this figure shows the effect of the eclipse on this variable in the morning after the eclipse ended as well as the effect of bad weather after midday and during the first part of the afternoon. In Fig. 4, we show only the section corresponding to NSAT variation during the eclipse from first to fourth contact, roughly from 08:21 to 10:58 at 1-minute intervals.

Instrumentation and air temperature measurements
Graphically, all three curves show a delay or lag in relation to the central phase, which has been quantified from the data (see also Table 2). The drop of temperature is more significant at 2 cm height than the other two heights. Generally, the surface layer is the warmest due its contact (and consequent thermal conduction) with the radiatively heated ground; therefore, it cools down more rapidly (see Fig. 3).
Submitted to Journal of Geophysical Research -Atmosphere (March, 2019 7 The whole pattern displayed by our measurements in Fig. 3 is typical for cloudy or/and rainy weather. It is quite similar (mainly after 11:00 up to past 14:00) to that published by Pintér et al. (2010) for the same TSE and to that published by Winkler et al. (2001) for the 1999 TSE at Garching, Germany.

Analysis of the relationship between solar radiation and air temperature
In a previous paper, Peñaloza-Murillo & Pasachoff (2015) presented detailed methodological considerations in relation to the problem of how to analyze the relationship between solar radiation and air temperature during a total solar eclipse following the works of Phillips (1969), Szałowski (2002), Tzanis (2005), and Pintér et al. (2008) (2015)] but none of them attempted to undertake a specific mathematically analysis between solar radiation and local NSAT. The worst region for observing this occultation was England, where the sky was heavily cloudy or practically overcast (e.g., Camborne, Cornwall); even so, some micro-meteorological measurements were made at several sites in that country [e.g., Hanna (2000), Leeds-Harrison et al. (2000), Morecroft et al. (2000), Aplin & Harrison (2003)]. In particular the latter authors tried to interpret theoretically their temperature measurements in the light of the diurnal-cyclones theory and the cold-core eclipse-cyclone hypothesis proposed by Clayton (1901) at the onset of Submitted to Journal of Geophysical Research -Atmosphere (March, 2019 the previous century [to update research on Clayton's cold-core cyclone hypothesis, see Gray & Harrison (2012)].
Our first challenge was to obtain a theoretical model of solar radiation under cloudy and eclipse conditions for our observation site from which we can derive theoretical models for NSAT measurements presented in the curves of Fig. 4. For these goals it was necessary first to get the occultation and obscuration function, via limb-darkening integration as was done by Peñaloza-Murillo & Pasachoff (2018) and to which the reader is referred for details. Our challenge now is to apply the pioneering Phillips's method (Phillips, 1969), in combination with that of Peñaloza-Murillo & Pasachoff (2018), to retrieve the temperature profile directly from a radiative model of the solar radiation's collapse and recovery during the eclipse process, this time total, but under cloudy conditions.
It is based on a sort of calibration curve of the type "air temperature vs. solar radiation" from which we can extract the air temperature during the phenomenon. In this case, clouds of different types and heights affected the solar radiation before, during, and after the eclipse (Peñaloza-Murillo & Pasachoff, 2018). Therefore, our first task, of this part of the investigation, was to formulate a solar-radiation model under cloudy conditions, as if the occultation had not happened, in order to be taken subsequently as such in the eclipse situation, as was obtained by Peñaloza-Murillo & Pasachoff (2018) (see Fig. 5).

NSAT profiles
To a first approximation the daily ambient air temperature, and in particualr the NSAT, for a given location, is directly related to daily global radiation, modulated, of course, by many factors including weather and geography. The idea that this relation could be used to model air temperature during a solar eclipse under clear skies came first from the work of Phillips (1969). It has successfully been applied by Peñaloza-Murillo & Pasachoff (2015) in a cloudless situation. Phillips proposed a methodology based on the construction of a plot relating air temperature to global solar radiation, omitting temperatures measured during the occultation. Global solar radiation values were obtained from the corresponding model. In this way, a sort of calibration curve of the type "Air Temperature vs. Global Solar For every temperature profile of Fig. 4 we constructed calibration charts, which provided the calibration curves ( Fig. 6). From these curves, the instantaneous thermal response of the air, at the three specified heights, were found as depicted in Fig. 7. Here, instantaneous thermal response stands for the air temperature that should be attained in absence of any kind of delay or lag, in phase with the solar radiation change and also with the obscuration function. Defined in this way, this variable can be called "instantaneous temperature," Tinst.
In comparing these instantaneous profiles to measurements as shown in Figs  In above context, it is worthy to note that Aplin & Harrison (2003) found a similar effect at Camborne (England), during the TSE of August 11, 1999, under overcast skies. The temperature minimum at that eclipse actually occurred before totality was reached and not after, as expected. This inverse delay can be referred to as a "negative lag" due to cloudiness. In the present case some negative lags are observed clearly in Figs. 8, 10 and to a lesser extent in Fig. 9. As long as the effect of decreasing cloudiness tended to be small (as it was observed around totality), the measurements, in a first stage and up to some point, came earlier than the theoretical values (negative lag); afterwards and inversely, the theoretical values came first, that is to say earlier, then the increasing values of the temperature measurements, as it is normally expected (positive lag). Toward the final partial phase after totality, at +2 cm ( Fig. 8), we can observe another lag inversion.
This temporal inter-changeability between negative and positive lag is the result of the combined effect of clouds on solar radiation variability, during the eclipse, and the natural thermal complex response of the ambient air to the phenomenon (Rabin & Doviak, 1989 For the remainder of this work, we will focus on analysing the NSAT fluctuations. The analysis and quantification of negative lag found at the different heights n this research will be made in future work.

Analysis of air temperature fluctuations
The notable existence of NSAT fluctuations, of different magnitude, during the eclipse is evident for the three sensing situations presented in Fig. 4 (see also Figs. 8 -10). These fluctuations are a recognizable phenomenon attributable to convective turbulence, which in general tends to disappear or minimize as long as the sunlight diminishes (Nieuwstadt & Brost, 1986) including that due to the eclipse (Kadygrov et al., 2013), and return to normal conditions following the eclipse when this event occurs in the morning. This same recovery would likely not be seen in an afternoon eclipse (Peñaloza-Murillo & Pasachoff, 2015). This convection suppression led to a more stable condition of the air in a certain period of time around totality, for the three cases considered here. The mechanism behind these changes is a product of the abrupt alteration in insolation, causing cooling in the surface layers of the atmosphere and damping of atmospheric turbulence from the surface upwards. Mixed with these fluctuations, there are those coming from cloudiness variation.
To analyze these fluctuations, as in our previous work (Peñaloza-Murillo & Pasachoff, 2015), we follow the method of Szałowski (2002) based on a variance analysis and residuals calculations of the convective turbulence. In doing so, it is convenient to make our analysis separately to each of the three cases involved in this investigation: case I, at 2 cm; case II, at 10 cm; and case III, at 2 m above the ground, respectively.

Case I (+ 2 cm)
Focusing on the measurements of Fig. 4 in detail (or Fig. 8), we observe in this case two temporal segments in which the convective activity is remarkable. The first, at the beginning, goes from 08:21 to 09:06. The other at the end, goes from 10:02 to 10:57. In between, we have the stable segment corresponding to the interval 09:07 to 10:02. We note, however, that the first exhibits appreciable fluctuations in the sub-interval 08:21 -08:46 (sub-interval AI) and smaller ones in the next sub-interval 08:47 to 09:06 (subinterval BI). For the last segment, we have similar behavior. In the sub-interval 10:03 -10:35 (sub-interval DI), we have small fluctuations, and in the final sub-interval, from 10:36 to 10:57 (sub-interval EI), the convective activity becomes increasingly higher again in accordance to what one can expect late in the morning. The middle stable segment is designed, then, as sub-interval CI. Under this temporal distribution of five sub-intervals, to some extent arbitrarily chosen on the base of an only visually different temperature fluctuation, we proceed to apply the method of Szałowski (2002) to each of these subintervals.
The method states that the variance is a common and good parameter to measure directly temperature fluctuations owing to convectional turbulent activity but certain conditions apply. Szałowski (2002) defines the temperature fluctuation as: where represents the mean temperature and T(t) represents the measured temperature at time t. If this mean varies negligibly, as happens especially for short measurements series investigating high frequency temperature fluctuations in stable weather conditions, the analysis of variance is direct. If, on the other hand, the fluctuation process is random, it implies that the mean of fluctuations is zero, ¢ = 0, allows for estimating by least-squares fit. Then, = Tpred and the residuals, for each realization of temperature measurement in time instant ti, are given by, where Tpred is the regression equation obtained via that fit. Here Tobs(ti) is the measured temperature.
Figures 11 (a) -(b) depict the fluctuation results for 2 cm above the ground. In Fig. 11 (a), the regression curves are shown, and Fig. 11 (b) presents the temperature residual variation. Fig. 11 (c) gives the histogram of these residuals over the whole series of measurements along with its normal distribution. Table 3

Case II (+ 10 cm)
On closer inspection, Fig. 4 (or Fig. 9) also reveals appreciable temperature fluctuations during most of the event at +10 cm. Specifically at the eclipse onset, we have sub-interval AII from 08:21 to 08:50 followed by sub-interval BII from 08:51 to 09:11. In the middle, we have sub-interval CII with minimum fluctuations from 09:12 to 10:03. The fluctuations begin to increase again in sub-interval DII from 10:04 to 10:30, and finally they amount to higher values in sub-interval EII from 10:31 to 10:57. The results are shown in  Table 4. The regression curves are portrayed in Fig. 12 (a) and Fig.  12 (b) provides graphically the corresponding residuals. From Table 4 we observe that 29 min past the first contact, the variance is reduced by a factor of 4.3, but in the next interval CII, around totality, there is a reduction in the fluctuations by one order of magnitude. In the subsequent two sub-intervals DII and EII, the convective activity returns to similar levels as in the first two sub-intervals, respectively.
In comparing sub-interval CI (Table 3) with sub-interval CII (Table 4), we see that there has been a decline of variance by a factor of 0.5 around and during totality. we see a simultaneous diminishing of convection with height. Graphically, this effect can be noticed in sub-intervals AII and DII, respectively; its corresponding variances in relation to subintervals AI and DI of Table 3 are quite similar in magnitude. This latter comparison means that no change in convectional activity was detected with a small change of height. Figure   12 (b) also includes the regression line fitted to residuals, which, as before, is almost exactly equal to zero, demonstrating the quality of the smoothing [the histogram and its normal curve of Fig. 12 (c), show evidence of a normal distribution of NSAT residuals].

Case III (+ 2 m)
With regard to the third case, Fig. 4  Perhaps other factors or mechanisms, different from convection, were at work, which may explain these specific fluctuations. Afterwards, fluctuations drop off again but in a lesser degree from 10:16 to 10:39 (sub-interval DIII), and finally, from 10:40 to 10:57 (sub-interval EIII), convective activity recovers its expected level. In terms of variance (see Table 5 A graphic representation of fluctuation variation with time is given in Fig. 13

Discussion
In China other NSAT measurements were made within the TSE shadow track by different teams Pintér et al., 2010;Stoeva et al., 2009;Wu et al., 2011;Zainuddin et al., 2001). To some extent a direct or strict comparison of the NSAT changes observed by these teams were not possible given the different ways how they found these changes or due to insufficient information available Lu's team observed the eclipse from a site located in Chongqing along the Changjiang river; they measured solar radiation, air temperature and RH at 1.5 m height at Chongqing University, 245 m above sea level (Huxi campus). In particular, they found that at 8:07, while the eclipse was still in progress, the temperature was still increasing, reaching a maximum of 31.2 ºC at 8:17 before gradually decreasing and reaching a minimum of 28.8 ºC at 9:16; this value was sustained until 9:25 when the temperature began to gradually increase again. Therefore, the NSAT decrease (in this case DTABS) was 2.4 ºC during the eclipse. In order to determine the maximum drop in temperature caused by an eclipse, these authors chose two consecutive days with clear weather for comparison. From their figure 3, it can be inferred that between July 21 and July 22, the variation and value of air temperature were similar outside the eclipse's time interval, and the difference in air temperature across two days was maximized at 9:24, with a maximum difference of 4.6 ºC; therefore, this result gives an idea of how DTLIN was for this eclipse in that location.
In the case of Pintér et al. (2010), whose team observed the eclipse in a site 130 km south-west from Shanghai, their results are presented in their anomaly neither an absolute anomaly as they are defined by Clark (2016). Instead, they correspond to DT as it is defined here in Table 2. Only two of these results are comparable as they correspond to the same height, say, that at 10 cm and 2.0 m; however, the degree to which land or surface type influences the immediate meteorological response to the reduction in solar radiation matters. The ability to compare these results with one another or with other measurements is severely limited because of the possible uncontrolled influences of the surface microclimate on the measurements in each case. This team reported windy conditions, that did not apply to our case, and some clouds during the eclipse. Our instruments were installed in a green-vegetation environment at 809 m above sea level. The vegetative and soil moisture differences of different sites may alter significantly the local response to a radiative reduction by action of a TSE. But, unfortunately, these researchers did not identify the particular micrometeorological environment in which the measurements were taken. The only information that we were able to get from their observation-site coordinates was that they were next to the sea.
Thus, any possible comparison is approximate and not identical.
Stoeva's team Stoev et al., 2012), observed very close to our observation site at three different heights of 10 cm, 50 cm and 2 m; their results are reproduced in Fig. 14 and Table 6 (numerical values of temperature drops are estimated by the difference between the minimum and maximum temperatures plotted in Fig. 14). In comparison to Stoeva et al. (2009) our observed temperature trends are similar, with clouds producing similar effects in the early stages of the eclipse; however, we measure a smaller temperature drop at 10 cm. The difference may be explained by local micrometeorological and observing conditions. They state an instrument resolution of 0.1 °C (manufactured by ExBit, Stara Zagora, Bulgaria) and show images of the equipment setup and its environment. We note that the ground appeared to be a combination of pieces of concrete surrounded by dried greenish-grass. Although our sensors were located very close to where their sensors were, there was a marked differentiation in surface albedo, which could potentially explain some difference between their observations and our measurements. Pintér et al. (2010), on the other hand, observing from a point close to Shanghai found the same effect as ours in their measurements at four different heights (see Table 6) before totality (see their Figs. 2b, c, d, e), which may also be attributable to clouds at their observing site. According to the information given by these authors, taken from a satellite image (see their anomaly of 2.12 ºC for the first and 2.03 ºC for the second (see their figs. 3c and 3d). In Table 6 we attempt to give a first comparison of all these results.
As can be observed from this a value of 29.9 ºC is given as maximum temperature at 2 nd contact, and a value of 27.9 ºC is given as minimum temperature but before 3 rd contact. Thus, a decrease of 2.0 ºC occurred in this interval, which does not correspond to any anomaly considered in this work. Also, these authors do not give at what height above the ground these measurements were taken; hence, this additional anomaly was not included in Table 6.
The activity of the atmospheric boundary layer, extensively studied in the past during temperature following the same methodology as that we used in our previous paper (Peñaloza-Murillo & Pasachoff, 2015), based on an earlier paper by Szałowski (2002).  Fig. 8 of Szałowski (2002)]. However, in comparing our results (Table 7) with those from the latter author it can also be seen that it was found a higher convective activity for the morning 1999 solar eclipse, which was observed at Szczawnica, Poland [see Table   3 of Szałowski (2002)], than that of the morning 2009 TSE at Tinhuangping, a clear indication of the cloudiness effect over convection.
The discussion of the calibration curves involves a matter over a novel method already developed in our previous paper (Peñaloza-Murillo & Pasachoff, 2015), which was based on an early methodology suggested by Phillips (1969). Bearing in mind the cloudiness, it was a complicated task to derive these curves in comparison with the case where the sky was clear, i.e., in Zambia in 2001(Peñaloza-Murillo & Pasachoff, 2015. Curves like these have never been published before; however, we think that they are consistent and reliable given their performance in reproducing the instantaneous temperature profiles which will be used in our subsequently analysis of NSAT lag in relation to solar radiation (see Fig.   7).

Conclusions and final comments
Though totality was visible (Petrov et al., 2010;Pasachoff et al., 2011), variable cloudiness complicated observations and our subsequent interpretation of the thermal response of the atmosphere due to the eclipse. Despite the cloudy conditions (Peñaloza-Murillo & Pasachoff, 2018), the method applied in this investigation turns out to be practical and it is affordable to be repeated and rechecked in future similar conditions. In other words, using a simple set of NSAT measurements obtained during solar eclipses even under adverse weather allows a mathematical analysis of these measurements and its relation to changes and fluctuations of it can still be attempted following the methods presented here (Phillips, 1969;Szałowski, 2002) along with that presented by Peñaloza-Murillo & Pasachoff (2018) in which an analysis of the cloudiness and solar radiation during this eclipse was undertaken.
The anomalous discrepancies displayed in Table 6 are indications of the different ambient conditions in which the respective measurements of NSAT were obtained by different teams in China although some trends were, in principle, detected during this eclipse: it is seen that the variations in temperature (or anomalies) decrease as we go up in the atmosphere (Kapoor et al., 1982). Our team confirmed the detection of cloudiness effects over NSAT measurements during the eclipse in terms of the lag reversals found before and after totality. Moreover, the observations made by another two teams, one of them observing far away from our site, seem to reveal also the same effects.
It seems that the technic of applying a virtual variable, defined and used here and in our previous work (Peñaloza-Murillo & Pasachoff, 2015) as "instantaneous temperature," implicitly suggested by Phillips (1969) via "calibration curves," is a workable and convenient way of studying the temperature response during a TSE.
The measurements confirm that the occurrence of a stable stratification in the low boundary layer can be expected due to a total solar eclipse.        Pintér et al. (2010), He et al. (2010), Chen et al. (2011), Zainuddin et al. (2013, Kwak et al. (2011), Chung et al. (2010), Wu et al. (2011), Kumar (2014, Rao et al. (2013), Jeon (2011), Wang & Liu (2010 and Jeon & Oh (2011). (*) These are the lags for air temperature reduction DT" at specified heights measured from the time of second contact. For the same spot, but in a different environment where their measurements were taken, Stoeva et al. (2009) observed a lag of ~ 1 min after the end of total phase for three different heights above the ground, namely, of +10 cm, +50 cm and +2 m.       The measurements were stopped at around 14:40 due to bad weather (overcast and rain). The effect of the eclipse on measurements is clearly seen as well as the effect of bad weather around 11:30 onwards. These noisy patterns are the result of different combined factors like cloudiness, convection, altitude, solar radiation, etc., that intervene in determining the temperature variation over time. Uncertainties are estimated to be ± 0.25 ºC.

FIGURE 6.
Approximate calibration curves for the three indicated heights above the ground. These curves enable converting solar flux during the eclipse (Fig. 4) into the so-called instantaneous temperature (Fig. 5). They were estimated following the procedure of Phillips (1969), which was subsequently applied by Peñaloza-Murillo & Pasachoff (2015). . Because they are all in phase, the models for this instantaneous temperature are used, instead of the global solar radiation variation due to the eclipse to study the NSAT lag and the delay function (the kinks of the curves observed at 8:50, 10:10 and 10:20 are artificial and come out from calculations of the occultation function).

FIGURE 8.
Theoretical radiative model (black dots) of NSAT at 2 cm above the ground. This theoretical curve is considered to be the virtually instantaneous response of the air to the TSE on 22 July 2009, at that height in Tianhuangping, because it is in phase with the solar radiation model described in Figs. 5 and 7. Note that before totality approximately between 09:04 and 09:12 measured temperature coincides with Tinst, having no lag in that interval. In the previous interval there is a clear and significative unexpected negative lag until 09:12. After totality there are a least three times where both temperatures are equal, at 10:02, 10:28 and 10:36, approximately. Yet from the second of these times onwards there is an unexpected reversal of the lag with a small fluctuation where this third time is.

FIGURE 9.
Theoretical radiative model (black dots) of NSAT at 10 cm above the ground. Similarly, it is considered as the virtually instantaneous response of the air to the TSE on 22 July 2009, at that height in Tianhuangping, because it is in phase with the solar radiation model described in Figs. 5 and 7. Note that before totality there are at least two times where measured temperature is equal to Tinst, approximately at 08:30 and 08:57; in between, there is an unexpected negative lag. After totality, at 10:13 measured temperature is equal to Tinst. From this time up to 10:25 there is an unexpected reversal of the lag. From this time up to 10:45, approximately, values of measured temperature and Tinst are practically the same; after that this lag reversal continues until the end of the eclipse.  FIGURE 10. Theoretical radiative model (black dots) of NSAT at 2 m above the ground. Equally, it is considered as the virtually instantaneous response of the air to the TSE on 22 July 2009, at that height in Tianhuangping, because it is in phase with the solar radiation model described in Figs. 5 and 7. As in the previous cases, there is an unexpected negative lag before totality, between 08:26 and 09:12. Between 09:12 and 09:19 values of measured temperature are equal to Tinst. Afterward, the lag is as expected for the rest of the eclipse.

FIGURE 13 (c).
The histogram of air temperature residuals [ºC], over the whole series of measurements, presented in Fig. 13 (b) for 2 m above the ground. A normal distribution-curve fit is shown in the upper corner inset. Also, it is skewed a little to the right.