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A simple parameterization to predict population characteristics of boundary-layer cumulus clouds Berg, Larry Keith 1996

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A S I M P L E P A R A M E T E R I Z A T I O N T O P R E D I C T P O P U L A T I O N C H A R A C T E R I S T I C S O F B O U N D A R Y - L A Y E R C U M U L U S C L O U D S by L A R R Y K E I T H B E R G B . S c , The Pennsylvania State University, 1993 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES Department of Geography Atmospheric Science Programme We accept this thesis as conforming to the required standard The University of British Columbia November 1996 © Larry Keith Berg, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of G The University of British Columbia Vancouver, Canada Date DE-6 (2/88) A B S T R A C T Estimates of fair-weather cumulus size distributions are made from the joint frequency distribution (JFD) of virtual potential temperature (6V) vs height of the lifting condensation level (zLCL) collected from a single surface weather station. Conceptually, the JFD represents the likelihood that a parcel wi l l rise and the likelihood that condensation wi l l occur. The 6V and the zLCL for each point of the JFD can be compared to the mean 6V of the mixed layer. If the parcel has a 6V less than that of the mixed layer the parcel wi l l not rise. If the parcel has a larger 6V the parcel wi l l rise dry adiabatically. A subset of the these rising parcels wi l l reach their zLCL and form clouds. These parcels wi l l continue to rise, moist adiabatically, until they reach the stable layer above the convective mixed layer. Other rising parcels wi l l not condense but wi l l continue to rise, dry adiabatically, as clear air parcels until they reach the stable layer. The cloud model was designed to use a JFD measured near the top of the surface layer using fast-response instruments mounted on a research aircraft flying over a large area. It is very expensive to obtain surface-layer data using an aircraft. It would be desirable i f a JFD based on inexpensive surface measurements could be used. These experiments wi l l not only investigate the CuP model results, but wi l l also determine i f a less expensive JFD computed from a single surface weather station can be used instead. Using a J F D of 6V vs zLCL calculated from a single surface station, cloud ensemble estimates are compared to cloud measurements made at the Atmospheric Radiation Experiment ( A R M ) site in central Oklahoma during the spring and summer 1994 and 1995 intensive operations periods. There was some skill predicting the cloud-base height — in ii most cases the model estimates were bracketed by observations. No observations of cloud-thickness are made at the A R M site. However, model estimates of cloud-thickness are nearly log-normally distributed, consistent with observations by Lopez (1977) and Stull (1988). Using a JFD constructed from a single-surface station there is little skill predicting cloud cover. iii T A B L E O F C O N T E N T S Abstract i i Table of Contents iv List of Tables v i List of Figures v i i i Chapter One Introduction, Motivation and Literature Review 1 Chapter Two Theory 5 The Joint Frequency Distribution 5 Cloud Cover and Cloud-Field Prediction 6 Daily Evolution of Cloud Cover 9 Computation of the Joint Frequency Distribution 11 Chapter Three Site Description 14 Instrument Description 17 Chapter Four CuP Model Meteorological Input 21 Determination of the Mixed Layer Depth 21 Calculation of the Joint Frequency Distribution from Single Stations 21 Calculation of the Mixed Layer 0V and zLCL 24 Error Analysis 25 Chapter Five Case Study Days 27 Date: 1 May 1994 27 Date: 27 July 1994 27 Date: 28 July 1994 28 Date: 31 July 1994 28 Date: 27 June 1995 29 Date: 6 July 1995 29 Date: 9 July 1995 30 Date: 11 July 1995 30 Date: 13 July 1995 31 iv Chapter Six CuP Model Sensitivity 32 Changes in the Mean of the JFD 32 Slope of Bowen-ratio Ax i s 34 Slope of Solar-Forcing Ax i s 37 Bowen ratio and Solar-Forcing Standard Deviations 39 JFD and 6V Interactions 41 Chapter Seven Results 46 Mix ing Line Analysis 47 Model Accuracy and Measurement Errors 49 Detailed Results 51 Daily Results 68 Chapter Eight Conclusions and Future Work 106 Shortcomings and Improvements 107 Other Future Work 109 References 111 Appendix A Instrument Uncertainty 116 Appendix B Comparison of Empirical and Parcel Determination of zLCL 118 Appendix C Sample Error Calculation 121 Appendix D Cloud and Weather Observations 127 Appendix E JFD Parameters 155 v L I S T O F T A B L E S 3.1 Instruments at each of the A R M facilities 15 4.1 Errors for the S M O S 25 4.2 Propagation of errors 26 6.1 Times of sensitivity plots 32 7.1 Calculated and critical statistics for a log-normal fit 62 7.2 Mean and variance of cloud base height observed at the C F 65 7.3 Statistical tests comparing CuP and observed means 66 7.4 Statistical tests comparing CuP and observed variances 67 7.5 Values of z. , , and zLCL ML 68 A . 1 Accuracy of S M O S pressure, humidity and precipitation measurements 116 A . 2 W i n d accuracy for a given wind speed for S M O S 13 116 A . 3 Temperature accuracy for a given wind speed for S M O S 13 117 A . 4 Accuracy of E B B R measurements 117 A . 5 Accuracy of sonde measurements 117 B . 1 Values zLCL calculated from analytical and iterative methods 118 D . 1 Cloud descriptions used by human observers at the A R M C A R T site 127 D.2 Hourly observations from 1 May, 1994 at the Central Facility 133 D.3 Hourly cloud coverage by sky quadrant at the Central Facility 1 May, 1994 134 D.4 Hourly overhead cloud amounts from 1 May, 1994 135 D.5 Hourly observations from 27 July, 1994 at the Central Facility 136 D.6 Hourly cloud coverage by sky quadrant at the Central Facility 27 July, 1994 137 D.7 Hourly overhead cloud amounts from 27 July, 1994 138 D.8 Hourly observations from 28 July, 1994 at the Central Facility 139 D.9 Hourly cloud coverage by sky quadrant at the Central Facility 28 July, 1994 140 D . 10 Hourly overhead cloud amounts from 28 July, 1994 141 D . 11 Hourly observations from 31 July, 1994 at the Central Facility 141 D . 12 Hourly cloud coverage by sky quadrant at the Central Facility 31 July, 1994 142 D . 13 Hourly overhead cloud amounts from 31 July, 1994 143 D . 14 Hourly observations from 27 June, 1995 at the Central Facility 144 D . 15 Hourly cloud coverage by sky quadrant at the Central Facility 27 June, 1995 145 D . 16 Hourly overhead cloud amounts from 27 July, 1995 146 D . 17 Hourly observations from 6 July, 1995 at the Central Facility 147 vi D . 18 Hourly cloud coverage by sky quadrant at the Central Facility 6 July, 1995 148 D . 19 Hourly overhead cloud amounts from 6 July 1995 149 D.20 Hourly observations from 9 July, 1995 at the Central Facility 149 D.21 Hourly cloud coverage by sky quadrant at the Central Facility 9 July, 1995 150 D.22 Hourly overhead cloud amounts from 9 July, 1995 150 D.23 Hourly observations from 11 July, 1995 at the Central Facility 151 D.24 Hourly cloud coverage by sky quadrant at the Central Facility 11 July, 1995 151 D.25 Hourly overhead cloud amounts from 11 July, 1995 152 D.26 Hourly observations from 13 July, 1995 at the Central Facility 152 D.27 Hourly cloud coverage by sky quadrant at the Central Facility 13 July, 1995 153 D . 28 Hourly overhead cloud amounts from 13 July, 1995 154 E . 1 JFD parameters used as input to the CuP model 155 vi i LIST O F FIGURES 1.1 Surface and mixed-layer thermals 1 2.1 Properties of surface-layer parcels 6 2.2 Properties of surface-layer parcels with 9V profile 7 2.3 Properties of surface-layer parcels with adiabats 8 2.4 Daily evolution of cloud cover 10 2.5 Slopes of Bowen-ratio and solar-forcing axes 12 3.1 Map of North America with case study area marked 14 3.2 Monthly average maximum and minimum temperatures at Ponca City and Enid Oklahoma 16 3.3 Monthly average precipitation at Ponca City and Enid Oklahoma 17 3.4 Sample Belfort Ceilometer and Micropulse Lidar cloud base observations 20 6.1 CuP model sensitivity to changes in z L C L 33 6.2 CuP model sensitivity to changes in 0V 34 6.3 CuP model sensitivity to changes in the slope of the Bowen-ratio axis 36 6.4 J F D with different Bowen-ratio axis slopes 37 6.5 CuP model sensitivity to changes in the slope of the solar-forcing axis 38 6.6 J F D with different solar-forcing axis slopes 39 6.7 CuP model sensitivity to changes in standard deviation along the Bowen-ratio axis 40 6.8 CuP model sensitivity to changes in standard deviation along the solar-forcing axis 41 6.9 Sample JFD and Gv profiles 42 6.10 Sample clear and cloudy updrafts 44 6.11 Sample CuP predicted cloud thickness 45 7.1 Observed and modeled cloud amounts 47 7.2 M i x i n g lines between surface and mixed layer values of 6V and 48 7.3 CuP predicted frequency of a given cloud thickness for 28 July 1994 52 7.4 CuP predicted frequency of a given cloud thickness for 6 July 1995 53 7.5 Profiles of 0„ taken at the C F on 6 July 1995 55 7.6 Profiles of zLCL taken at the C F on 6 July 1996 56 7.7 Plot of CuP cloud thickness vs. height for 1430 L S T on 27 July 1994 57 7.8a Cloud thickness as predicted by the CuP model 59 7.8b Cloud thickness as predicted by the CuP model 60 7.9 Cloud thickness as predicted by the CuP model 61 7.10 CuP modeled up drafts for 28 July 1994, 1430 L S T 63 7.11 CuP modeled up drafts for 6 July 1995, 1430 L S T 64 vi i i 7.12 Profiles of dv taken from C F sondes on 1 M a y 1994 71 7.13 Profiles of r taken from C F sondes on 1 M a y 1994 72 7.14 Profiles zLCL taken from C F sondes on 1 M a y 1994 73 7.15 Observed and CuP modeled cloud cover on 1 M a y 1994 74 7.16 Observed and CuP model predicted cloud-base heights for 1 May 75 7.17 Profiles of 6V taken from C F sondes on 27 July 1994 77 7.18 Observed and CuP model predicted cloud cover on 27 July 1994 78 7.19 Observed and CuP model predicted cloud-base height for 27 July 1994 79 7.20 Profiles of Qv taken from C F sondes on 28 July 1994 80 7.21 Profiles of zLCL taken from C F sondes on 28 July 1994 81 7.22 Observed and CuP model predicted cloud cover on 28 July 1994 82 7.23 Observed and CuP model predicted cloud-base height for 28 July 1994 83 7.24 Profiles of dv taken from C F sondes on 31 July 1994 84 7.25 Profiles of zLCL taken from C F sondes on 31 July 1994 85 7.26 Observed and CuP model predicted cloud cover on 31 July 1994 86 7.27 Observed and CuP model predicted cloud-base height for 31 July 1994 87 7.28 Profiles of 6V taken from C F sondes on 27 June 1995 88 7.29 Profiles of zLCL taken from C F sondes on 27 June 1995 89 7.30 Observed and modeled cloud cover for 27 June 1995 90 7.31 Observed and CuP modeled cloud-base heights for 27 June 1995 92 7.32 Profiles 6V taken from C F sondes on 6 July 1995 93 7.33 Profiles of r taken from the C F sondes on 6 July 1995 94 7.34 Profiles zLCL taken from C F sondes on 6 July 1995 95 7.35 Observed and modeled cloud cover for 6 July 1995 96 7.36 Observed and CuP predicted cloud-base heights for 6 July 1995 97 7.37 Profiles 0V taken from C F sondes on 9 July 1995 98 7.38 Observed and modeled cloud cover for 9 July 1995 99 7.39 Profiles of 9V taken from C F sondes on 11 July 1995 100 7.40 Observed and CuP modeled cloud cover for 11 July 1995 101 7.41 Profiles 6V taken from C F sondes on 13 July 1995 102 7.42 Profiles of zLCL taken from C F sondes on 13 July 1995 103 7.43 Observed and modeled cloud cover for 13 July 1995 104 7.44 Observed and CuP modeled cloud-base height 13 July 1995 105 B.2 Differences between calculated from empirical equation and parcel method 119 B.3 The calculated from empirical equation vs. parcel method 120 ix 1.0 Introduction, Motivation, and Literature Review During periods of free convection, boundary-layer cumulus clouds are created by convective thermals. The core of each thermal contains relatively undiluted surface-layer air as shown in figure 1.1 (Crum and Stull 1987). The two most important parameters in the formation of these clouds are temperature and humidity of the surface layer, which is controlled by surface properties and solar radiation (Rabin et al. 1990). Figure 1.1. Sketch of surface and mixed-layer thermals. The mixed-layer depth is shown by the heavy solid line. The top of the surface layer is marked with the broken line. Thin lines mark the outlines of individual mixed-layer and surface-layer thermals. The core of surface-layer air in each thermal is represented by the heavy dark shapes. The right-most thermal has a cumulus-humilis cloud at its top. Heterogeneous land surfaces cause small differences in air temperature and humidity in the horizontal. These landscape-induced variances can enhance those differences already present in the turbulent boundary layer. A Cumulus Potential (CuP) model has been developed to account for these effects on the observed cloud field. The CuP model, described in section 2, w i l l be tested against cloud distributions observed on several days from 1994 and 1995 at the Atmospheric Radiation Measurement 1 ( A R M ) site centered in north-central Oklahoma. The CuP model was developed to use aircraft data collected over a large area in the mid to upper surface layer. These experiments wi l l not only investigate the accuracy of the CuP model but w i l l also determine i f a JFD computed from a single surface weather station can be used to form the JFD. The instrumentation at the A R M site w i l l be described in section 3. Calculations and methods w i l l be discussed in section 4. Weather for the study days w i l l be described in section 5. Model sensitivity to input parameters w i l l be reported in section 6. Model results w i l l be compared to both human observations and instruments in section 7. Conclusions and future research efforts w i l l be presented in section 8. Boundary-layer cumulus clouds play an important role in the earth's radiation budget and large-scale dynamics. Stull (1992) observed scattered boundary-layer clouds on 261 days of the year over the upper-midwest U S , 33% of the low clouds were boundary-layer cumulus, and 48% were stratocumulus. Raga and Jonas (1993) found that boundary-layer cumulus near the British Isles change the earth's albedo on a horizontal scale smaller than a typical Atmospheric Global Climate Model ( A G C M ) grid cell. Boundary-layer cumulus are important in model simulations of the Indian Monsoon because they transport moisture from the boundary layer to the free atmosphere (Slingo et al. 1988). In many A G C M ' s the cumulus parameterization is for only deep precipitating cumulus (e.g. Donner 1993). Forecasts of the nonprecipitating cloud amount are generally made using: grid box relative humidity, precipitation rate, cloud mass flux, or layer-average mass flux (Sud et al. 1991, Tiedtke 1989, and Slingo 1987). X u and Krueger 2 (1991), using a cloud-resolving model, showed that these methods, with the exception of the cloud mass-flux scheme, are unsatisfactory for representing convective clouds. Cloud amounts predicted also have a strong dependance on model vertical resolution (Tiedtke 1993, X u and Krueger 1991). Computer modeling efforts have shown that the formation of boundary-layer cumulus is sensitive to both the state of the atmosphere and the underlying surface. Many authors (Liu and Avissar 1996, Chen and Avissar 1994, Hong et al. 1995, and Rabin et al. 1990) have found that land and atmospheric characteristics can enhance the formation of cumulus clouds and precipitation. Researchers are working to improve the cloud parameterizitions. Wilde et al. (1985) developed a cumulus-cloud model that used the distributions of surface moisture and entrainment-zone height. Smith (1990) developed a cloud scheme that assumes a distribution of thermodynamic and water variables about the grid box mean. Tiedtke (1993) developed a prognostic cloud scheme which treats boundary-layer cumulus in the cumulus convection scheme. Wetzel (1990) compared several different cloud models by predicting cloud cover during the Wangara experiment. He used Wilde 's scheme, a simple parcel method, a nine parcel method and the relative humidity at the top of the boundary-layer. Wetzel (1990) found that the nine parcel and single parcel methods gave the best results. The CuP model is similar to the nine parcel model purposed by Wetzel, both use a distribution of surface temperature and humidity. Wetzel and Boone (1995) have included an air parcel cloud model in their surface-atmosphere model. In their model a mixing distribution of surface and mixed-layer air is prescribed. 3 Research has also explored the size distributions and spatial relationships of cumulus clouds. Wiel icki and Welch (1986) studied cumulus-cloud fields over both land and water. Hozumi et al. (1982) and Plank (1969) used aerial photographs to study fair-weather cumulus clouds over the ocean. Lopez (1977) found that both cumulus-cloud heights and diameters have a log-normal distribution over many geographic areas. Joseph and Cahalan (1990), Sengupta et al. (1990) Weger et al. (1992) and Zhu et al. (1992) investigated clustering and randomness in cumulus-cloud fields. Cahalan (1991) found a break in the power-law relationship between cloud size and number distribution near a cloud diameter of 2 k m for clouds over ocean surfaces. The CuP also model predicts the size distribution of the clouds based on buoyancy information contained in the JFD. 4 2.0 Theory 2.1 The Joint Frequency Distribution Boundary-layer cumulus clouds form near the top of mixed-layer thermals. The roots of these thermals are near the top of the surface layer (Williams and Hacker 1992). These thermals rise, largely undiluted through the convective mixed layer. Some thermals may rise past their level of condensation and form clouds. During times of free convection and negligible shear-generated turbulence, surface heating is the driving force behind the thermals. Heterogeneity in the surface can help enhance the turbulence in the convective boundary layer. Different parcels of surface-layer air w i l l have different values of temperature and humidity caused by heterogeneous heat and moisture-flux coupling with the ground. Figure 2.1 shows a sketch of surface-layer parcels and their temperature and humidity characteristics. The parcel shading represents temperature; those that are darker are warmer. The humidity of the parcel is represented by the height of the lifting condensation level ( z ^ ) . Warmer parcels can be associated with dry fields, stronger solar insolation, or a small albedo. Parcels that are more moist can be associated with irrigated fields, or areas that received recent rainfall. The temperature and humidity of each parcel can be used to compute the virtual potential temperature (0V) a measure of buoyancy, and , the height that a parcel needs to rise to form a cloud (Schrieber et al. 1996). The number of parcels having various combinations of zWL and 6V can be counted to form a joint frequency distribution (JFD). The JFD for a range of land-use types can be quite complicated with many modes. But 5 Schrieber et al. (1996) show how this complex JFD can be modeled as the sum of simpler distributions. The measured or modeled JFD can then be compared with a mean mixed-layer 6V profile to predict the cloud coverage. A Z L C L O O O I O t l O © O x I • Figure 2.1. Sketch of temperature and moisture of surface air parcels. Darker parcels are warmer. Dashes correspond to the z ^ of the parcel. The shaded region is the range of z ^ values. 2.2 Cloud-Cover and Cloud-F ie ld Predict ion 2.2.1 Cloud Cover and Cloud-Base Altitude Figure 2.2 shows a sketch similar to figure 2.1, along with a sample JFD and mean environmental 6V profile. The shaded region marks the entrainment zone, the range of heights to which buoyant parcels are expected to rise. Some parcels are cooler than the environment, they are more dense than their surroundings and wi l l not rise. Parcel one is an example of such a parcel, and its location in the JFD is marked. A l l similar parcels to the left of the dashed line are cooler then the environment and wi l l also not rise. The rest of the parcels are warmer then the environment, so they are buoyant and wi l l rise. Of the 6 parcels that rise, some, like parcel two, w i l l reach the entrainment zone and stop rising before reaching its z ^ . These parcels w i l l form clear air updrafts. The rest of the rising parcels, such as parcel three, w i l l rise and reach their z ^ . These parcels w i l l condense and continue to rise as a clouds. Height Above A Ground or Z L C L e v (°c) Figure 2.2. Similar figure 2.1 but with the mean 8V profile and a JFD of and dv (oval) shown on the right. The location of surface parcels 1, 2 and 3 on the JFD are shown. The shaded area is the entrainment zone and is the height to which most parcels w i l l rise. Cloud coverage can be computed by comparing the number of rising cloudy parcels to the number of total parcels. This is equivalent to the portion of the JFD that is below and to the right of the dv profile. Since different parcels in the JFD have different zWL values, a range of cloud-base heights is expected, consistent with the findings of Plank (1969). 7 2.2.2 Cloud Height and Cloud Thickness After condensation occurs in a parcel, it w i l l continue to rise moist adiabatically. Tops of both clear and cloudy thermals are determined by the location at which the parcel reaches the environmental 6V. The clear thermal top formed by parcel 2 and the cloudy thermal top formed by parcel 3 are marked in figure 2.3 by the arrows. Because the cloudy parcels follow the moist adiabat for part of their ascent, they can rise to greater depths than i f they had remained cloudless. Height Above Ground or Z L C L 4 ^ * l o o o X e v ( ° Q Figure 2.3. Similar to figure 2.2 but with moist adiabats included on the JFD (broken arrows). The height to which parcels 2 and 3 would rise are marked on the J F D with arrows. The shaded area marks the height range of cloudy thermal tops. The hashed area marks the height range of clear thermal tops. In this example the area with white hashes lies within the shaded area. 8 Cloud thickness is the difference between cloud top and zWL. The thermals w i l l create a cloud field having a range of heights. The CuP model predicts a range of both clear and cloudy thermal tops because the parcels producing the clear and cloudy thermals have different and 9V values. 2.2.3 Implications The CuP model defines three different layers in the cloud-topped boundary layer. The bottom layer is the typical cloud-free boundary layer, and the top layer is a region of completely cloudy updrafts. In between is a unique layer that includes both clear and cloudy updrafts. This layer is not quite the same as the clear-air transition layer described by Malkus (1958) for tropical cumulus. It also is not like the entrainment zone found in the tank experiments described by Deardorff et al. (1980). It is not quite like the L C L zone described by Wilde et al. (1985) which assumes that buoyancy and moisture content of thermals are independent. 2.3 Daily Evolution of Cloud Cover Early in the day the mixed layer depth ( z ; ) is small, the J F D is typically located well above the turbulent mixed layer (figure 2.4), which implies no clouds. As the day progresses the layer w i l l continue to warm, moving the 6V profile to the right. The JFD would warm as well , moving to the right at approximately the same rate as the mixed layer. Since both the 8V profile and J F D are moving in unison, there is little effect on the amount of cloud cover predicted. However, surface heating does increase the probability of cloud 9 formation by causing z, to grow. If the surface layer becomes more moist due to evaporation from the surface, the J F D would be expected to move down relative to the 6V profile, which could increase cloud formation. If the layer dries with time, the JFD would then rise relative to the profile reducing the probability of cloud formation. In figure 2.4 the mixed layer becomes more moist between A and B , and z{ has grown. Clouds would begin to form when the JFD and the profile first intersect. Cloud cover would then increase as the mixed layer continues to grow. The surface layer has dried between B and C but the amount of cloud cover wi l l still increase in this hypothetical scenario because of the growth of z, . Height Above Ground or 0 V (°C) e v (°C) 0 V (°C) Figure 2.4. A sample evolution of 8V profile and JFD. Figure A corresponds to an early morning situation, while B and C would be typical later in the morning. The mixed layer is very thin in A , but grows through the residual layer throughout the morning. 10 2.5 Computation of the Joint Frequency Distribution. Measurements of zLCL and 6V can be used to form a distribution of data points. This distribution can be approximated with a simple function to create a JFD for use in the CuP model. Unfortunately zLCL and Gv are not independent because both are linked by the surface energy budget, warmer areas tend to be drier, so the major and minor axes of the JFD would not be parallel to the zLCL and 6V axes. A set of variables that are independent would be more convenient for fitting the distribution. Schrieber et al. (1996) chose to use a coordinate system based on the surface fluxes. Schrieber et al. (1996) found that the Bowen ratio and the total flux (the sum of the sensible and latent heat flux) can be used to define the JFD. They expressed the total flux by the solar forcing, which is proportional to the temperature difference between the mixed layer and ground skin that would be needed to drive the total flux (Stull 1988). Equations for zLCL and 6V can be derived based on both the Bowen ratio and solar forcing (Schrieber et al. 1996). Figure 2.5 shows a lines of constant Bowen ratio and solar forcing plotted in zLCL and 6V space. Although these lines do not appear to be geometrically orthogonal in the zLCL and 6V plot, they are physically orthogonal. The lines of constant Bowen ratio converge at the mixed-layer value of Bowen ratio. The slope of each line can change relative to the zLCL and 6V axes, and each line is linear in zLCL and 6V space. 11 e (K) V v ' Figure 2.5. Example of 6V and zLCL as a function of the Bo wen ratio B (solid lines) and the solar forcing temperature 6F (dashed lines). Larger Bowen ratios occur over drier ground. Larger solar forcing can be caused by higher sun angles, smaller albedo, and/or less cloud shading (after Schrieber et al. 1996). The Bowen ratio and solar forcing are related to boundary-layer physics. Changes in solar forcing can be attributed to variations in albedo, partial shading by clouds, or changes in sun angle. These variations would cause the JFD to spread along lines of constant Bowen ratio. Variations in Bowen ratio can be caused by differences in soil moisture or crop type. Bowen-ratio variations would cause the JFD to spread along lines of constant solar forcing. In nature the JFD is controlled by a combination of both types of forcing. Schrieber et al. (1996) fit a Gaussian distribution in Bowen ratio and solar forcing space using maximum-likelihood procedures. The shape parameters used to define the JFD 12 were the slope of the Bowen ratio and solar forcing axes in zLCL and 6V space and the standard deviation along each of the axes. The Gaussian distribution takes on the form: G(m,c): 1 exp \ m u j + \CdsJ (2.1) where m is a surrogate measure of location on the Bowen ratio axis projected onto the zLCL axis, c is a surrogate measure of location on the solar forcing axes projected onto the 9V axis, mhd (m) is the corresponding surrogate standard deviation along the Bowen ratio axis , and cds (K) is the corresponding surrogate standard deviation along the solar-forcing axis. While the Bowen ratio and solar forcing axes are more convenient for fitting a JFD to observations, zLCL and 9V are directly related to cloud formation. Therefore the computed Gaussian distribution is converted back to zLCL and 6V coordinates using geometric arguments, for use in the CuP model. 13 3.0 Site Description Data used for verification of the CuP model was collected at the United States Department of Energy Atmospheric Radiation Measurement ( A R M ) site (36.6° N , 97.9° W ) . The site encompasses an area of over 1.2 x 10 5 k m 2 and includes parts of Oklahoma and Kansas (figure 3.1). Land use in the region varies from agricultural to urban. Instruments are distributed among the Central Facility (CF), three boundary facilities and 27 extended facilities, as listed in table 3.1 Figure 3.1. Map of North America with the A R M site marked with the large white box. The box represents the approximate size of the A R M domain. 14 Table 3.1. Instruments at each of the A R M facilities (Splitt et al. 1995). Items in italics are variables measured. Central Facility Sondes: Temperature Profile Humidity Profile Wind Profile Microwave Radiometer: Liquid Water Path Micropulse Lidar: Cloud Base Height Belfort Ceilometer: Cloud Base Height Whole Sky Imager: Cloud Cover Human Observations: Cloud Cover Cloud Type Weather Atmospherically Emitted Radiance Interferometer: Temperature Profile Humidity Profile Extended Facilities Energy Balance Bowen Ratio: Sensible Heat Flux Latent Heat Flux Solar and Infrared Observations Station: Solar Direct Beam Irradiance Solar Diffuse Irradiance Total Solar Irradiance IR Irradiance Surface Meteorological Station: Temperature Humidity Pressure Winds Boundary Facilities Sondes: Temperature Profile Humidity Profile Wind Profile Microwave Radiometer: Liquid Water Path The central facility (CF) and two extended facilities are located in southeastern Grant county, Oklahoma. The area near the C F is mostly cultivated — only a small amount remains as range land or other uses. A l l of the towns near the C F are small (less than 6 km 2 ) . Crops near the C F are primarily (60-80%) non-irrigated wheat, but some hay, sorghum, and alfalfa are also grown. There are some trees, generally less than 10 m tall, 15 along fence rows and in drainage areas. The predominate soil type in Grant county is silt loam, but the C F is located in an area of silty clay loam. The region's climate is continental, with frequent inflow of hot humid air from the Gulf of Mexico during the summer. Winds are generally southerly throughout most of the year, but switch to a northerly direction in the winter. Rainfall in north-central Oklahoma is heaviest during May, June, and July. Monthly average maximum and minimum temperatures are plotted in figure 3.2 for Ponca City (40 km east of the CF) and Enid (40 km southeast of the CF) , and monthly average precipitation is plotted in figure 3.3. -30 -I 1 1 1 1 1 1 1 1 1 1 1 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Fig 3.2. Monthly average maximum, minimum, and average temperature at Ponca City (lines) and Enid (circles), Oklahoma. Tick marks show the record maximum or record minimum at either of the locations (Ruffner 1985). 16 Jan Feb Mar Apr May Jun Jul Aug Sep Oct N o v Dec Month Fig 3.3. Monthly average precipitation at Ponca City (lines) and Enid (circles), Oklahoma. Tick marks show the maximum monthly precipitation at either of the locations (Ruffner 1985) Intensive Operations Periods (IOPs) occur several times a year at the A R M site. During IOPs more sondes are launched and routine maintenance on instruments is avoided. Regular IOPs occur during each season. Other IOPs, of more limited scope, occur as required by scientists. Data from the Regular Spring 1994, Summer 1994, Summer 1995, and the Surface Energy Exchange IOP (summer 1995) were used to verify the CuP model. 3.1 Instrument Description 3.1.1 Energy Balance Bowen Ratio ( E B B R ) Instruments Latent and sensible heat fluxes at most of the extended facilities are measured using energy balance (Bowen ratio) methods. The E B B R is a set of instruments to measure the net radiation near the surface, soil energy storage, soil heat flow, and near-surface gradients of air temperature and moisture. Soil temperature and moisture are measured at five locations around the E B B R at a depth of 0.0 to 0.05 m below ground level ( B G L ) . 17 Soil heat flux is measured using five soil heat flux plates, 0.05 m B G L . A i r temperature and humidity are measured at 0.8 and 1.8 m above ground level ( A G L ) , using an Omega Engineering Inc. Chromel-constant thermocouple and Vaisala Inc. probe. The net radiation is measured at 2.3 m A G L . Atmospheric pressure is measured using a Met One barometer. Uncertainties are presented in appendix A . These instruments sample every 30 seconds. The samples are reduced into five-minute averages (Cook personal communication 1996). 3.1.2 Surface Meteorology Stations (SMOS) The S M O S measures wind speed and direction at 10 m, air temperature and relative humidity at 2 m, atmospheric pressure at 1 m, rainfall, snowfall, and snow cover. One-second samples of each variable, except for pressure, are taken and then averaged to provide half-hour averages. One-minute samples of atmospheric pressure are taken and averaged to give half-hour averages. The half-hour standard deviation is also reported. Accuracies of the S M O S sensors are reported in Appendix A (Wesely personal communication 1996). 3.1.3 Balloon Borne Sonding System (BBSS) The B B S S measures profiles of temperature, humidity, wind speed, and wind direction. Launches occur every three hours on the half-hour during regular IOPs starting at 0230 U T C . Thermodynamic variables are sampled every 2 seconds and wind variables are sampled every 10 seconds. The humidity sensor is slow to report high relative 18 humidities upon entering clouds, and slow to return to lower values when leaving the cloud (Wesely personal communication 1996). Other accuracies are listed in Appendix A . 3.1.4 Belfort Laser Ceilometer ( B L C ) The Belfort Laser Ceilometer Model 7013C uses a 976.6 H z laser and a 30 second time step to measure cloud-base altitude. The ceilometer sampling interval is 5.12 seconds. The instrument's vertical resolution is 7.6 m, with a range of 15 to 7625 m. The B L C has difficulties measuring cloud height in rain, fog, snow and cases with very high thin clouds during periods of strong sunlight (Wesely personal communication 1996). 3.1.5 Micropulse Lidar (MPL) Ceilometer The Scientific Engineering Services micropulse lidar uses a 2.5 k H z laser. Resolution of the M P L is 300 m with a range of 270 m to 15 km. Sampling time for the M P L is one minute (Wesely personal communication 1996). Turner (1996) found that the B L C reports a slightly higher cloud base than the M P L . Figure 3.4 shows a comparison of cloud-base heights from the M P L and B L C taken at the A R M site. Results from both instruments wi l l be compared to CuP model estimates. 19 T3 o 4000 3500 — 3000 — 2500 -2000 -1500 -1000 -500 — • Micropulse Lidar O Belfort Ceilometer fi8 8© O § m • T " 8 10 12 14 16 Time of Day (LST) 18 Fig . 3.4. Belfort Ceilometer and Micropulse Lidar cloud base observations for 28 July 1994. 3.1.6 Human Observations Human observers make hourly observations of cloud coverage, cloud height, and weather observations. Cloud base is reported to within 100 m and coverage is reported in tenths for three levels in each sky quadrant. Stull and Eloranta (1985) showed that human estimates of cloud base height can be inaccurate and they wi l l not be used in this study. 20 4.0 CuP Model Meteorological Input 4.1 Determination of the Mixed Layer Depth The CuP model requires the mixed layer depth (z.) as input. The value of z- was found using an equal area method from the 6V profiles (Driedonks 1982). If z, could not be determined from the profile of 6V, then the profile of mixing ratio (r) , wind direction, wind speed and/or zLCL were used to determine z-. Conserved variables for both moist and dry adiabatic motions, such as zLCL should be nearly constant through the mixed layer (Betts 1985). Heights above ground level were found using the hypsometric equation and the temperature and humidity profile from the C F sonde. The C F sonde has a vertical resolution of approximately 10 m for both temperature and moisture. 4.2 Calculation of the Joint Frequency Distribution From Single Stations Joint Frequency Distributions (JFD) of 6V and zLCL were made from measurements at the A R M site. Schrieber et al. (1996) found several features that their JFD's shared: strong central tendency about a dominant mode, sharply pointed peak, spread of the distribution along the Bowen ratio and solar forcing axes, asymmetric tails, maximum ranges, and an irregular perimeter. Values of 6V and zLCL were calculated from the relative humidity, atmospheric pressure, atmospheric temperature measured at the SMOSs . The saturation vapor pressure was found from the temperature using Teten's formula (Stull 1988). The vapor pressure 21 was found using the definition of relative humidity. Teten's formula was inverted to find the dewpoint (TD): 35.861n(e/eJ-4717.31 TD = i (4.1) D \nielej-17.2694 The value of zLCL is found using (Barnes 1968, Wilde et al. 1985): zLCL~a(T-TD) (4.2) where a is 125 m K 1 . The value of 9V is found using standard methods (Stull 1988). The slope of the Bowen-ratio axis and the slope of the solar-forcing axis were calculated using both mixed layer and surface layer variables. Schrieber et al. (1996) showed that the slope of the Bowen-ratio axis (b) can be expressed by: t = ,p±£L (4.3) where B is the surface Bowen ratio, BML is a mixed layer moisture parameter, 6ML is the mixed layer 6, a is as defined in equation 4.2, and ft is a constant equal to 2.44 x 10"4 K _ 1 . Half-hour mean values of Bowen ratio from the C F that bracket the sonde launch time were averaged together for use in the calculations. The slope of the solar-forcing axis (s) can be expressed by (Schrieber et al. 1996): s = *7^4 (4-4) Standard deviations along Bowen ratio and solar forcing axes were calculated from the S M O S measured standard deviations of 6V and zLCL. The standard deviations measured at the C F which bracket the sonde launch timer were combined using the expression for the variance (o~2): ( T 2 = ^ N i>^2+x{™,(c,-c)2} (4.5) where N is the total number of observations, n is the number instruments, m, is the 22 number of observations made with instrument i, o f is the variance reported by instrument i, ci is the mean value reported by instrument i, and c is the population mean. The standard deviations were converted into the Bowen ratio, solar forcing coordinate system using simple geometric arguments (Schrieber et al. 1996). Cutoffs along the Bowen ratio and solar forcing axes were set to twice the measured standard deviation. Schrieber et al. (1996) computed JFDs from fast-response instruments on an aircraft. N o area-average fast-response measurements were made at the A R M site during 1994-95, so slow-response (approximately 1 Hz) instruments near the C F were used. The hypothesis to be tested is whether the half-hour mean and standard deviations computed by the slow-response sensors at a single point would be an adequate substitute for those found by the more costly fast-response instruments on an aircraft sampling a broader area. Using all of the stations at the A R M site is not justified due to the mesoscale variations that typically occur in the atmosphere. Temperatures and humidities measured far from the C F are not representative of the conditions close to the C F . Stull and Eloranta (1985) found that observed zLCL were not correlated with distant cloud-base height, but were almost perfectly correlated with local cloud-base height. Therefore, only one S M O S , located at the Central Facility was used to calculate the single station JFDs. The station was located at 36.07° N , 97.49° W . A disadvantage of using only one S M O S is that it is not representative of the region. It is located over pasture, so crop land and other land uses wi l l not be represented in the JFD. 23 4.3 Calculation of Mixed Layer 6V and zLCL Values of 6V were calculated at each level of the profile using the methods described in section 4.2. Mean mixed layer values of 6V (6vML) were calculated by simply averaging over the points in the interior of the mixed layer. The starting point was taken to be 500 m, the height at which the sondes become reliable in a convective-boundary layer (Wesley personal communication). The stopping points for the average, which were near the top of the well-mixed layer, but below the base of the capping inversion, were found by eye. When the mixed-layer depth was less then 500 m the average was taken over the layer of nearly constant 6V. Values of zLCL through the mixed layer were calculated from the sondes using a parcel method, rather than equation 4.2 which was used to determine zLCL from surface sensors. A parcel from each level of the temperature profile was lifted by small increments while recalculating temperature until the parcel cooled to saturation; this height was assumed to be zLCL. Comparisons in appendix B between the parcel method and equation 4.2 show that both methods yield nearly identical results in the boundary layer. Mixed-layer averages of zLCL (zLCLML) were computed by taking the average over the interior of the mixed layer using the same endpoint altitudes used for 6V M L . The average over the entire layer was used even in the cases where zLCL increased slightly with height. 24 4.4 Error Analysis Uncertainties in measured quantities are propagated through the calculations to determine errors in zLCL and 6V. Uncertainties in measured relative humidity, atmospheric pressure and atmospheric temperature from the S M O S are given in appendix A . Details of the error propagation calculations are given in appendix C. Table 4.1 shows typical uncertainties for zLCL and 6V found from the S M O S . Table 4.1. Average, standard deviation, maximum and minimum errors for the S M O S . Data was taken from all of the case-study days S M O S zLCL Error (m) Bv Error (K) Average 167.97 0.71 Standard Deviation 53.87 0.31 Max Error 437.73 2.28 M i n Error 103.30 0.46 The uncertainty in the surface Bowen ratio is thought be be ± 5 % (Cook personal communication). However near sunrise and sunset the measurement errors using the Bowen ratio method can be quite large (Stull 1988). The sonde instrument uncertainties should not have a large effect on predicted cloud cover because they are reduced when the mixed-layer average is computed. But the instrument uncertainties from the SMOSs could have an important effect. There are sampling uncertainties in the representation of the environment by both the sondes and surface instruments. Uncertainties arise because the sonde and surface instruments provide only a point measurement in a continuously varying field. In addition, 25 sondes only provide a point measurement in time, they may rise through an active thermal or an area of weak subsidence between thermals. The uncertainty was estimated to be on the order of ±0.5 K for 6V and 150 m for zLCL, as observed from data collected during the Boundary-Layer Experiment 1996 (Stull et al. 1996). Uncertainties in z. measured from a sonde profile can be as large as ±0.5 z,. Uncertainties in the JFD parameters, the slopes of the axes and the standard deviations, were estimated from the known instrument uncertainty and the environmental sampling uncertainty. The same error propagation methods were used to trace this error through the calculations of the JFD parameters. Results using typical values of the variables are listed in table 4.2. The affect of the instrument and environmental errors on the CuP predictions wi l l be discussed in section 7.1. Table 4.2. Propagation of errors through calculations of mixed layer variables and JFD parameters. Errors in the calculated JFD means from the SMOSs are listed in table 4.1. Instrument Environ Sampling Variable Uncertainty Uncertainty Total Uncertainty ±0 .02 ±0 .5 ±0 .52 TD,ML (K) ±0 .06 ±1 .0 ±1 .06 ZLCL,ML (M) ±8 ±140 ±148 Bowen Ratio Slope (K n r 1 ) ±0 .003 ±0 .005 ±0 .008 Solar Forcing Slope ( K n r 1 ) ±0 .00001 ±0 .0004 ±0 .0004 Bowen Ratio Standard Deviation (m) ± 3 ±7 ± 1 0 Solar Forcing Standard Deviation (K) ±0 .2 ±0 .3 ± 0 . 5 26 5.0 Case Study Days The CuP model was tested against nine case-study days from the Spring 1994, Summer 1994, and Summer 1995 IOPs. Criteria for test days were: weak pressure gradients with light winds, the formation of boundary-layer cumulus or clear conditions, and free convection. Cloud type and amounts were taken from human surface observations made at the C F . Free-convective conditions were determined from the wind profile in the mixed layer. Such free-convective cases should have light winds or little wind shear with height. Details of the cloud and hourly observations are in Appendix D . 5.1 Date: 1 May 1994 A weak upper-level ridge over the Texas panhandle moved to the east and weakened, while the 50 kPa flow over the C F was nearly zonal. A surface high, located near Kansas City drifted to the southeast. The C F was under a region of weak surface pressure gradient. Overnight skies changed from overcast to clear. Some fog formed in the low-lying areas around the C F . Cumulus-humilis clouds were reported through the late morning and afternoon. Winds shifted from northerly to southeasterly near noon. W i n d speeds ranged from 1 to 6 m s _ 1. Temperatures at the C F ranged from 6.9 to 15.4 °C. 5.2 Date: 27 July 1994 A trough located over Lake Michigan, and a ridge centered over Nevada dominated the weather. Winds at 50 kPa over the C F were from the northwest. The C F was under a large region of high surface pressure with little pressure gradient. Wind speeds ranged 27 from 3 to 8 m s"1. Wind direction shifted from northwesterly to northly near 1200 L S T . Some dew, haze, altocumulus and cirrocumulus were reported in the morning. In the afternoon cumulus humilis and a small amount of cirrocumulus were reported. Temperatures at the C F ranged from 14.4 to 27.3 °C 5.3 Date: 28 July 1994 The trough over the eastern US deepened and continued to move toward the east. The ridge to the west weakened and moved over Utah. The C F was under a region of high surface pressure with weak pressure gradients. Winds throughout the day were northwesterly with speeds ranging from 0 to 5 m S"1. Morning fog, dew, and haze were reported at the C F . Altocumulus clouds were reported in the morning. Throughout the afternoon cumulus humilis, along with some periods of cirrocumulus and cirrus, were reported. Temperatures at the C F ranged from 16 to 28 °C. 5.4 Date: 31 July 1994 A n upper level trough reaching from Lake Michigan to Arkansas moved to the east and weakened, while a ridge over the southwestern U S shifted east. The C F was under an area of weak cyclonic curvature at 50 kPa. At the surface the C F was under a ridge of high pressure with a moderate gradient. Surface winds were southerly with speeds ranging from 5 to 9 m s _ 1. The temperature at the C F ranged from a low of 18 to a high of 30 °C. Cirrocumulus were observed overnight and into the morning. Altocumulus, dew, and fog were observed in the morning. Cumulus humilis and some periods of altocumulus, cirrus, 28 and cirrostratus were observed in the afternoon. A tornado was spotted 72 km northwest of the C F at 1600 L S T . 5.5 Date: 27 June 1995 A 50 kPa trough was located over the Mississippi valley and a weak 50 kPa ridge over Utah and Colorado remained stationary throughout the day. The 50 kPa winds over the site weakened throughout the day. A n area of surface high pressure moved from southwestern Nebraska into Kansas and weakened. Pressure gradients over the the C F were weak, and the pressure over the C F dropped slightly during the afternoon. Surface winds were light, ranging from 0 to 4 m s _ 1, and changed from northwesterly in the morning to southerly in the afternoon. The temperature at the C F ranged from 17 to 34 °C. 5.6 Date: 6 July 1995 A n upper-level ridge over the southwestern U S began to strengthen, while the upper-level trough over the central U S continued to move eastward. The C F was under the transition region between the 50 kPa ridge and trough. Winds at 50 kPa were northwesterly. A low-level trough began to develop over western Kansas causing surface winds in the region to change from northwesterly to southerly. Winds overnight from 5 to 6 July were light and southwesterly. The C F was under a region of high pressure, the pressure gradient was weak in the morning, but strengthened in the afternoon. Winds throughout the day were variable with speeds ranging from 0 to 5 m s _ 1. Low-level moisture flow into the region increased with the southerly winds. Temperatures at the 29 central facility ranged from 18 to 40 °C. Altocumulus were reported overnight and into the morning. Cumulus humilis were reported throughout the day. Smoke was observed at the C F . 5.7 Date: 9 July 1995 A n upper-level ridge over Colorado moved to the east during the day, while a weak surface trough moved over the southern portions of the site. The C F remained between the 50 kPa ridge and a trough to the east. Winds at 50 kPa changed from northwesterly to northeasterly during the day. Several isolated thunderstorms developed along the trough and moved east. A weak surface high moved in the northern areas of the A R M site and dissipated. Surface pressure gradients over the C F were weak. N o low-level clouds were reported. Some mid-level clouds were reported between 0500 and 0800 L S T . Temperatures at the C F ranged from 22 to 38 °C. 5.8 Date: 11 July 1995 A n upper-level ridge moved over the site while a weak 50 kPa trough began to form over the western U S . Near sunrise a surface trough was located over the site. Winds were southerly and light in the morning. Surface pressure gradients over the C F strengthened some during the day. Peak wind speeds near 6 m s _ 1 were observed between 1400 and 1500 L S T . Haze and smoke were observed at the C F throughout the day. Altocumulus was reported in the mid-morning. Temperatures ranged from 22 to 45 °C. No low-level clouds were reported on this day. Smoke from many wheat-field fires was reported during the day. 30 5.9 Date: 13 July 1995 The ridge aloft continued to drift slowly past the C F . A n area of low pressure from the northern plains began to move southward. Surface pressure gradients at the C F remained weak. During the day showers and thundershowers developed over the northwestern areas of the site. Surface winds at the C F were southerly with speeds ranging from 0.4 to 4.9 m s _ 1. Temperatures ranged from 24 to 41 °C. Light haze and smoke were reported throughout the day. Altocumulus and cirrocumulus were observed in the mid-morning. Cumulus humilis were reported in the mid-moming and in the afternoon. 31 6.0 CuP Model Sensitivity Each of the JFD parameters: the slope of the Bowen-ratio and the solar-forcing axes, the standard deviations along the Bowen-ratio and solar-forcing axes, the mean value of zLCL, and the mean value of Gv were changed independently to test the sensitivity of the CuP model. Ranges of input parameters were chosen to cover at least the measurement error, or at least the range of values observed over all days and times studied. Only a subset of the model runs were duplicated for sensitivity tests. Dates and times used are listed in table 6.1. The mean value of 9V and zLCL of the JFDs were set to the mean mixed-layer values for the sensitivity tests. Table 6.1. Times (LST) shown in sensitivity plots for each cloudy day 27 June 95 6 July 95 13 July 95 1128 1130 1131 1430 1431 1420 6.1 Changes in the Mean of the J F D The value of zLCL was allowed to range ±2000 m from the measured mean value of zLCL used in the original calculations. Figure 6.1 shows how cloud cover changes relative to the difference between the measured zLCL and a test value of zLCL. Although the curves are different they share the same general features. As the JFD is allowed to get more moist the amount of cloud cover increases nearly 50%. Fifty percent cloud cover is not reached because of the discrete bin sizes used to represent the JFD in the CuP model. As the J F D is 32 allowed to dry, the amount of cloud cover decreases to zero. Between is an area of rapid change near the measured value of zLCL. In the sensitivity studies the 50% limit on cloud cover occurs because the mean 6V of the J F D has been set to the mixed layer mean value. Half of the parcels would be too cool to rise and form clouds regardless of the humidity. In the real atmosphere the JFD might be at a temperature warmer than the mean mixed layer value so that cloud cover greater than 50% could occur. Research is ongoing to help determine the relationship between the JFD and the 6V profile. The strange step appearance in the cloud cover curves near 40% cloud cover are the result of a warm layer below z ( that exists in the observed profiles. In the CuP model these warm layers can stop a rising parcel before it reaches the capping inversion. Once ZLCL drops below the warm level, the cloud cover increases. Z L C L Difference (m) Figure 6.1. CuP model sensitivity to changes in zLCL for selected times on each day. The zLCL difference is the difference between the measured mean zLCL value and the value used in the sensitivity test. Vertical lines indicate typical uncertainty. 33 The mean value of 6V was allowed to vary ±8 °C from the measured value. Cloud cover values ranged from 0 to 100% over this temperature range (figure 6.2). The curves are similar to those found for the sensitivity to zLCL. In most of the cases the mean 0V is in a region where the CuP model is very sensitive. Only near predicted cloud cover of 0 and 100% is the CuP model not sensitive to the mean 6V value. The slope of the sensitivity curves is about the same for all the times tested. -8 -6 -4 -2 0 2 4 6 8 Temperature Difference ( °C) Figure 6.2. CuP model sensitivity to changes in 9V for selected times on each day. The 6V difference is the difference between the measured mean 6V value and the value used in the sensitivity test. Vertical lines indicate typical uncertainty. 6.2 Slope of Bowen-ratio Axis The slope of the Bowen-ratio axis was allowed to range over ±0.15 K n r 1 from the calculated values. Typical slopes are close to-1 x l O ^ K n r 1 ; the range includes all reasonable values of the slope. Note that the slopes presented are the inverse of the usual definition of slope. 34 Figure 6.3 shows a plot of cloud cover as a function of the difference between the Bowen-ratio slopes for the times listed in table 6.1. The CuP model is moderately sensitive to the Bowen-ratio slope for most times. Each of the curves has a minimum as the slope of the Bowen-ratio axis approaches the slope of the solar-forcing axis. The JFD is undefined when the slopes are equal. The slopes of the axes approach each other as the mixed-layer Bowen ratio approaches the negative of the mixed layer Qv times a constant as defined in equation 4.4. But a negative mixed-layer Bowen ratio was not observed on any of the case study days, and would be unlikely to occur in a convective mixed layer. 35 50 4 5 ^ 40 A T 1 1 1 1 1 1 1 -0.10 -0.05 -0.15 -0.00 0.05 0.10 0.15 Bowen Ratio Slope Difference ( K m ) Figure 6.3. CuP model sensitivity to changes in the slope of the Bowen-ratio axis for selected times on each day. The Bowen-ratio slope difference is the difference between the measured mean slope of the Bowen-ratio axis value and the value used in the sensitivity test. Vertical lines show typical error. Closed circles correspond to the slopes used in figure 6.4. The compression occurs because of the way the standard deviations of the distribution are specified. They are calculated in terms of 6V and zLCL and then projected into the Bowen-ratio and solar-forcing coordinate system. Sample standard deviations have been added in figure 6.4, these lines are not the ones used in the calculations, but serve as an example. A s the slope gets tilted toward vertical the distance along the solar-forcing axis represented by the standard deviation decreases. This causes the J F D to be compressed along that one axis. 36 A negative change in the slope of the Bowen-ratio axes corresponds to a moistening of the surface layer or the drying of the mixed layer. As shown in figure 6.4, as the slope gets smaller the central frequency of the JFD increases and the spread along the minor axis decreases. This compression of the JFD along the minor axis, with little increase in the length of the major axis causes the central frequency to increase. 600 400 B 200 ~ i—i u . 1 0 - 2 0 0 - 4 0 0 - 6 0 0 - / r l , 1 , 1 , 1 , 1 ! - 2 - 1 0 1 a ; (K) - 2 - 1 0 1 2 e ; (K) Figure 6.4. Plot of JFD with different Bowen-ratio axis slopes. The plots are made using data from 27 June 1995 at 1430 L S T . Deviations of the 6V and zLCL are the axis labels. From left to right the slopes are: -5.17x 10" 3, -1.03x 10" 2, -2 .06x 10"2 ( K m- 1). The first contour is at 0.001, with an interval of 0.002. Broken lines mark the solar-forcing axis, solid lines the Bowen-ratio axis. Horizontal lines at 100 and -100 m represent a hypothetical standard deviation. - 2 - 1 0 1 2 e v' (K) 6.3 Slope of the Solar-Forcing Axis To test the sensitivity of the CuP model to changes in the slope of the solar-forcing axis, slope values were allowed to vary from ±0.01 K n r 1 . This allowed the slope of the solar-forcing axis to change by a factor of three. Only positive values of the slope of the solar-forcing axis have physical meaning so negative values are not allowed. Figure 6.5 37 shows how the predicted cloud cover changed as a function of the difference between the tested solar-forcing slope and the measured values. 45 40 A 35 -=\ ^ 30 S-H > O U O 0 2 5 ^ 2 0 ^ 27 June 1130 L S T • a — 27 June 1430 L S T - I - - - 6 July 1130 L S T - X - - 6 July 1430 L S T • - - 13 July 1130 L S T 13 July 1430 L S T -5.0e-03 0.0e+00 5.0e-03 1.0e-02 Solar Forcing Slope Difference ( K m _ 1) Figure 6.5. CuP model sensitivity to changes in the slope of the solar-forcing axis for selected times on each day. The solar-forcing slope difference is the difference between the measured mean slope of the solar-forcing axis value and the value used in the sensitivity test. Closed circles correspond to the slope difference used for figure 6.6. As the slope of the solar-forcing axis approaches horizontal the J F D gets compressed along its major axis, the central frequency becomes larger, and the J F D gets tilted to the right (figure 6.5). The physical explanation for this behavior is the same as was presented in section 6.2, although the standard deviations are specified in terms of 6V. Although the central frequency is larger the JFD spans a larger 6V range than at smaller values of slope. For the days with observed cloud cover, the tilting of the JFD to the right, and the stretching would cause the cloud cover to increase. The value of slope used 38 in figure 6.6 is marked on figure 6.5. A n increase in slope of the solar-forcing axis can be caused by an increase in the mixed-layer Bowen ratio, or an increase in the mixed layer 0V. Figure 6.6. Plot of JFD with different solar-forcing axis slopes. The plots are made using data from 27 June 1995 at 1430 L S T . Deviations of the 6V and zLCL are the axis labels. From left to right the slopes are: 2 . 3 3 x l O - 3 , 4 . 6 6 x l 0 - 3 , 9.32 x 10-3 ( K m- 1). The first contour is at 0.001, with an interval of 0.003. Broken lines mark the solar-forcing axis, solid lines the Bowen-ratio axis. 6.4 Bowen-ratio and Solar-Forcing Standard Deviations The sensitivity of the CuP model to both the Bowen-ratio and solar-forcing standard deviations was also tested. The standard deviation along the Bowen-ratio axis was allowed to vary from ±100 m, while the standard deviation along the solar-forcing axis was allowed to vary by ±2.0 K . The model is more sensitive to the standard deviation along the Bowen-ratio axis (figure 6.7). On 27 June 1995 at 1430 L S T the model seemed to be more sensitive than on the other days. Doubling the standard deviation caused the estimated cloud cover to increase from near 8 to 17%. Reducing the standard deviation by half caused the amount of cloud cover to drop to near 6%. On 13 July 1995 at 1430 L S T doubling the standard 39 deviation caused the cloud cover to increase from 35 to 40%. Reducing the standard deviation by half caused the cloud cover to drop to 31%. i i i r -100 -50 Bowen Ratio Standard Deviation Difference (m) Figure 6.7. CuP model sensitivity to changes in standard deviation along the Bowen-ratio axis for selected times on each day. The Bowen-ratio standard deviation difference is the difference between the measured standard deviation and the value used in the sensitivity test. 100 The CuP Model shows some weak dependence on the solar-forcing standard deviation (figure 6.8). The most sensitive day was 6 July 1995 at 1430 L S T . Doubling of the standard deviation caused the cloud cover to increase from 8 to 18%. Reducing the standard deviation by half caused the cloud cover to decrease from 8 to 4%. 40 40 35 H 30 ^ 25 -q J-l o 20 U O 0 15 A 10 J 5 0 -e—27 •-I- - -6 • X - - 6 13 13 27 Jlune 1130 L S T 1430 L S T 1130 L S T 1430 L S T 1130 L S T 1430 L S T June July July - -X-i—i—T~r*|*i"i~"r"r"j""r"r"r~ i—|—i—i—i—i—|—i—i—i—i—p -1.0 -0.5 0.0 0.5 1.0 1.5 Solar Forcing Standard Deviation Difference (K) r n r i 2.0 Figure 6.8. CuP model sensitivity to changes in standard deviation along the solar-forcing axis for selected times on each day. The solar-forcing standard deviation difference is the difference between the measured standard deviation and the value used in the sensitivity test. The relatively weak sensitivity to standard deviation is reassuring. Incorrectly determining the standard deviation should not greatly affect the model results. The model dependence on slopes was less than the dependence on mean 9V and zLCL. These results are consistent with those of Wetzel and Boone (1995). 6.5 JFD and 9V Interaction While not an exhaustive test, the CuP model was run with the same J F D and three contrived 9V profiles. These tests examine the affect of the 9V profiles on the model predicted clouds and thermals. Three different 9V profiles were used. In each case 9vML 41 was set to 30 °C, zLCL ML to 1000 m, and z{ to 1000 m. The inversion strength at the top of the mixed layer and the lapse rate above z. were allowed to change in each case. Figure 6.9 shows the J F D taken from 31 July 1994 at 1430 L S T , and the three Qv profiles. .SP 200 X C -400 N -600 - 2 - 1 0 1 2 0 ; and 6V (K) -2 - 1 0 1 2 0V' and 0V (K) - 2 - 1 0 1 2 6V' and 0V (K) Figure 6.9. J F D and 6V profiles used to examine affects of changing the 6V profile. Vertical axis shows the perturbation to zLCL ML or the difference between the height and z,. The horizontal axis is the 8V ML perturbation or the 8V excess or deficit relative to 6V. The same JFD is used in each plot and was take from 31 July 1994, 1430 L S T . Case A has a 2 °C inversion with a stable layer above. Only the small region to the right and below the profile w i l l produce clouds. Figure 6.10 shows the model-predicted thermals. Both clear and cloudy thermals are forced to stop at z{ due to the strong inversion. A small number of cloudy thermals do form, but they are shorter than the clear thermals because the right "end" of the JFD is above the 6V profile. The range of clear and cloudy thermals is due to the discrete nature of the JFD and the CuP model. Case B is very similar to case A , but with only a 0.25 °C inversion. In this case there is a larger range of both clear and cloudy thermal tops because of the slope of the 6V profile (figure 6.10). There are still clear thermals higher than the tallest cloudy thermals because the end of the JFD is still above and to the left of the 6V profile. 42 Case C is different. There is a 0.25 °C inversion at 1000 m, then 6V is constant to 1200 m. Above 1200 m Qi rapidly increases. The cloud field is much different in this case (figure 6.10). A t lower levels all thermals are clear. A t a height of 1000 m the thermals begin to reach the lower inversion creating the lowest step appearance. A l l of the thermals that do not reach their zLCL stop at 1000 m, only clear thermals that wi l l form clouds at higher heights are clear above 1000 m. The number of thermals remains constant up to 1200 m, where the thermals begin to reach the 6V profile again. Although the total number of thermals is constant, the ratio of clear and cloudy thermals changes above 1000 m, because the clear thermals are reaching their zLCL and the water vapor in the thermal is condensing. Near 1500 m the last remaining clear thermals have become cloudy. Because the slope of the 6V profile is less than that of the moist adiabat each thermal wi l l reach its level of neutral buoyancy and stop. A l l three diagrams show patterns similar to those observed on the case-study days, presented in section 7. 43 Height (m) 2200 2 0 0 0 | - A 1800 1600 1400 12001-1000 800 600 400 I I B • A l l rise - A l l clear • A l l cloudy • I 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 Frequency Frequency Frequency 6.10. Clear and cloudy updrafts for cases A , B , and C . " A l l rise" is the sum of clear and cloudy updrafts. Cloud thickness can also be plotted (figure 6.11). Case C has the most and also the deepest cloud cover, case A has the least and thinnest cloud cover. The unevenness in the curves is due to the discrete nature of the JFD. Smaller bin sizes for 6V and zLCL make a smoother curve of cloud thickness, but have little affect on the predicted cloud cover. 44 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 Frequency Figure 6.11. CuP predicted cloud thickness for test cases A , B , and C . 45 7.0 Results The CuP model was used to predict boundary-layer cumulus clouds on nine days in 1994 and 1995. A n overview and discussion of the shortcomings of using a J F D calculated from data collected at a single point wi l l be presented. General results, including typical predictions of cloud thickness wi l l be discussed. Results of the CuP model for the test days wi l l be shown in section 7.4. Plots of observed cloud amount and forecast cloud amounts wi l l be displayed for each day. The CuP model forecasts of cloud base wi l l be compared to B L C and M P L observations. The CuP model was run for the case study days using the JFD computed as described in section 4 and centered at the surface 6V (6V sfc) and zLCL (zLCL sfc). To summarize the results, the CuP model predicted cloud cover 45-100% in excess of observed cloud cover in most cases (figure 7.1). Additional experiments were done using the mean mixed layer values of 6V (6vML) and zLCL (zLCLML) as the J F D mean, keeping all other JFD parameters the same. This led to an estimate of cloud cover 0-20% smaller than observed. These latter experiments were conceived because of the nature of mixing in the surface layer as the parcels rise. This mixing hypothesis implies that the driving force behind mixed-layer thermals is not the JFD at a height of several meters, but rather the JFD near the top of the surface layer, where larger mixed-layer thermals are formed. 46 1.0 <D n o o 0.8 > o U O U 0.5 j2 0.4 o • i -H T3 O >-< &< 0.7 0.6 u 0.3 0.2 0.1 0.0 TT XT TT" • • • Surface Means O M i x e d Layer Means 0.00 0.05 0.10 0.15 0.20 0.25 Observed Overhead Cloud Coverage 0.30 Figure 7.1. Observed and CuP modeled cloud cover. Surface means correspond to cloud forecasts using the calculated JFD set to 8V sfc and zLCL sfc. Mixed layer means correspond to cloud forecasts using the calculated JFD set to 6vML and "LCL,ML • The solid line has a slope of 1. 7.1 Mixing Line Analysis A mixing line can be constructed between 6V ML and zLCL ML and 6V sfc and zLCL sfc (figure 7.2). The mixing line traces the range of 6V and zLCL values of any parcel that consists of a mixture of air from the mixed and surface layers (Betts 1982a, Betts 1982b, and Betts 1985). 47 3.0 2.8 h S — 1128 L S T H — 1431 L S T 2.6 h Mixed Layer 2.4 \ -2.2 Surface Layer 2.0 35 36 37 38 39 Figure 7.2. Plot of mixing lines connecting and mixed layer and surface 6V and zLCL for 6 July 1995. Mixed-layer values are at the left end of the line, surface values are at the right end The circle marks the mixture of 6V and zLCL where the CuP forecast matches the observed cloud cover on 6 July 1995. The center of the JFD was allowed to vary along this line to represent the mixing a convective thermal would undergo. A point along each line was found where the CuP model agrees with observations at the C F ; this best fit ratio is marked by the circles in figure 7.2. For example, at 1128 L S T on 6 July 1995 the CuP model predicted cloud cover matched the observed cloud cover when the JFD was centered at 35.6 °C and 2.15 km. These "best fit" JFD locations wi l l be referred to as 6V Best and zLCL Best. The ratios for each day and time were compared to many different combinations of typical mixed-layer mean quantity and flux scales, such as the friction velocity, Deardorff convective velocity scale, surface and mixed-layer temperature scales, zi, the temperature difference between the surface and mixed layers, and the Obukhov length. No significant correlations were 48 found. Wetzel and Boone (1995) had a similar difficulty defining the distribution for their cloud forecast model. 7.2 Model Accuracy and Measurement Errors A test was done assuming that the human cloud-coverage observations at the C F were in error by ±10%. The mixture of surface layer and mixed-layer air that gave the best CuP estimate of the observed cloud cover ±10% were found. The range in these values was as large as the scatter of the best-fit ratio for all days. This suggested that cloud coverage is very sensitive to air-parcel mixing, and the similar sensitivity of the CuP model makes forecasts of coverage extremely difficult given typical measurement errors. These errors could include: 1) the sondes were not representative of the mean mixed layer, and/or 2) the surface-based instruments were not representative of the surface layer over the area. In addition the theory of the CuP model could be incorrect. The accuracy of the sondes at representing the mean mixed-layer state was addressed in section 4.4 dealing with error analysis. Uncertainties ranged from ±0.5 K for 6V and 150 m for zLCL. Doran and Zhong (1995) found that zt can vary by over 1 km in an area 40 k m 2 . Given the sensitivity of the CuP model to the relationship between the J F D and the 6V profile these differences were substantial. The accuracy of using only one surface station to form the JFD can also be examined. A s discussed in section 4.2, the A R M station used gave a biased sample, it was over pasture. The incorrect estimation of cloud cover could be attributed to sampling error; namely cultivated areas and other land uses were missed in the observations. Most of the 49 cultivated land in the area was non-irrigated wheat. During July and August these areas would be bare with no evapotranspiration and would have a larger sensible heat flux, 8V and zLCL than other areas. Rabin et al. (1990) found that heat flux was the most important parameter for cloud formation. Several smaller JFDs could be used, one for bare ground, another for pasture/range, one for woodlands, etc. These could be added together to form a composite JFD that is more likely to be more representative than one large mono-model J F D (Schrieber et al. 1996). Given the biased sample, one might have expected the modeled J F D to be too cool, and that too few clouds would be forecast. But this was not the case, even the relatively cool JFD greatly overestimated the cloud cover. This would support the mixing hypothesis presented at the beginning of section 7.1. There may also be problems in the assumptions made to fit the JFDs to the data. Schrieber et al. (1996) fit JFDs to data collected with fast response sensors mounted on the N C A R King A i r that flew over a wide range of heterogeneous landscapes. Rather than use fast response aircraft data, we used observations from slower response surface-based instruments at the single point. It is hoped that the mean and standard deviations reported by these slow-response instruments would give similar results to the aircraft data. The standard deviations of the point measurements were similar to those measured by Schrieber et al. (1996) in France over a broader area. Another explanation for the performance of the CuP model is that the theory is not valid. Wetzel and Boone (1995) found that a multiple parcel model can give good cloud estimates. However they let parcels mix through the entire mixed layer. This modeling assumption differs from the observations of Crum et al. (1987), who found that some 50 parcels near the entrainment zone had mixing ratios identical to those measured near the surface, indicating that mixing is not important near the thermal core. Williams and Hacker (1993) found that once a thermal rises above 0.3 z, , there is little mixing between the thermal and the environment. It is impossible, from the data gathered at the A R M site to determine which of the scenarios is correct. The CuP model cloud forecasts wi l l be examined in detail below. 7.3 Detailed Results 7.3.1 Cloud Thickness Distributions of predicted cloud thicknesses were computed for all of the case study days using a JFD centered at 6vsfc and zLCLsfc, d^L and zLCLML, and 6vBest and zLCLBesl. No measurements were made of cloud thickness at the A R M site so it is impossible to verify this aspect of the CuP model results. Some distributions were bi-modal with a maximum at very thin cloud thicknesses and another maximum at greater thicknesses. The maximum at very small thicknesses can be explained by parcels in which the water vapor condenses just before reaching the top of the mixed layer. The parcel would rise only a short distance before reaching its level of neutral buoyancy in the capping inversion. Other cloudy parcels, in which the water vapor condensed at lower heights, were able to rise, moist adiabatically to much higher heights. These parcels rise beyond the capping inversion because the slope of the moist adiabat was less than that of the 6V profile. In some cases there were multiple maxima at larger thicknesses. In almost all of the cases the distribution of cloud thicknesses did not trace a smooth curve. This behavior can be 51 explained by slope changes in the 9V profile and the discrete nature of the JFD. Cloud tops may form where the slope of the profile was less than the slope of the moist adiabat. Cloud tops cannot occur where the slope of the 9V profile was greater than the slope of the moist adiabat. The cloud thicknesses were also a function of the mean used to define the JFD. The cloud thicknesses from 28 July 1994 with the JFD centered at 9vBest and zLCL Best are shown as an example (figure 7.3). This plot is typical of the case study days in 1994. 400 300-^ 1130 L S T 1430 L S T 0 | i i i i | I i i i 1 1 i i i | i i i i | 1 1 i i | i 11 i | i i 11 | i i i i 11 i i i | 11 0.00 0.01 0.02 0.03 0.04 0.05 Frequency 7.3. CuP predicted frequency of a given cloud thickness for 28 July 1994 with the JFD centered at 9vBest and zLCLBest. No clouds were predicted at 830 L S T . Much deeper clouds were predicted on the case study days in 1995. Figure 7.4 shows an example of the CuP predicted cloud thickness from 6 July 1995 using a J F D set to 9„ n„ 0, and ztr, . While cloud thicknesses are not recorded, the human observer at the 52 C F reported only cumulus-humilis clouds at the lower levels. Even on days with cumulus-humilis clouds, some deep clouds might be expected, but for the days in question most of the clouds were quite high. 10000 j 9 0 0 0 - i 8000-1 7000-3s <» 6000 CD C "o 5000 H 4000 o 3000 -I 2000-1 1000-3 0 • W • • _ _ _ _ _ _ __ 0.00 1130 L S T 1430 L S T Frequency 0.01 Figure 7.4. CuP predicted frequency of a given cloud thickness for 6 July 1995 using 6V Best and zLCL Best to center of the JFD. N o clouds were predicted at 830 L S T . The cause of these tall clouds can be determined from the 6V profile. Profiles from each of the different days in 1995 were similar in several important ways. Each had a thick nearly moist adiabatic layer, representing the cloud layer. Each plot also had a weak stable 53 layer above the cloud layer. In the CuP model this allows parcels that reach their zLCL to continue rising well past the observed cloud layer. Figure 7.5 is a plot of the 9V profile for 6 July 1995. Included in the plot are moist adiabats. In this case there was a moist adiabatic layer from approximately 3.5 to 6 km. The plot shows how a parcel could easily rise to great heights. The location or size of the JFD could be important in the formation of these deep clouds. But, these results are largely independent of the J F D used. The CuP model did a good job predicting the cloud base altitude (section 7.3.4) indicating that the altitude of the center location of the JFD is not a problem. The size and shape of the JFD was not the cause of the problem either because all of the cloudy parcels are rising to large heights, not just a small fraction. Some other aspect of the cloud-atmosphere system was keeping the clouds from rising to their level of neutral buoyancy. 54 Figure 7.5. Profiles of 9V taken at the C F on 6 July 1995. Solid lines are moist adiabats. One possible explanation is cloud mixing. Figure 7.6 is the zLCL profile taken from 6 July 1995. This plot showed a dry layer near 3.7 km. A s clouds enter this dry layer they 55 would be expected to mix with the environment. This mixing with dry air would tend to cool the clouds through evaporation so they would no longer rise moist adiabatically. Each of the days in 1995 had some sort of dry layer above the mixed layer that could provide the needed cooling. 0 1 2 3 4 5 6 7 8 9 10 Z L C L ( k m > Figure 7.6. Profiles of zLCL taken at the C F on 6 July 1996. Solid line separates clear and cloudy air. 56 Lopez (1977) found that populations of cumulus clouds form nearly log-normal thickness distributions in both maritime and continental regimes. It is useful to see i f the range of cloud thicknesses predicted by the CuP model are also log-normal. A sample from 27 July 1994 is shown in figure 7.7 along with the best fit log-normal curve. On this day the CuP predictions appeared to be log-normal. GO o H O 0 500 4 0 0 ^ 300-3 200-1° 100-3 1 — 1 — I — 1 — I — 1 — I — 1 — I — 1 — r 0.000 0.002 0.004 0.006 0.008 0.010 0.012 Frequency Figure 7.7. Plot of CuP cloud thickness vs. height for 1430 L S T on 27 July 1994. The solid line is a best-fit log-normal curve. The CuP-model estimated cloud thickness along with the best-fit log-normal distributions are shown in figures 7.8a, 7.8b and 7.9. These plots show the logarithm of cloud thickness verses the accumulated frequency on a log-probability scale. In these plots log-normal curves appear as straight lines. The CuP estimates, using the value of 6V Best and zLCL Best to locate the JFD, are marked with symbols in the figures. The straight lines in the figures are the best fit log-normal distribution to the CuP estimates. The best-fit lines 57 were found using maximum likelihood methods. Figure 7.8 a and b includes times that had cloud thicknesses ranged from near 10 to 300 m, figure 7.9 includes times that had cloud thicknesses ranged from 2000 to 10,000 m. At 1130 and 1430 L S T on 6 July 1995, and at 1130 L S T on 13 July 1995 the CuP model predicted a bimodal cloud distribution. Both modes are plotted for 1430 L S T on 6 July 1995 and 1130 L S T on 13 July 1995, at 1130 L S T on 6 July 1995 the second mode consists of only a few points so no curve was fit. The accumulated frequency of each mode was allowed to range from 0 to 100%. On most of the days the CuP model predicted a distribution of clouds that are nearly log-normal over part of the range of cloud thicknesses. The lowest cloud thicknesses are to the right of the best fit line in almost all of the cases plotted in figure 7.8 a and b. The model predicted more low cloud thicknesses than would be observed from a log-normal distribution. The CuP estimates fell below the the best-fit line at larger cloud thicknesses; the model predicted more high tops than would be observed from a log-normal distribution. These results were consistent with Lopez (1977) who found that at larger cloud thicknesses observations tend to drop below the log-normal curve. 58 10 -H 1 1 1 1—| 1—I [ I I I—I 1 1 1 1 1 h 0.01 0.1 0.5 2 5 10 30 50 70 90 95 98 99.5 99.9 99.99 Accumulated Frequency (%) Figure 7.8a. Cloud thickness as predicted by the CuP model. Symbols are the model output. The lines are a best-fit estimate of a log-normal curve to the CuP output. 59 3 0 0 T Cloud Thickness (m) 200 + 100 + 80 60 •• 50 •• 40 •• 30 •• 2 0 " + o V O 13 July 1994, 1130 L S T July 1994, 1430 L S T July 1994, 1430 L S T July 1995, 1130 L S T M i l l H h 0.01 0.1 0.5 2 5 10 30 50 70 90 95 98 99.5 99.9 99.99 Accumulated Frequency (%) Figure 7.8b. Cloud thickness as predicted by the CuP model. Symbols are the model output. The lines are a best-fit estimate of a log-normal curve to the CuP output. The second mode for 13 July is plotted in figure 7.8. The dot-dashed line is the best-fit curve for 28 July 1994, 1130 L S T . The dashed line is the best-fit curve for 28 July 1994, 1430 L S T . On the days with large cloud thickness the CuP model estimates were very close to a log-normal distribution (figure 7.9). A t large cloud heights the CuP estimates dropped below the best fit line, consistent with Lopez (1977). 60 11000 - r Cloud Thickness (m) 10000 + 9000 + 8000 7000 + 6000 + June 1995, 1430 L S T 1995, 1130 L S T 6 July 1995, 1430 L S T 13 July 1995, 1130 L S T 0.01 0.1 0.5 2 5 10 30 50 70 90 95 98 99.5 99.9 99.99 Accumulated Frequency (%) Figure 7.9. Cloud thickness as predicted by the CuP model. Symbols are the model output. The lines are a best-fit estimate of a log-normal curve to the CuP output. On 6 July 1995 the cloud thickness distribution was bimodal. Note the split vertical axis. The Kolmogorov-Smirnov goodness-of-fit test was used to determine i f the log-normal distribution was a good representation of the CuP predictions (Kirkpatrick 1974). Using a level of significance of 0.05, all but one of the CuP distributions were not significantly different from a log-normal distribution. The test compared the maximum difference in the cumulative probability functions. If the difference was larger than a 61 critical test statistic, than the null hypothesis (that the data is log-normal) is rejected. Table 7.1 lists the critical and calculated statistic used for the Kolmogorov-Smirnov test. Table 7.1. Calculated and critical statistics for a log-normal fit to the CuP cloud thicknesses. "Lower" after the date and times refers to the smaller cloud thickness at a given time, "upper" after the date and time refers to the larger cloud thickness at a given time. Date and Time (LST) Sample Size Calculated Statistic Critical Statistic Accept/Reject N u l l Hypothesis 1 M a y 1994, 1130 7 0.25 0.48 Accept 27 July 1994, 1130 16 0.03 0.34 Accept 27 July 1994, 1430 10 0.17 0.41 Accept 28 July 1994, 1130 10 0.03 0.41 Accept 28 July 1994, 1430 8 0.00 0.45 Accept 31 July 1994, 1430 12 0.00 0.37 Accept 27 June 1995, 1430 41 0.15 0.21 Accept 6 July 1995, 1130 86 0.12 0.15 Accept 6 July 1995, 1430 lower 20 0.22 0.29 Accept 6 July 1995, 1430 upper 44 0.27 0.21 Reject 13 July 1995, 1130 lower 6 0.36 0.52 Accept 13 July 1995, 1130 upper 43 0.13 0.25 Accept 7.3.2 Clear and Cloudy Updrafts The CuP model predicted the frequency of both clear and cloudy up drafts at any level. N o observations were made at the A R M site to verify these results. Figure 7.10 shows a plot of all rising thermals from 1430 L S T on 28 July 1994 using 6V Best and ZLCL Best t 0 center the JFD. This plot is very similar to those made on other days in 1994. The very lowest thermals were all cloud free. Cloudy thermals began to form near 1850 m and increased in number with height. The number of cloudy updrafts increased with height to some level. In general the number of clear thermals steadily decreases with height until 62 all thermals are cloudy. This plot shows many of the features that were discussed in section 6.5. The large step near 2000 m is caused by clear parcels reaching z-. In this case the inversion is strong enough that the cloudy parcels were not able to rise higher than the clear updrafts. 2500 2000 o S-H o <u > o < £ 1500 X 1000 A l l Updrafts Clear Updrafts Cloudy Updrafts 1 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Frequency 7.10. CuP modeled up drafts for 28 July 1994, 1430 L S T using surface layer means. A l l updrafts below 1000 m were clear. " A l l rise" is the sum of clear and cloud parcel at any given height. The CuP predicted updrafts are quite different for the 1995 case study days (figure 7.11). The plot shows many of the features that were discussed in section 6.5. The lower step was caused by clear parcels reaching z ( . Cloudy parcels were able to rise to 9000 m 63 before they begin to reach the 9V profile. A n explanation of the deep clouds is in section 7.3.1. T3 a o S - l o CD > o < 11000 10000 9000-1 8000-j 7000 4 6000 4 5000 4 .SP 4000 PC 3000-1 2000 - | iooo4 A l l Updrafts Clear Updrafts Cloudy Updrafts i | i | i | i | i | i | i | i | i | r-0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Frequency 7.11. CuP modeled up drafts for 6 July 1995, 1430 L S T using surface-layer means. A l l updrafts below 1000 m were clear. " A l l rise" is the sum of clear and cloud parcels at any given height. 7.3.3 Cloud-Base Height A s described in section 4, cloud-base height was measured by the Belfort Laser Ceilometer ( B L C ) and the Micropulse Lidar (MPL) at the Central Facility. The mean cloud base for the study period reported by the B L C was 2169.9 m, the standard deviation reported was 580 m. The mean cloud base for all of the study days reported by the M L P was 2039.6 m, the standard deviation reported was 744 m. Using a t-test the difference 64 between these means was not statistically significant at the 0.05 level of significance. But the P-value obtained (0.069) was close to the level of significance, indicating that the t-test results were weak. A test was also done comparing the variances. They were found to be different at the 0.05 level of significance (P-value of 0.001). The P-value is the probability that the sample outcome could have been more extreme than the observed one, given that the null hypothesis (such as equal means or variances) is true. Large (greater than the level of significance) P-values support the null hypothesis, while small (smaller than the level of significance) refute the null hypothesis. A P-value that is close to the level of significance indicates that the evidence is not as strong as would be obtained from a simple accept/reject test. Tests were made comparing the mean cloud-base height and variance computed from the CuP model using the JFD centered at three different locations: dv sjc and zLCL sfc,, 0 o.ML A N D A N D ev,Best a n d zLCL,Best • When using 6VS^C and zLCLs^c, the CuP model gave the lowest cloud-base heights (table 7.2). Using dv ML and zLCL ML the CuP model gave the highest cloud-base heights. The 6V Best and zLCL Best gave a result between the mixed layer and surface layer values. Table 7.2. Mean and variance of cloud base height observed at the C F with the B L C and M L P . The CuP estimates were made using the JFD set to the mean mixed layer, surface layer, and best estimate values of zLCL and 0V. See text for details. Mixed Surface Best M P L B L C Layer Layer Fit Mean(m) 2039.6 2169.9 1680.5 2269.8 1946.6 Variance (m 2) 552911.4 337500.3 231560.2 158735.2 342986.2 65 The CuP model estimated mean cloud base, using a JFD centered at 6V ML and ZLCL ML w a s g r e a t e r than the M P L , but statistically equivalent to the B L C values at the 0 . 0 5 level of significance (Table 7 .3 ) . However the small P-value between the CuP model and B L C indicates that the evidence was weak. The CuP model estimated mean cloud base using a JFD centered at the Gv s^c and zLCL sfc was less than the M P L and B L C values at the 0 . 0 5 level of significance. With the JFD centered at dvBesl and zLCL Best the CuP cloud base heights were less than the B L C , but equal to the M P L at the 0 . 0 5 level of significance (P-values of 0 . 0 0 1 and 0 . 3 2 , respectively). Table 7 . 3 . Statistical tests comparing CuP and observed means. Level of significance was chosen to be 0 . 0 5 . Means are represented by the symbol fi. The null hypothesis is rejected i f absolute value of the test statistic is greater than the critical value. Nul l Hypothesis Test Statistic Critical Value P-Value Accept/Reject t^BLC = t^sfc 1 0 . 4 0 7 1 .647 < 0 . 0 0 1 Reject MBLC = V-ML - 1 . 5 7 0 - 1 . 6 5 1 0 . 0 5 9 Accept ^BLC ~ f^Best 3 . 2 5 3 1 . 6 5 0 0 . 0 0 1 Reject UMPL ~ Hsfc 5 . 5 3 6 1 .648 < 0 . 0 0 1 Reject UMPL = f^ML - 2 . 7 4 6 - 1 . 6 5 3 0 . 0 0 3 Reject UMPL ~ t^Best 1 . 0 0 4 1 . 6 5 2 0 . 3 1 7 Accept The estimates of the variance by the CuP model using 6V ML and zLCLML, and 6V sfc and zLCL sfc to locate the JFD were statistically different than those observed by the B L C and M P L . The variance predicted by the CuP model using 6V Best and zLCLBest to locate the JFD was significantly different than the M P L observed variance, however the variance predicted 6 6 by the CuP model using 9vBest and zLCLBest to locate the JFD was not significantly different than the B L C variance at the 0.05 level. Table 7.4. Statistical tests comparing CuP and observed variances. Level of significance was chosen to be 0.05. Variances are represent by the symbol o~2. The null hypothesis is rejected i f test statistic is greater than the large critical value or less than the low critical value. Nul l Low Critical High Critical Accept/ Hypothesis Test Statistic Value Value P-Value Reject CTBLC = ^Ifc 1.457 0.779 1.283 0.001 Reject 2 2 BLC ~ ML 0.470 0.704 1.421 <0.001 Reject 2 _ 2 BLC ~ °Best 1.016 0.718 1.394 0.536 Accept 2 _ 2 °MPL ~ °sfc 0.419 0.695 1.437 <0.001 Reject 2 _ _2 ° M P L — M L 0.287 0.657 1.523 <0.001 Reject 2 _ 2 °MPL ~ °Best 0.620 0.664 1.507 0.011 Reject 67 7.4 D a i l y Results The values zi, mixed layer Bv ( 9 v M L ) , mixed layer zLCL (zLCLML), the slopes of the J F D axes, and standard deviations for the CuP model were determined as described in section 4. Table 7.5 lists values of zi, 6vML, and zLClMh, while values of the other JFD parameters are listed in appendix E . Values of the Bowen ratio and solar-forcing slopes, and the standard deviations along each of the axes are consistent with those found by Schrieber et al. (1996). Table 7.5. Values of z-, 6vML, and zLCLML taken from sondes for all case study days (continued on next page). Date Time z,. (km) 6vML (°C) z L C L M L (km) 1 M a y 1994 0838 0.718 8.7 1.142 1130 0.932 11.5 1.196 1452 1.057 14.7 1.331 1730 1.372 16.5 1.635 27 July 1994 0830 0.138 22.1 1.118 1130 2.372 26.0 2.002 1430 2.499 27.1 2.221 1730 2.321 28.6 2.407 28 July 1994 0830 0.234 23.8 1.004 1135 0.820 27.5 1.604 1430 1.981 28.7 2.060 1730 1.937 29.4 2.269 31 July 1994 0830 0.509 27.3 1.050 1130 0.752 32.6 1.700 1430 2.030 35.1 2.302 1730 2.434 35.5 2.380 68 Table 7.1 continued. Values of z., 6V M L , and zLCL ML taken from sondes for all case study days Date Time z. (km) 0..ML CO ZLCLML (KM) 27 June 1995 0830 0.229 29.6 1.428 0910 0.470 30.8 1.721 1128 1.753 32.9 2.183 1429 2.081 34.6 2.130 6 July 1995 0829 0.177 31.3 1.559 1128 1.833 35.5 2.185 1431 3.083 37.7 2.730 9 July 1995 0830 0.309 24.0 1.443 1130 0.705 38.0 2.239 1431 1.079 39.4 2.390 11 July 1995 0830 0.357 34.7 1.619 1130 0.671 41.7 2.869 1430 2.932 43.8 3.394 13 July 1995 0830 0.405 35.3 1.307 1131 1.855 38.8 2.008 1430 2.314 40.0 2.190 7.4.1 Date: 1 May 1994 Profiles of 6V from 1 May are shown in figure 7.12. A t 1130 L S T z. was about 0.95 km. The 1130 LST6V profile was nearly moist adiabatic from 1.3 to 1.6 km. But this layer was above z{, indicating the observed cloud layer may not be turbulently coupled to the mixed layer. A t 1130 and 1452 the mixing ratio (r) (figure 7.13) was almost constant to 1.0 km. A t 1730 L S T , r decreased slowly with height to an altitude of about 1 69 km where r began to decrease more quickly with height. There was no jump in r to indicate z. as there was in the earlier profiles. A plot of zLCL with height (figure 7.14) showed a well-mixed layer below 1.0 km at 1130 L S T . There was a jump in zLCL near 0.90 km at z, . The layer from 0.7 to 1.0 k m could be the Betts (1982) transition layer. There was a cloud layer from 1.0 to 1.7 km. This implied the cloud layer was only weakly linked to the well mixed layer, as shown by the mixing line structure on the zLCL profile. Betts (1985) found that there was often a layer between the well mixed layer and the cloud layer that had a zLCL gradient different than that of the cloud layer. The zLCL gradient in the well mixed layer should be zero. More examples of the transition layer are shown for some of the later case study days. The zLCL measured by the sonde never reached the height reported by the sonde, because the sonde did not rise through a cloud. 70 Figure 7.12. Profiles of 6V taken from C F sondes on 1 M a y 1994. Solid lines are moist adiabats. 71 0.2 0.8 1.2 1.8 2.2 2.8 3.2 3.8 4.2 4.8 Mixing Ratio (g kg"1) Figure 7.13. Profiles of r taken from C F sondes on 1 May 1994 72 Z L C L 0™) Figure 7.14. Profiles zLCL taken from C F sondes on 1 M a y 1994. Thin solid line is z equal to zLCL. Cloudy air is above the line, clear air below. Figure 7.15 shows both observed and CuP modeled cloud cover. The observed cloud cover at 1130 L S T may not have been due to local boundary-layer processes, because of the weak turbulent coupling between the mixed and cloud layers. Perhaps the clouds were advected from a neighboring region. Model results for 1 May were typical. With the mean of the JFD set to the 9vMl and zLCLML the CuP model underestimated the 73 cloud cover. Using a JFD with its mean set 6v sfc and zLCL sfc the model greatly overestimated the cloud cover. One exception occurred on 1 May. At 1200 L S T the human observer at the C F reported 80% cloud cover. A t that time both the M P L and the B L C did not report any cloud-base heights. It was unlikely that there are so many clouds over the C F with no reported cloud bases, the human probably over estimated the cumulus-cloud cover at 1200 L S T . Some high clouds were observed at 1600 and 1700 L S T , but have not been included in figure 7.7. The time interval between the CuP calculations was caused by the B B S S launch times. t-H > O U T 3 =3 O U 100 90 80 70 60 50 40 30 20 10 0 J • Observed CuP, M L Means CuP, Sfc Means • I 1 I 1 I 10 12 • • 1 I 1 1 14 i 16 18 Time of Day (LST) Figure 7.15. Observed and CuP modeled cloud cover on 1 May 1994. CuP cloud cover was determine using a JFD set to the both the mixed layer ( M L ) and surface-layer (Sfc) means. Cloud amounts that were above the convective boundary layer have been removed (see text for details). Values and ranges of cloud base heights predicted by the CuP model were consistent with observations (figure 7.16). The mean cloud-base height from the CuP model, using a JFD centered at 6V sfc and zLCL sfc were smaller than the observed sample mean cloud-base height from the B L C and larger than the sample mean from the M P L . 74 Statistical t-tests were used to determine i f the mean cloud-base height predicted by the CuP model was the same as the inferred population mean from the B L C and M P L . Differences between the CuP cloud-base heights, and the M P L and B L C cloud base heights were statistically significant at a 0.05 level (P-values 0.0089 and 0.019, respectively) indicating that the CuP mean was probably between the B L C and M P L means. The B L C and M P L did not report any clouds later in the day, although clouds were reported by the human observer. The CuP model did predict cloud coverage later in the day when using Gv sfc and ZLCL sfcto center the JFD. The variance predicted by the CuP model was less than the sample variance measured by the B L C . A l l M P L observed cloud-base heights were at same level so no variance could be determined. Tests were made to determine i f the CuP and B L C variances were the same. The model overestimated the variance of cloud-base heights compared to the B L C (P-value of <0.0001). _ 3000 & 2500 -i-> "§> 2000 H * 1500-1 pq 1000-1 o 500-1 U • M P L O B L C • CuP, Sfc Means 4 i 1 r 8 10 12 14 " > — i — 1 — r 16 18 20 Time of Day (LST) Figure 7.16. Observed and CuP model predicted cloud base heights for 1 M a y 1994. CuP points are the predicted mode cloud-base height. Error bars on the CuP points correspond to range of cloud base heights predicted by the model. Error bars on the M P L and B L C correspond to the difference between the observations. 75 7.4.2 Date: 27 July 1994 The 6V profiles for the C F sondes are plotted in figure 7.17. The mixed layer reached a steady-state depth by 1130 L S T . The capping inversion at the top of the mixed layer remained strong throughout the day. The value of zi decreased from 2.5 km at 1430 L S T to 2.3 km at 1730 L S T , probably due to advection and/or subsidence. The layer from 2.4 to 2.7 km was nearly moist adiabatic at 1430 L S T , while the layer from 2.1 to 2.5 km was nearly moist adiabatic at 1730 L S T . 76 0 (°C) V v ' Figure 7.17. Profiles of 6V taken from C F sondes on 27 July 1994. Solid lines are moist adiabats. Observed and modeled cloud cover is presented in figure 7.18. Again, using a J F D with means set to dvML and zLCLML the CuP model predicted no cloud cover at most times. A t 830 L S T the model did predict a very slight amount of coverage. This was caused by an 77 unusually large J F D . Using 6V^C and zLCL sfc the model greatly overestimated the cloud cover, with predicted cover values reaching 100%. S - l > O U O U 100 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 • Observed • CuP, M L Means • CuP, Sfc Means T 8 10 12 14 16 18 Time of Day (LST) Figure 7.18. Observed and CuP model predicted cloud cover on 27 July 1994. CuP cloud cover was determine using a JFD set to the both the mixed layer ( M L ) and surface-layer (Sfc) means. Using 8V sfc and zLCL sfc to center the JFD, the CuP model mode cloud-base height was less than the cloud-base heights observed by the B L C (figure 7.19). A t 830 L S T the ZLCL sfc w a s a ^ S 0 q u i t e l ° w a r *d the CuP prediction for the mode cloud-base height was very close to the ground, although no fog was reported. Tests were made to determine i f the mean from the CuP model and the population mean of the observations were the same. The difference in the means was significant at a 0.05 level (P-value <0.0001). The CuP model, using 6V ML and zLCL ML also had a smaller mean daily averaged cloud base. The difference between the CuP mean and the B L C population mean was significant at the 0.05 level (P-value <0.001). 78 The variance predicted by the CuP model using both 6V ,c and zLCL ,, and &v ML and zLCLML was larger than the sample variance measured by the B L C . The CuP variance was larger than B L C population variance at the 0.05 level (P-value <0.001). 4000 § 3500 Jc 3000 'S 2500 <D 2000 fg 1500 'g 1000 Q 500 o Belfort Ceilometer X CuP, M L Means # CuP, Sfc Means T j * I j i i T 8 T 10 12 14 Time of Day (LST) 16 18 Figure 7.19. Observed and CuP model predicted cloud base height for 27 July 1994. CuP points are the predicted mode cloud-base height. Error bars correspond to range of cloud base heights predicted by the model. The M P L was inoperative. Note that the time axis does not cross the cloud base axis at 0. 7.4.3 28 July 1994 Profiles of 0V for 28 July are plotted in figure 7.20. B y 1135 L S T there was only a small inversion between the well-mixed and the residual layers near 0.8 km. The mixed layer reached steady state between 1130 and 1430 L S T . A t 1730 L S T 6V began to increase some with height above 1 km. A t 1730 the zLCL profile also began to increase slowly with height above the same level (figure 7.21). These changes could show that the layer was not completely well mixed or that there was a sampling problem with the sonde. Perhaps it drifted into a region of warm and dry entrained free-atmosphere air. The layer from 1.6 to 79 2 k m at 1730 L S T was the Betts transition layer, it was turbulently coupled to the well mixed layer and the cloud layer. e ( ° o V v ' Figure 7.20. Profiles of 0V taken from C F sondes on 28 July 1994. Solid lines are moist adiabats 80 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Z L C L <km) Figure 7.21. Profiles of zLCL taken from C F sondes on 28 July 1994. Thin solid line is z equal to zLCL. Cloudy air is above the line, clear air below. The observed and modeled cloud cover is shown in figure 7.22. Using 6V ML and ZLCL,ML t n e m ° d e l predicted 0% coverage at all times. Using 8vsfc and zLCL sfc the model over predicted the cloud coverage by 90% through much of the day. Some high clouds where reported at 1700 L S T but have not been included in figure 7.23. 81 > o U T3 O G 100 ^ • • 9 0 - • Observed 80 - • CuP, M L Means 7 0 - • CuP, Sfc Means 6 0 -5 0 -4 0 -3 0 -2 0 -1 0 - • • • • • 0 - 1 <? T - T " P — T * i — i — i * i 9-10 12 14 Time of Day (LST) 16 18 Figure 7.22. Observed and CuP model predicted cloud cover on 28 July 1994. CuP cloud cover was determine using a JFD set to the both the mixed layer ( M L ) and surface-layer (Sfc) means. Cloud amounts that were above the convective boundary layer have been removed (see text for details). Using a J F D set to 9V sfc and zLCL sfc the CuP model mean cloud-base height was smaller than those measured by the M P L and B L C . A t-test was used to determine i f the CuP mean was the same as the inferred population mean of the observations at the 0.05 level of significance. The tests found that the means were different (P-values were both <0.0001). Although the CuP means were smaller, the mode cloud-base height predicted was within the margin of error of the B L C and the M P L (figure 7.23). The CuP variance was larger than the B L C and M P L sample variances. Tests showed that the CuP variance and the inferred population variances from the B L C were different at the 0.05 level of significance (P-value <0.0001), but no statistical difference could be determined between the CuP and M P L observations (P-value of 0.859). The instantaneous range of cloud-base height reported by the CuP model appears to be larger than the range reported by the B L C and M P L . 82 4000 § 3500 j£ 3000 "53 2500 DC <D 2000 q§ 1500 *3 IOOO G 500-1 • Micropulse Lidar O Belfort Ceilometer • CuP, Sfc Means 8 " i 1 — i — 1 — r 10 12 14 Time of Day (LST) 16 18 Figure 7.23. Observed and CuP model predicted cloud-base height for 28 July 1994. CuP points are the predicted mode cloud-base height. Error bars correspond to range of cloud base heights predicted by the model. 7.4.4 Date: 31 July 1994 Profiles of 6V from the C F sonde are shown in figure 7.24. The mixed layer reached steady state between 1130 and 1430 L S T . The 0V profile above the mixed layer remained almost unchanged throughout the day, indicating that advection and subsidence are not important. The 6V increases with height from 1.2 to 2.2 km in the 1430 L S T profile. The Betts transition layer was evident below cloud base in the 1430 and 1730 L S T sondes from 1 to 2 km (figure 7.25). Below the transition layer and at 1130 L S T the bottom layer was well mixed. 83 84 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Z L C L < k m ) Figure 7.25. Profiles of zLCL taken from C F sondes on 31 July 1994. Thin solid line is z equal to zLCL. Cloudy air is above the line, clear air below. Observed and modeled cloud cover is presented in figure 7.26. Some cirrus and cirrocumulus were reported at 0600 L S T . These cloud amounts were not included in figure 7.18 because they are well above the boundary layer. Observed cloud cover peaked at 1400 with on onset time of 1300 L S T . At 1600 L S T a mixture of stratocumulus and cumulus were reported. With 8V ML and zLCL ML the CuP model predicts 0% cloud 85 coverage at each time. Using the surface-layer means the model predicted 0% at 830 L S T . A t the other times the model over predicted cloud cover, but seemed to capture the trend. > o U =5 O U 100 - r 9 0 -8 0 -7 0 -6 0 -5 0 -4 0 -3 0 -2 0 -1 0 -0 -• Observed • CuP, M L Means • CuP, Sfc Means • T 8 T " 10 12 14 Time of Day (LST) 16 Figure 7.26. Observed and CuP model predicted cloud cover on 31 July 1994. CuP cloud cover was determine using a JFD set to the both the mixed layer ( M L ) and surface layer (Sfc) means. Cloud amounts that were above the convective boundary layer have been removed (see text for details). 18 At 0830 L S T both the M P L and B L C reported clouds well above the boundary layer (figure 7.27). M P L data was missing through much of the afternoon. The CuP model daily mean cloud-base height using dv sft and zLCL sfc was smaller than those observed by the B L C and M P L . The CuP mean and inferred M P L population mean are the same at the 0.05 level of significance (P-value of 0.086). The CuP mean was found to be less than the inferred B L C population mean (P-value <0.0001). The range of CuP cloud-base heights fell within the range of uncertainty of the B L C . The variance predicted by the CuP model was larger than the sample variance reported by the B L C . Tests showed the difference to be significant at the 0.05 level (P-86 value of 0.015). A l l cloud-base heights reported by the M P L in the afternoon were at the same height so no sample variance was computed. 4000-§ 3500-£ 3000-'53 2500-« o 2 0 0 0 -,1 1 5 0 0 -*g 1 0 0 0 -£ 500 • Micropulse Lidar o Belfort Ceilometer • CuP, Sfc Means ° fl fit o 0 0 * ^ A Q • I I 7 8 T 10 T 12 14 T 16 Time of Day (LST) Figure 7.27. Observed and CuP model predicted cloud base height for 31 July 1994. CuP points are the predicted mode cloud-base height. Error bars correspond to range of cloud base heights predicted by the model. 7.4.5 Date: 27 June 1995 Profiles of 6V taken from the C F sonde are shown in figure 7.28. The 0830 L S T sonde stopped reporting near 7.0 km so a second sonde was launched at 0910 L S T . A l l of the dv curves seemed to collapse on each other between 1.6 and 2.2 km. The zLCL plot showed that the boundary layer at 1128 is not as well mixed in the vertical as might be guessed from the dv profile because zLCL increases with height (figure 7.29). The Betts' transition layer between the cloud and well mixed layer was evident in the zLCL profiles at 1429 L S T between 1.9 and 2.2 km. 87 88 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Z L C L < k m ) Figure 7.29. Profiles of zLCL taken from C F sondes on 27 June 1995. Thin solid line is z equal to zLCL. Cloudy air is above the line, clear air below. The time evolution of the cloud cover is shown in figure 7.30. The observer at the C F reported cumulus humilis coverage near 30% at 0800 and 0900 L S T , with bases near 1 or 1.5 km. The profiles of 6V at those times showed there was a very shallow mixed layer (0.2 km). The clouds were in the residual layer and not associated with mixed-layer 89 physics and have not been included in figure 7.30. The B L C and the M P L did not report any cloud-base heights at those times to confirm the observed cloud bases. A t 830 L S T the model, using both the surface and mixed-layer mean values, predicts 0% coverage. Through the rest of the day the model over predicted the cloud coverage using the surface-layer means. A t 1430 L S T the model came very close to the observed values using the mixed-layer means. > O U O 0 100 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 • Observed • CuP, M L Means • CuP, Sfc Means T 8 10 12 • • 14 16 Time of Day (LST) Figure 7.30. Observed and modeled cloud cover for 27 June 1995. CuP cloud cover was determined using a JFD set to the both the mixed-layer ( M L ) and surface-layer (Sfc) means. Cloud amounts that were above the convective boundary layer have been removed (see text for details). 18 CuP model estimated cloud-base heights and observed cloud-base heights are shown in figure 7.31. The CuP predictions were within the region of uncertainty of the B L C and M P L (figure 7.31). A t 1130 L S T no clouds were reported by the B L C or M P L . The CuP daily mean cloud-base heights were smaller than those observed by the B L C regardless of the center location of the JFD. The CuP mean was smaller than the population mean inferred from the B L C and M P L at the 0.05 level (P-values of <0.001 in 90 each case). Using a JFD centered at 6V sfc and zLCL sfc the CuP model mean was less than the M P L inferred population mean at the 0.05 level (P-value of <0.001). Using a JFD centered at 6vML and zLCLML, and dvBest and zLCLBest the CuP mean cloud-base heights were close to those observed by the M P L . Tests indicated that the CuP mean and the inferred population mean from the M P L were the same (P-values of 0.190 and 0.765, respectively). While both agree with the M P L , (Table 7.3) there was stronger agreement between the M P L and the CuP model using 6V Best and zLCL Best. The CuP model did a good job predicting the variance in cloud-base height. The CuP model variance using a JFD centered at 8V sfc and zLCL sfc was close to both the B L C and M P L sample variances. Tests showed evidence that the variances were the same at the 0.05 level of significance (P-values of 0.37 and 0.34, respectively). The CuP model variance using a JFD set to 6vML and zLCL ML, and 6vBest and zLCL Best was less than observed sample variance. With a JFD centered at 6V Best and zLCL Best there was a difference in the variances of the CuP model and the M P L (P-value of 0.045). Tests indicated that the CuP variance using dv ML and zLCL ML was less than the B L C and M P L observed population variance (P-values of <0.0001 and 0.014, respectively). 91 4000 § 3500 £ 3000 too "S 2500 9 2000 m 1500 O 1000 500 10 • Micropulse Lidar O Belfort Ceilometer X CuP, M L Means • CuP, Sfc Means 12 O • 14 Time of Day (LST) 16 Figure 7.31. Observed and CuP modeled cloud base heights for 27 June 1995. CuP points are the predicted mode cloud-base height. Error bars on the CuP points correspond to the range of cloud base heights predicted. Note the change of scale on the vertical axis, compared to previous graphs. 7.4.6 Date: 6 July 1995 A much deeper mixed layer developed on 6 July 1995 than was observed on the other days. A t 1128 L S T z, was estimated to be 1.8 km. From the 6V profile, however it appeared that a much higher z ( might be appropriate because the inversion near 1.8 km was weak (figure 7.32). But, the profile of r showed that the well mixed layer extended to near 1.8 k m where there was a 4 g k g - 1 jump in r (figure 7.33). A t 1431 L S T zi was near 3.1 km. A typical boundary-layer structure could be seen in the zLCL profile at 1431 L S T (figure 7.34). The well mixed layer extended from the surface to 2.2 km, a subcloud transition layer ranged from 2.2 to 2.5 km and there was a cloud layer from 2.5 to 3.3 km. 92 Figure 7.32. Profiles 6V taken from C F sondes on 6 July 1995. Solid lines are moist adiabats 93 r (g/kg) Figure 7.33. Profiles of r taken from the C F sondes on 6 July 1995 94 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Z L C L ( k m > Figure 7.34. Profiles zLCL taken from C F sondes on 6 July 1995. Thin solid line is z equal to zLCL. Cloudy air is above the line, clear air below. The model did a good job predicting the amount of cloud cover observed at 1431 and 1730 L S T using the mixed-layer means (figure 7.35). Using the surface-layer means the model overestimated the amount of cloud cover. A t 0800 and 0900 L S T cumulus humilis were reported at the C F , but the CuP model predicted no cloud cover. A t this time 95 of day the mixed layer was very shallow and the clouds were not caused by convective thermals. Neither the M P L nor the B L C reported clouds at that time. A t 1100 L S T some patches of altocumulus were reported. The clouds at 0800, 0900, and 1100 L S T were not included in figure 7.36 because they were above the boundary layer. iuu — 9 0 - • Observed g 8 0 -7 0 -• • CuP, M L Means CuP, Sfc Means • S H 6 0 -> O 5 0 - • U T3 4 0 -O 3 0 - • U 2 0 -1 0 - • • • • 0 - cp • . n T * • q ? 1 1 — < ? 6 8 10 12 14 16 Time of Day (LST) Figure 7.35. Observed and modeled cloud cover for 6 July 1995. CuP cloud cover was determined using a JFD set to the both the mixed-layer ( M L ) and surface-layer (Sfc) means. Cloud amounts that were above the convective boundary layer have been removed (see text for details). Model predicted and observed cloud-base heights are shown in figure 7.36. The model mode cloud-base heights were very close to the observations. The daily mean cloud-base heights predicted by the CuP model were less than the sample mean heights observed by the M P L and B L C , with one exception. The CuP model, using a J F D centered at 6V ML and zLCL ML, and the inferred M P L population means, were the same at the 0.05 level of significance, although the test was weak because the P-value was only 0.0567. 96 The CuP model variances were smaller than those observed regardless of the JFD. Tests showed that the differences were significant. The P-values ranged from 0.01 between the M P L and CuP using 6vML and zLCLML and <0.001 between the B L C and the CuP model using Gvsfc and zLCLsfc.. x ! .»—i <D X o 1/3 a PQ o U 4000 3500 3000 2500 2000 1500 1000 500 "O Micropulse Lidar O Belfort Ceilometer X CuP, M L Means • CuP, Sfc Means () B 10 12 ~r~ 14 16 Time of Day (LST) Figure 7.36. Observed and CuP predicted cloud base heights for 6 July 1995. CuP points are the predicted mode-cloud base height. Error bars on the CuP predictions correspond to the range of cloud base heights. 7.4.7 Date: 9 July 1995 While z. was quite high on 6 July 1995, values were much lower on 9 July 1995 (figure 7.37). Values of z, changed due to the passage of a weak surface trough overnight on 8 to 9 July 1995. A shallow mixed layer was apparent at each observation with little growth between times, probably due to subsidence over the area. The mixed layer was not very well-mixed for any of the profiles. The change in zLCL with height is a good measure of how well-mixed the mixed layer is. In a perfectly well mixed layer dzLCL/dz should be zero. On 9 July at 1130 L S T dzLCL I dz was near 0.72 and at 1430 L S T it was nearly 0.3. In contrast, at 1430 L S T on 13 July 1995 dzLCLl dz was only 0.05. 97 Figure 7.37. Profiles 6V taken from C F sondes on 9 July 1995. Solid lines are moist adiabats No low-level clouds were observed and the CuP model predicted no cloud cover at 0830 and 1130 L S T . Using a JFD centered at 9V ML and zLCL ML the model predicted no 98 I-H > O U O U • cloud cover at 1430 L S T . With a JFD centered at 0V sfc and zLCL sfc the model predicted coverages near 40% at 1430 L S T (figure 7.38). 100 90 80 70 60 50 40 30 20 10 0 Observed CuP, M L Means CuP, Sfc Means 8 10 12 14 16 18 Time of Day (LST) Figure 7.38. Observed and modeled cloud cover for 9 July 1995. CuP cloud cover was determined using a JFD set to the both the mixed-layer (ML) and surface-layer (Sfc) means. 7.4.8 Date: 11 July 1995 The warmest, deepest, dryest mixed layer of any day used in the study occurred on 11 July. Figure 7.39 shows plots of 6V with height. A t 1130 L S T the classic convective mixed layer was not apparent. There was a relative maximum near the bottom of the mixed layer in the 6V profile, below the level of confidence for sonde measurements. The mixed-layer depth was difficult to define in this case, but was estimated to be near 0.7 km. B y 1430 L S T the mixed layer had taken on the classic shape and had grown to a depth of nearly 3 km. The mixed layer had also dried, so that zLCL ML was near 3.4 km. The CuP model did not predict any cloud cover using a JFD centered at 6vML and zLCL ML, but 99 overestimated the cloud coverage by as much as 30% using a JFD centered at 0V sfc and ZLCL,S/C ( f i g u r e 7 - 4 0 ) -S-H > O U T3 O 0 100 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 • Observed • CuP, M L Means • CuP, Sfc Means T 8 10 12 14 16 18 Time of Day (LST) Figure 7.40. Observed and CuP modeled cloud cover for 11 July 1995. CuP cloud cover was determined using a JFD set to the both the mixed-layer ( M L ) and surface-layer (Sfc) means. 7.4.9 Date: 13 July 1995 Plots of 6V are shown in figure 7.41. A well defined layer was evident at each time, although the layer was not very well mixed. There was a temperature jump at 1131 L S T near 0.3 km, Qv then decreased slowly through the top of the mixed layer. A t 1430 L S T there was a region near 0.6 km that was slightly warmer than the rest of the mixed layer. The profile of zLCL showed that at 1131 zLCL was fairly constant, while at 1430 zLCL steadily increased with height throughout the layer (figure 7.42). In both cases the strange behavior seen in the 6V profile was not apparent. At 1131 and 1430 L S T the cloud layer above 2.0 km was fairly well mixed. The Betts' transition layer was evident from about 1.8 to 2.2 km at 1130 L S T and from 2 to 2.2 km at 1430 L S T . Above these layers was the cloud layer. 101 Figure 7.41. Profiles 9V taken from C F sondes on 13 July 1995. Solid lines are moist adiabats. 102 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Z L C L dm) Figure 7.42. Profiles of zLCL taken from C F sondes on 13 July 1995. Thin solid line is z equal to zLCL. Cloudy air is above the line, clear air below. Some scattered cloud cover was reported by the human observer near sunrise, but these have not been included in figure 7.43 because they were above the boundary layer. The CuP model, using both a JFD centered at 6V ML and zLCL ML, and 6V sfc and zLCL sfc predicted no cloud cover at 830 L S T . Later in the day the CuP model overestimated the 103 cloud coverage using a JFD centered at 0V sfc and zLCL sfc. A t 1130 L S T no cloud was At 1430 the model overestimate the cloud estimated with a JFD at 6V ML and zLCL ML coverage, even with the mixed-layer means. t-i > o U O U 1 0 0 ^ • 1 9 0 - • Observed 8 0 - • CuP, M L Means 7 0 - • CuP, Sfc Means 6 0 - • 5 0 -4 0 -3 0 -2 0 - • • 1 0 - • • • • 0 - 1 • T ' i V T V i T i 1 T i 1 I i i i i i i i i 10 12 14 16 Time of Day (LST) 18 Figure 7.43. Observed and modeled cloud cover for 13 July 1995. CuP cloud cover was determined using a JFD set to the both the mixed-layer (ML) and surface-layer (Sfc) means. Cloud amounts that were determined to be disconnected from the boundary layer have been removed (see text for details). CuP cloud base heights and observed cloud-base heights for 13 July are shown in figure 7.44. The CuP model results fell between the B L C and M P L observations. Using a JFD centered at dvML and zLCLML, and 6V sfc and zLCL sfc the CuP model daily mean cloud-base heights were larger than the sample mean observed by the M P L . Tests supported a difference between the CuP mean and the inferred M P L population mean (P-values <0.001). With the same JFD the CuP mean cloud-base height were smaller than the inferred B L C population mean (P-values of <0.001). Using a JFD centered at 8V Best and zWL,Best m e CuP mean was smaller than that observed by the B L C and slightly larger than 104 the M P L observations. Statistical tests indicated that the CuP mean and inferred M P L population means were the same. Using a JFD centered at 6vML and zLCLML the CuP variance was smaller than that observed by the B L C and M P L . The CuP variance and the B L C inferred population variances were the same (P-value of 0.38), but not the CuP variance and the M P L population variance (P-value of 0.01). With the JFD centered at 6V Best and zLCL Best the CuP variance was greater than the sample variance obtained by the B L C , but less than the sample variance from the M P L . Tests showed that differences between the CuP and B L C were significance at the 0.05 level (P-values of <0.001). The CuP variance and the inferred M P L population variance were the same although the evidence was weak (P-value of 0.07). J3 X o 0 4000 3500 — 3000 -2500 -2000 -1500 -1000 — 500 — 10 • Micropulse Lidar O Belfort Ceilometer X CuP, M L Means • CuP, Sfc Means 12 e o. D 8 i 14 Time of Day (LST) 16 Figure 7.44. Observed and CuP modeled cloud base height 13 July 1995. CuP points are the predicted mode-cloud base height. Error bars on the CuP points correspond to range of predicted cloud base heights. 105 8.0 Conclusions and Future Work The CuP model was designed to provide a quick method for determining the amount of fair-weather cumulus cloud cover, cloud onset time, cloud-base height and cloud thickness. The verification of CuP model results wi l l be reviewed first. A discussion of some possible in shortcomings and corrections wi l l follow. A brief look at future work related to the study of both the CuP model, the JFD, and the cloud-atmosphere system wi l l be presented. The model showed skill predicting the cloud-base altitude. With the mean of the J F D set to the values of 6V and zlCL which gave the observed cloud cover, the predicted cloud-base estimates were nicely bracketed by the Micropulse Lidar (MPL) and Belfort Laser Ceilometer ( B L C ) observations. Although the predicted cloud base was greater than the M P L observations on all days, on half of the days the difference was not statistically significant. The CuP cloud-base heights estimated with the mean of the JFD set to the surface values of 6V and zLCL were greater than those observed by either the M P L or B L C , while the CuP estimates using a JFD set to the mean mixed layer 6V and zLCL were lower than those observed. Predictions of cloud cover using a single station as input, for the case-study days were not encouraging, but also not conclusive. On the case-study days there was little skill determining the cloud cover. Using a JFD calculated from surface instruments at the Central Facility (CF) the cloud cover and variance were overestimated. Using a J F D with the same size and shape, but with it centered at the mixed-layer values of 6V and zLCL, the cloud cover and variance were underestimated. 106 Estimates of the vertical size distribution of clouds are provided, but no data existed to verify these results. However, on all but one of the days the cloud thicknesses were nearly log-normally distributed consistent with the observations of Lopez (1977) and Stull (1988). On some of the days the model predicted cloud thicknesses well above 8 km. These very large thicknesses are not consistent with the observations made at the C F . 8.1 Shortcomings and Improvements Errors can be traced to four probable causes: 1) the representation of the mean mixed layer from the sondes, 2) the adequacy of the surface observations used to make the JFD, 3) the physics in the CuP model and 4) advection of clouds. From the data collected at the A R M site it is impossible to determine which scenario is dominant, although a combination of each is likely. Work has started to address problems 1 and 2. During the summer of 1996, a field program was conducted during which high-resolution data was collected by aircraft at six heights in the mixed layer to examine how the JFD changes with height. The aircraft also measured vertical profiles from the surface to above cloud top. These aircraft profiles are more representative of the mean mixed layer than a radiosonde profile, because the plane passes through many convective thermals during its slant ascent and descent. Cloud cover wi l l be determined from the upward looking radiometer on the plane, and from cloud cover estimates based on cloud shadows, as observed by the airborne scientist. Thus the main areas of uncertainty wil l be addressed with this new data source and a more conclusive determination of the CuP scheme wi l l be possible. 107 The physical basis of the the CuP model wi l l be examined. Wetzel and Boone (1995) and Wetzel (1989) have reported success using a parcel model. Crum et al. (1987) found that some parcels near the entrainment zone had mixing ratios identical to those measured near the surface, indicating individual parcels are lifted from the surface to the top of the mixed layer. The CuP model addresses only the formation of clouds due to rising thermals. Many other important physical processes, such as cloud-atmosphere interactions, cloud-cloud interactions, radiative properties of the clouds, advection, and the effects of cloud shading on the surface energy balance are not included. These physical processes could to be addressed to develop an accurate cumulus parameterization. We have hypothesized that the very deep clouds predicted by the CuP model are due to the absence of entrainment-induced evaporative cooling in the cloud. Bretherton (1988) found that clouds have some equilibrium spacing from their nearest neighbor. These type of affects are important to include in a cumulus parameterization. Unfortunately these parameters are hard to quantify for the case-study days used because, with the exception of the sondes, all of the instruments at the A R M site are surface based. Advection is a very difficult problem which was ignored in this case study. The days used had light winds, in part to help minimize the advection of clouds and other atmospheric variables. However, the winds are rarely calm through the depth of the mixed layer so that advection could be contributing some of the cloud cover. A few possibilities exist for estimating the advection of cloud cover. One method would be to use a computer model, such as a Large Eddy Simulation (LES) model that would explicitly predict the clouds along the boundary of the case-study region. Each cloud in the model could be 108 tracked as it moved into or out of the study region. Problems exist with this method. The computer model would include uncertainty, and large errors in predicted cloud cover could exist. Another source of insight into the advection would be a time series of satellite images. Individual cloud fields could be tracked and the advection of clouds estimated. A difficulty of this method would be tracking individual cloud fields from the relativity course resolution satellite data. 8.2 Other Future Work A more complete statistical picture of the cloud cover wi l l be constructed from data at the A R M site for comparison with the CuP model. Hourly human observations wi l l be combined with the M P L , B L C , and the whole sky imager data to construct longer term statistics. Investigation of the skill of the CuP's predicted cloud onset time could be done using data from a more continuous ground-based sensor, although in general at the expense of vertical resolution. The CuP model could also be placed into a meso-scale or boundary-layer forecast model to utilize greater temporal resolution and gain a more representative picture of the mean-mixed layer. In section 6 we showed that the cloud characteristics predicted by the CuP model were very sensitive to the atmospheric conditions. It is important to determine i f the formation of boundary-layer cumulus in the atmosphere is equally sensitive. A L E S model could be used to help determine the sensitivity of the real atmosphere, assuming an accurate representation of cloud formation and other boundary-layer processes in the model. Small random perturbations could be added to the L E S parameters to ascertain the sensitivity of 109 the cloud-atmosphere system. If the atmosphere is as sensitive as the CuP model, than the accurate prediction of boundary-layer cumulus clouds in A G C M s would be impossible due to inherent uncertainty in the A G C M . In many cases the behavior of the atmosphere has been shown to have a sensitive dependence on the initial conditions, the formation of boundary-layer cumulus could be an example. A boundary-layer cumulus scheme needs to be further developed to include both forced and free convection. This wi l l allow forecasts of different cloud types with the same parameterization. Perhaps rather than looking at 6V to determine buoyancy, some other energy parameter could be used that includes both forced and free convection. 110 R E F E R E N C E S Angevine, W . M . , A . B . White, and S. K . Avery, 1994: Boundary-layer depth and entrainment zone characterization with a boundary-layer profiler. Boundary-Layer Meteo., 68, 375-385. 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D . , 1996: Comparisons of the Micropulse Lidar and the Belfort Laser Ceilometer at the A R M S G P C A R T . U.S . Department of Energy, 1990: Atmospheric Radiation Measurement Program Plan, 1990, DOE/ER-0441 . Washington D . C . X u , K . , and S. K . Krueger, 1991: Evaluation of cloudiness parameterizations using a cumulus ensemble model. Mon. Wea. Rev., 119, 342-367. Zhu, T., J. Lee, R. C. Weger, and R. M . Welch, 1992: Clustering, randomness, and regularity in cloud fields: 2. cumulus cloud fields. J. Geophys. Res., 97, 20537-20558. 115 Appendix A . Instrument Uncertainty Table A . 1. Accuracy of S M O S pressure, humidity and precipitation measurements. Precipitation uncertainty increases in cases of high winds and heavy rain greater then 75 mm h r 1 (Wesely personal communication 1996). Measurement Accuracy Pressure ± 0.035 kPa Humidity ± 2.06% for relative humidity less then 90% ± 3.04% for relative humidity greater then 90% Precipitation ± 0.254 mm Table A .2 . Wind accuracy for a given wind speed for S M O S 13 (Wesely personal communication 1996) Wind Speed Speed Accuracy Direction Accuracy 2.5 to 30 m/s ± 1% ± 5 ° 2.0 m/s -0.12 to +0.02 ± 5 ° 1.5 m/s -0.22 to +0.00 ± 5 ° 1.0 m/s -0.31 t o - 0 . 2 0 ± 180.0° 0.5 m/s -0.51 t o - 0 . 4 9 ± 180.0° 116 Table A . 3 . Temperature accuracy for a given wind speed for S M O S 13 (Wesely personal communication 1996) Wind Speed Accuracy >6.00 m/s ± 0 . 4 5 °C 3.00 m/s ± 0 . 8 9 °C 2.00 m/s ± 1.46 °C 1.00 m/s ± 3 . 0 7 °C Table A.4 . Accuracy of E B B R measurements (Wesely personal communication 1996). Measurement Accuracy Pressure ± 0 . 1 4 k P a Temperature ± 0.5 °C Humidity ± 2% for relative humidity less then 90% ± 3% for relative humidity greater then 90% Table A . 5 . Accuracy of sonde measurements (Wesely personal communication 1996). Measurement Accuracy Pressure ± 0.05 kPa Temperature ± 0.2 °C Humidity ± 2 % Wind direction ± 5 ° Wind speed ± 0 . 1 m/s 117 Appendix B. Comparison of Empirical and Parcel Determination of z Table B . 1. Values zLCL calculated from equation 4.7 and calculated from an iterative method for 27 July 1994, 1430 L S T . Difference is the absolute value of the difference in the two methods. Difference (%) is the calculated from the iterative method and the difference. Pressure zLCL (km) from zLCL (km) (kPa) Approximation from Iteration Difference (m) Difference (%) 97.97 2.375 2.368 6.891 0.291 95.91 2.223 2.208 15.207 0.689 94.95 2.248 2.242 6.717 0.300 94.03 2.220 2.208 12.308 0.557 93.02 2.214 2.208 5.732 0.260 92.05 2.204 2.194 10.186 0.464 91.05 2.236 2.225 10.238 0.460 90.07 2.203 2.194 9.314 0.424 89.07 2.174 2.176 1.975 0.091 87.99 2.228 2.225 2.195 0.099 86.98 2.276 2.268 7.869 0.347 86.01 2.270 2.268 2.724 0.120 85.05 2.290 2.292 1.571 0.069 80.02 2.424 2.422 1.905 0.079 75.00 2.806 2.814 8.154 0.290 70.01 6.151 6.004 147.666 2.460 64.99 7.264 7.073 190.253 2.690 60.05 6.831 6.713 118.813 1.770 118 -25 0 25 50 75 100 125 150 175 200 225 250 275 300 Z Difference (m) Figure B.2 . Difference between zLCL calculated from empirical equation 4.2 and parcel method using the C F sonde. Both methods are described in section 4. Thick solid lines mark zi for that day and time. There is good agreement between the two methods, especially in the boundary layer. 119 1 2 3 4 5 6 7 8 9 10 Empirical Z (km) Figure B.3 . The zLCL found from the parcel method vs zLCL the calculated using equation 4.2 for three of the case-study days. The straight line is perfect agreement. 120 Appendix C . Sample Error Calculation Uncertainties in calculated quantities arise from errors in measured variables. Standard error analysis techniques were used to estimate error propagation (e.g. Bevington 1969). In this appendix the general equations and a specific example wi l l be presented. A temperature of 20 °C and a relative humidity of 88% are assumed. The uncertainty in temperature was ±0.89 °C, while the uncertainty in relative humidity was 2.06%, as defined for the SMOSs . Uncertainty in the measured pressure for the S M O S is ±0.035 kPa . C . l Error Calculation for 0V The atmospheric water vapor mixing ratio ( r ) was calculated in several steps. Teten's equation is used to find the saturation vapor pressure (es): es = eso e X P a(T- 273.16) (T-b) (CI) where a is 17.2694, b is 35.86, T is the temperature in K , and eso is the saturation vapor pressure at the triple point of water. The uncertainties in saturation vapor pressure using Teten's Equation is found in several steps. First the error inside the square brackets of equation C I wi l l be found. We wi l l let N be the numerator, errN be the error in numerator as represented by the stanard deviation, D be the denominator, and errD be the error in denominator as represented by the standard deviation. The error propagation from multiplying a variable by a constant is: product = ± a ( e r r A ) (C2) 121 where errA is the uncertainty and a is a constant. Using (C2) the error in our example case becomes: errN = ±a(errT) = ±(17.2694 x 0.89) = ±15.369 (C3) The value of N is 345.388. The error in the denominator, errD is errT. The value of D is 257.3. The error propagation due to the division is: N \(errN\ DTK N I D ) (C4) Equation (C4) becomes: err div 257.3 VV345.388J U 5 7 . 3 J Now the error propagation from computing the exponential wi l l be found. The error propagation is defined as: e r r c x P = ± e x P — err div (C6) where N , D, and errdiv are defined as before. Equation C6 becomes: e r r e x p = ± e x p 345.388"\ >v 257.3 j x 0.0599 = ±0.2293 (C7) The error propagation in es is found by using (C2): err — ±e err e s so exp (C8) Equation (C8) becomes: erres = ± 0 . 6 1 0 7 8 x 0 . 2 2 9 3 = ±0.1401 (C9) and es is 2.337 kPa. For each instrument platform err€s was combined with the error in measured relative humidity (err^) to find the error in the vapor pressure, erre. For the example 122 casee is 2.0566 kPa. The equation for the error propagation in a product is: errAB=AB. For the example case (CIO) becomes: err = ±RH x e„ U 'errB^ { A , ) I B J (CIO) ( errRH { RH err ( C l l ) where R H is the relative humidity. Substituting values for the test case, ( C l l ) becomes: err = ±0.88 x 2.337 x . f0 .1401Y f0.0206^ ^ 2.337 J o.88 ; ±0.1324 (C12) The mixing ratio (r) is found using: r = ee p-e (C13) where p is the atmospheric air pressure and e is the ratio of the dry air and water vapor gas constants. The error in e was found using (C12). The error propagation in the numerator of (CI3) is found using (C2): err, =±exe = ±0.622 x 0.1324 = ±0.0824 (C14) The value of N is 1.27918. The error propagation due to adding two numbers when each have some uncertainty is: err^^^errZ+err* (C15) The error propagation in the denominator of (CI3) becomes: errD = ±^jerr*+err? = ±A/0.035 2 + 0.1324 2 = ±0.1369 (C16) where errp is the uncertainty in the pressure measurement. The denominator is 95.843 kPa. The cumulative error in the mixing ratio can then be found using (CI4): 123 err, = ± 1.27918 f 0.0824 ^ 95.843 x U .27918J f 0.1369 V 95.843 J = ±8.995 x l O - 4 (C17) Uncertainty in 6V occurs from errors in the measured temperature, pressure or mixing ratio. The error propagation from calculating 6 is found by first finding the error propagation from p0 Ip using (C6) where N is set to pn, D is set to p, errN is set to errp, and errD is set to 0. Equation (C6) becomes: ^ 100.0 err,:,. = ± x . 'div 97.90 fomrtj^ = ±3.652xl0-. ( C 1 8 ) ^ 97.90 J UOO.O 1 The error propagation from rising a quantity to a power is defined as: errpoaer=±nA"-WrA (C19) where n is the power, and A is value being raised to the power n. Equation (CI9) becomes: f 100.0 n 0 2 8 6 _ 1 errpawer - ±0.286 x >v 97.90 x 3.652 x l O - 4 = 1.028 x l O " 4 (C20) The value of errvower is then combined with errT to give the error in 6 using (C10): / N O . 2 8 6 Po erre = ±T x Equation example (C21) becomes: err e = ± 2 9 3 . 1 6 x 1.006 x . err x || — r - I + T err. 0 . 2 8 6 (C21) f 0.89 V T 1.028 x l O - 4 ^ U 9 3 . 1 6 1.006 = ±0.896(C22) For this example, 6 was found to be 294.93 K . The value of 6V is then found using: 6V =0(1 + O.61r) (C23) 124 The error propagation for the right most term inside the brackets is found using (C2) err = ±0.61 x 8.995 x 10"4 = ±5.487 x 10"5 (C24) Equation (CIO) is used to complete the the uncertainty calculations for dv: errg = ±294.93 x 1.008 x ( 0.896 f f 5.487 x l 0 " 5 > ) U 9 4 . 9 3 ; 1.008 = ±0.903 (C25) J C.2 Error Calculation for z LCL Teten's equation is inverted to find the dew point (TD): T -_ 35 .86 ln(e /e s o ) - 4717.31 ln(e/ej-17.2694 (C26) The uncertainty associated with erre/e is found using (C6): , 2.0566 0.1324 i n „ „ a err,p = ± x = ±0.2168 e , e*° 0.61078 2.0566 (C27) (C28) The error propagation due to the natural logarithm is expressed by: err errln = ±—-y where y is the argument of the logarithm and erry is the uncertainty in y. In this case it becomes: errlB = ±-err e/ec, ± 5 ^ = ±0.0644 3.3671 C29 errN = ±35.86 x errXa = ±2.309 Once the error in the logarithm is found the errors in the numerator are found using (C2): (C30) The error in the denominator remains errXa. The error propagation in T D is then found using (C4): , -4671.2076 errT = + x 2.309 ^ -16.046 ^ - 4 6 7 1 . 2 0 7 6 ; 125 2 0.0644 ^ ' -16.046; = ±1.177(C31) While TD is found to be 291.11 K . The zLCL is then found from the simple empirical equation: zLCL=a(T-TD) (C32) The uncertainty in the brackets is found using (CI5): errAdd = i - ^ n - r +errjD = ±Vo.892 +1.177 2 = ±1.476 (C33) The uncertainty in zLCL is then found using (C2): errZLa = ±125.0 x errAdd = ±125.0 x 1.476 = ±184.5 (C34) In the example zLCL was found to be 256.25 m. These calculations were carried out at each time for the S M O S calculated 6V andz L C L , and the 9V calculated from the sondes. 126 Appendix D. Cloud and Weather Observations D . l Cloud Description Table D . l . Cloud descriptions used by human observers at the A R M C A R T site (Cederwall Personal Communication). These codes are used in the daily tables of observed cloud type. Acceptable low cloud types for any case study day was type 1 or 2. L o w Cloud Layer Type Technical Description Non-Technical Description 0 N o Stratocumulus, Stratus, No low clouds Cumulus or Cumulonimbus 1 Cumulus humilis or Cumulus fractus other than of bad weather, or both 2 Cumulus mediocris or congestus, with or without Cumulus of species fractus or humilis or Stratocumulus, all having their bases at the same level 3 Cumulonimbus calvus, with or without Cumulus, Stratocumulus or Stratus 4 Stratocumulus cumulogenitus Fair-weather Cumulus with little vertical extent, and/or ragged Cumulus Cumulus with moderate to strong vertical extent, generally with bulges in the form of domes or towers, they can be accompanied by other Cumulus or by Stratocumulus, all with bases at the same level Cumulonimbus whose summits, at least partially, lack sharp outlines, but are neither clearly fibrous nor in the from of an anvil; Stratocumulus, Cumulus, or Stratus may also be present Stratocumulus formed by the spreading out of Cumulus; Cumulus may also be present 5 Stratocumulus other then Stratocumulus not resulting from the stratocumulus cumulogenitus spreading out of Cumulus 127 L o w Cloud Layer (continued) Type Technical Description Non-Technical Description 6 Stratus nebulosus or Stratus fractus other than of bad weather, or both 7 Stratus fractus or Cumulus fractus of bad weather, or both (pannus), usually below Altostratus or Nimbostratus 8 Cumulus and Stratocumulus other then Stratocumulus cumulogenitus, with bases at different levels 9 Cumulonimbus capillatus (often with an anvil), with or without Cumulonimbus calvus, Cumulus, Stratocumulus, Stratus or pannus x L o w clouds invisible owing to darkness, fog, blowing dust or sand, or other similar phenomena Fair-weather Stratus in a more or less continuous sheet or layer, or in ragged shreds, or both Bad weather Stratus fractus or bad weather Cumulus fractus of, or both (pannus), below Altostratus or Nimbostratus Cumulus and Stratocumulus other than those formed from the spreading out of Cumulus;the base of the Cumulus is at a different level from that of the Stratocumulus Cumulonimbus, with a clear fibrous (cirriform) upper part, or an upper part in the form of an anvil, may or may not be accompanied by Cumulonimbus without an anvil or fibrous upper part, by Cumulus, Stratocumulus, Stratus or pannus Any low cloud invisible owing to darkness, fog, blowing dust or sand, or other similar phenomena 128 M i d Cloud Layer Type Technical Description Non-Technical Description 0 N o Altocumulus, Altostratus or Nimbostratus 1 Altostratus translucidus 2 Altostratus opacus or Nimbostratus 3 Altocumulus translucidus at a single level 4 Patches (often lenticular) of Altocumulus translucidus, continually changing and occurring at one or more levels 5 Altocumulus translucidus in bands, or one or more layers of Altocumulus translucidus or opacus, progressively invading the sky; these Altocumulus clouds generally thicken as a whole 6 Altocumulus cumulogenitus (or cumulonimbogenitus) 129 No mid clouds Altostratus, most of which is semitranspar-ent; through which the sun or moon may be weakly visible, as through ground glass Altostratus, most of which is sufficiently dense to hide the sun or moon, or Nimbo-stratus Altocumulus, most of which is semi-transparent; the elements of the cloud change slowly and are all at a one level Patches (often in the from of almonds or fish) of Altocumulus, the most of which is semi-transparent; the clouds occur at one or more levels and the elements are continually changing in appearance Semi-transparent Altocumulus in bands, or Altocumulus in one or more fairly continuous layers (semi-transparent or opaque), progressively invading the sky; with clouds generally thickening as a whole Altocumulus resulting from the spreading out of Cumulus (or Cumulonimbus) M i d Cloud Layer (continued) Type Technical Description Non-Technical Description Altocumulus translucidus or opacus in two or more layers, or Altocumulus opacus in a single layer, not progressively invading the sky, or Alto-cumulus with Altostratus or Nimbostratus Altocumulus in two or more layers, usually opaque in places, and not progressively invading the sky; or an opaque layer of Altocumulus, not progres-ively invading the sky; or Altocumulus together with Altostratus or Nimbostratus Altocumulus castellanus or floccus Altocumulus with sproutings in the from of small towers or battlements, or Al to-cumulus having the appearance of cumuli-form tufts Altocumulus of a chaotic sky, generally at several levels Altocumulus of a chaotic sky, generally at several levels 130 High Cloud Layer Type Technical Description Non-Technical Description 0 No Cirrus, Cirrocumulus or Cirrostratus No high clouds Cirrus fibratus, sometimes uncinus, not progressively invading the sky Cirrus in the form of filaments, strands, or hooks, not progressively invading the sky Cirrus spissatus, in patches or entangled sheaves, which usually do not increase and sometimes seem to be the remains of the upper part of a Cumulonimbus; or Cirrus castellanus or floccus Dense Cirrus, in patches or entangled sheaves, which usually do not increase and may seem to be the remains of the upper part of a Cumulonimbus; or Cirrus with with sproutings in the form of small turrets, or Cirrus having the appearance of cumuliform tufts Cirrus spissatus cumulonimbogenitus Dense Cirrus, often in the from of an anvil, which are the remains of the upper parts of a Cumulonimbus Cirrus uncinus or fibratus, or both, progressively invading the sky; they generally thicken as a whole Cirrus in the form of hooks and/or of filaments, progressively invading the sky; generally becoming denser as a whole Cirrus (often in bands) and Cirrostratus, or Cirrostratus alone, progressively invading the sky; they generally thicken as a whole, but the continuous veil does not reach 45 degrees above the horizon Cirrostratus and/or Cirrus (often in bands converging towards one point or two opposite points of the horizon); in either case, they are progressively invading the sky, and generally growing denser as a whole, but the continuous veil does not reach 45 0 above the horizon 131 High Cloud Layer (continued) Type Technical Description Non-Technical Description 6 Cirrus (often in bands) and Cirrostratus and/or Cirrus (often in bands Cirrostratus, or Cirrostratus converging towards one point or two alone, progressively invading opposite points of the horizon); in either the sky; they generally case, they are progressively invading the thicken as a whole, but the sky, and generally growing denser as a continuous veil extends more whole, the continuous veil extends more than 45 0 above the horizon, than 45 ° above the horizon, without the without the sky being totally sky being totally covered covered 7 Cirrostratus covering the V e i l of Cirrostratus covering the celestial dome whole sky 8 Cirrostratus not progressively Cirrostratus not progressively invading invading the sky and not the sky and not completely covering the sky entirely covering it 9 Cirrocumulus alone, or Cirrocumulus alone; or Cirrocumulus Cirrocumulus predominant among accompanied by Cirrus or Cirrostratus, the high clouds or both, with Cirrocumulus predominant 1 3 2 D.2 Hourly Weather and Cloud Observations for the Case Study Days D.2.1 Date: 1 May 1994 Table D.2. Hourly observations from 1 May, 1994 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s"Vdeg) (kPa) (°C) (%) Coverage Type 0000 3.5/029 98.74 6.2 88 Overcast 0100 3.3/017 98.71 5.9 87 Overcast 0200 3.4/013 98.66 4.9 87 Clear 0300 1.5/332 98.71 4.0 92 Clear 0400 1.3/340 98.70 3.6 95 Clear 0500 1.7/295 98.72 3.4 94 Clear 0600 1.7/333 98.74 2.5 97 Clear 0700 1.9/019 98.73 4.3 94 Clear 0800 1.9/019 98.73 4.3 94 Clear 0900 3.4/062 98.72 6.8 73 Clear 1000 2.9/072 98.75 8.6 64 Clear 1100 2.2/090 98.74 9.6 61 Scattered 1200 2.2/142 98.70 10.3 59 Scattered 1300 3.4/110 98.61 12.2 59 Scattered 1400 2.5/114 98.48 12.6 57 Scattered 1500 3.5/118 98.33 14.7 58 Scattered 1600 3.5/114 98.24 14.5 59 Scattered 1700 4.9/121 98.11 15.3 56 Broken 1800 5.9/139 98.05 15.4 58 Broken 133 Table D.3. Hourly cloud coverage by sky quadrant at the Central Facility 1 May, 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d Time Amt Height Type Amt Height Type (LST) (km/10) (km/10) Amt High Height Type (km/10) 0900 N W 1000 N E 0.1 15 S E 0.1 15 S W 0.1 15 N W 0.2 15 1100 N E 0.1 15 S E 0.1 15 S W 0.1 15 N W 0.1 15 1200 N E 0.4 15 S E 0.3 15 S W 0.4 15 N W 0.4 15 1300 N E 0.3 15 S E 0.6 15 S W 0.3 15 N W 0.2 15 1400 N E 0.1 15 S E 0.1 15 S W 0.1 15 N W 0.1 15 1500 N E 0.1 15 S E 0.1 15 S W 0.2 15 N W 0.3 15 1600 N E 0.1 15 S E S W N W 0.1 090 1 0.1 050 0.1 0.1 090 090 1 6 .4 .3 .6 .4 050 050 050 050 134 Table D.3. continued. Hourly cloud coverage by sky quadrant at the Central Facility 1 May , 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 1700 N E .8 050 1 S E .7 050 1 S W .6 050 1 N W .9 050 1 Table D.4. Hourly overhead cloud amounts from 1 May, 1994. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 1000 0.1 015 1 1100 0.2 015 1 1200 0.8 015 1 1300 0.1 015 1 1400 0.1 015 1 1500 0.1 015 1 1600 0.2 050 1 1700 0.7 050 1 135 D.2.2 Date: 27 July 1994 Table D.5. Hourly observations from 27 July, 1994 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s_ 1/deg) (kPa) (°C) (%) Coverage Type 0000 4.7/317 98.06 17.7 85 Clear 0100 4.3/303 98.06 16.7 89 Clear 0200 4.2/282 98.05 16.2 89 Clear 0300 4.7/282 98.03 15.4 91 Clear 0400 4.3/289 98.04 15.1 92 Clear 0500 4.5/282 98.06 14.4 94 Scattered 0600 4.2/300 98.10 14.6 92 Scattered 0700 3.7/297 98.13 16.7 85 Scattered light haze 0800 3.0/326 98.16 19.2 77 Scattered light haze 0900 3.5/354 98.17 22.3 61 Scattered very light haz 1000 5.3/360 98.16 24.2 49 Scattered 1100 6.0/347 98.15 24.9 45 Scattered light haze 1200 7.2/003 98.10 25.6 45 Scattered 1300 7.2/003 98.10 25.6 45 Scattered 1400 5.7/020 98.05 26.3 42 Scattered light haze 1500 6.3/355 98.01 27.1 43 Scattered light haze 1600 5.2/002 97.95 26.9 39 Scattered 1700 5.8/015 97.89 27.3 37 Scattered 1800 7.7/020 97.89 27.1 36 Scattered 136 Table D.6. Hourly cloud coverage by sky quadrant at the Central Facility 27 July, 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Ty (LST) (km/10) (km/10) (km/10) 0500 N E 0.1 55 7 0600 N E 0.1 55 7 0700 N E 0.2 60 4 0.2 100 9 S E 0.1 100 9 0800 N E 0.3 60 4 0.2 100 9 S E 0.2 100 9 0900 N E 0.2 60 4 0.4 100 9 S E 0.3 100 9 1000 N E 0.2 60 4 0.2 100 9 S E 0.1 60 4 0.4 100 9 1100 N E 0.1 15 1 S E 0.1 15 1 0.1 60 4 0.2 100 9 S W 0.1 15 1 0.3 100 9 N W 0.1 15 1 1200 N E 0.2 15 1 S E 0.2 15 1 S W 0.3 15 1 N W 0.1 15 1 1300 N E 0.3 12 8 S E 0.3 15 1 S W 0.3 15 1 N W 0.2 15 1 1400 N E 0.3 12 8 S E 0.3 12 8 S W 0.3 15 1 N W 0.2 15 1 1500 N E 0.2 15 1 S E 0.2 12 8 S W 0.2 15 1 0.2 100 9 N W 0.1 15 1 0.2 100 9 137 Table D.6 continued. Hourly cloud coverage by sky quadrant at the Central Facility 27 July, 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 1600 N E 0.3 15 1 S E 0.3 15 1 S W 0.4 15 1 N W 0.4 15 1 1700 N E 0.1 15 1 S E 0.2 15 1 S W 0.1 15 1 N W 0.2 15 1 Table D.7. Hourly overhead cloud amounts from 27 July, 1994. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 1200 0.1 015 1 1300 0.1 015 1 1400 0.1 015 1 1500 0.1 015 1 138 D.2.3 Date: 28 July 1994 Table D.8. Hourly observations from 28 July, 1994 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s_ 1/deg) (kPa) (°C) (%) Coverage Type 0000 0.4/034 97.94 20.7 60 Clear 0100 2.6/256 97.92 18.3 76 Clear 0200 3.9/267 97.94 17.8 79 Clear 0300 4.1/295 97.96 16.1 86 Clear 0400 4.1/335 97.99 15.5 88 Clear 0500 4.4/291 97.99 15.8 86 Clear 0600 3.6/306 98.04 15.5 86 Scattered 0700 3.0/357 98.07 17.6 84 Scattered light fog/moderate dew 0800 2.6/359 98.13 20.9 75 Scattered light haze/dew 0900 1.1/008 98.15 22.1 67 Scattered Haze 1000 2.5/066 98.15 24.7 57 Clear moderate haze 1100 2.1/095 98.13 25.3 51 Scattered Haze 1200 3.7/034 98.07 26.2 50 Scattered Haze 1300 4.7/342 98.02 26.9 44 Scattered Haze 1400 5.5/048 97.99 27.3 41 Scattered 1500 2.7/060 97.96 27.6 41 Scattered 1600 5.5/048 97.91 27.9 40 Scattered 1700 4.8/065 97.89 37.3 39 Scattered 139 Table D.9. Hourly cloud coverage by sky quadrant at the Central Facility 28 July, 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 0600 N E 0.1 12 4 0700 N E 0.3 100 9 S E 0.3 100 9 0800 N E 0.2 60 4 0.1 100 9 S E 0.1 60 4 0.2 100 9 0900 N E 0.2 60 4 0.1 100 9 S E 0.3 60 4 1100 N W 0.1 15 1 1200 N E 0.2 15 1 S E 0.2 15 1 S W 0.2 15 1 N W 0.3 15 1 1300 N E 0.3 15 1 S E 0.4 15 1 S W 0.3 15 1 N W 0.4 15 1 1400 N E 0.1 15 1 S E 0.3 15 1 S W 0.3 15 1 0.3 100 9 N W 0.3 15 1 0.3 100 9 1500 N E 0.1 15 1 S E 0.2 15 1 S W 0.3 15 1 N W 0.3 15 1 1600 N E 0.1 15 1 S E 0.1 15 1 S W 0.1 15 1 0.3 90 1 N W 0.1 15 1 0.1 90 1 1700 N E 0.1 90 1 S W 0.3 90 1 N W 0.3 90 1 140 Table D.10. Hourly overhead cloud amounts from 28 July, 1994. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 1200 0.1 015 1300 0.1 015 1400 0.1 015 1500 0.1 015 1700 0.1 090 D.2.4 Date: 31 July 1994 Table D . l 1. Hourly observations from 31 July, 1994 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (ms-Vdeg) (kPa) (°C) (%) Coverage Type 0000 6.5/162 97.64 21.3 84 Scattered 0100 4.5/172 97.81 20.3 88 Scattered possible light forming on N 0200 5.5/160 97.8.1 20.2 89 Scattered very light dew 0300 5.4/154 97.63 19.3 91 Scattered 0400 6.1/154 97.83 18.7 93 Clear Dew 0500 6.3/163 97.87 18.7 90 Scattered Dew 0600 6.6/174 97.71 19.1 85 Broken light fog 0700 7.2/184 97.93 21.1 80 Scattered 0800 9.1/182 97.90 23.1 76 Scattered 0900 6.0/192 97.91 25.1 67 Clear 1000 7.1/196 97.89 27.3 56 Clear 1100 5.9/180 97.87 29.0 54 Clear 1200 4.5/188 97.82 30.3 51 Clear Haze 1300 7.1/158 97.78 31.4 46 Scattered 1400 5.3/143 97.74 32.1 41 Scattered 1500 5.7/191 97.72 32.9 42 Scattered 1600 7.2/162 97.68 31.9 41 Scattered 1700 5.2/170 97.67 29.4 54 Scattered 141 Table D.12. Hourly cloud coverage by sky quadrant at the Central Facility 31 July, 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 0000 S W 0.4 100 9 N W 0.4 100 9 0100 N E 0.4 100 9 S E 0.2 100 9 S W 0.2 100 9 N W 0.5 100 9 0200 N W 0.2 100 9 0300 N W 0.7 100 9 0500 N E 0.1 10 5 0.1 60 4 0.1 100 9 S E 0.3 60 4 0.1 100 9 S W 0.3 60 4 0.2 100 9 N W 0.4 100 9 0600 N E 0.1 60 4 0.3 100 9 S E 0.1 60 4 0.6 100 9 S W 0.3 60 4 0.3 100 9 N W 0.2 12 8 0.1 60 4 0.2 90 2 0700 N E 0.4 90 1 S E 0.2 90 1 S W 0.1 12 2 0.2 90 1 N W 0.3 12 2 0.3 90 1 0800 N E 0.1 90 1 S E 0.3 90 1 S W 0.2 90 1 N W 0.3 90 1 1300 N E 0.2 15 1 S E 0.2 15 1 S W 0.3 15 1 N W 0.4 15 1 1400 N E 0.2 15 1 S E 0.3 15 1 S W 0.4 15 1 N W 0.4 15 1 142 Table D . 12 continued. Hourly cloud coverage by sky quadrant at the Central Facility 31 July, 1994 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 1500 N E 0.2 15 1 S E 0.1 15 1 S W 0.1 15 1 N W 0.3 15 1 0.1 90 1 1600 N E 0.1 12 8 S E 0.1 12 8 S W 0.2 12 2 0.1 55 7 0.1 90 8 N W 0.3 12 2 0.1 55 7 0.1 90 8 1700 N E 0.1 15 1 0.1 90 1 S E 0.1 15 1 0.1 90 1 S W 0.1 15 1 N W 0.1 15 1 Table D.13. Hourly overhead cloud amounts from 31 July, 1994. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 0500 0.2 100 9 0600 0.1 090 2 0.4 100 9 1300 0.3 015 1 1400 0.3 015 1 1500 0.1 015 1 1600 0.1 012 8 143 D.2.5 Date: 27 June 1995 Table D.14. Hourly observations from 27 June, 1995 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s_ 1/deg) (kPa) (°C) (%) Coverage Type 0000 0.0/000 98.94 20 64 Clear 0100 0.0/250 98.92 19 72 Scattered 0200 0.0/232 98.93 18 76 Scattered 0500 0.0/285 98.91 17 80 Scattered 0600 0.0/307 98.95 19 76 Scattered 0700 0.0/334 98.95 23 65 Scattered very light haze 0800 4.0/002 98.92 28 52 Broken 0900 0.0/170 99.03 35 31 Broken Haze 1000 1.3/231 99.06 36 31 Scattered Haze 1100 0.4/150 99.05 35 29 Scattered 1200 1.3/210 98.97 35 29 Scattered light haze/smoke 1300 2.7/204 98.92 34 30 Scattered smoke 1400 0.4/178 98.90 34 33 Scattered smoke/haze 1500 2.7/153 98.85 33 36 Scattered light haze/smoke 144 Table D . l 5 . Hourly cloud coverage by sky quadrant at the Central Facility 27 June, 1995 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Ty (LST) (km/10) (km/10) (km/10) 0600 N E 0.4 55 7 S E 0.3 55 7 S W 0.2 55 7 N W 0.3 55 7 0700 N E 0.4 15 1 0.1 100 9 S E 0.2 10 5 0.2 60 4 0.1 100 9 S W 0.3 10 5 0.1 60 4 N W 0.3 15 1 0.2 60 4 0.1 100 9 0800 N E 0.3 15 1 0.2 100 9 S E 0.3 10 5 0.1 60 4 S W 0.4 15 1 N W 0.2 15 1 0.3 60 4 0900 N E 0.1 10 5 0.1 60 4 0.2 100 9 S E 0.2 10 5 0.2 60 4 0.2 100 9 S W 0.3 12 4 0.2 100 9 • N W 0.1 15 1 0.1 60 4 0.2 100 9 1000 N E 0.1 100 9 S E 0.4 60 4 0.2 100 9 S W 0.3 60 4 0.1 100 9 N W 0.2 60 4 0.1 100 9 1100 N E 0.1 60 4 S E 0.1 15 1 0.3 60 4 0.1 100 9 S W 0.1 15 1 0.1 60 4 0.1 100 9 N W 0.1 15 1 0.3 60 4 0.1 100 9 1200 N E 0.1 15 1 0.2 60 4 S E 0.1 15 1 0.2 60 4 0.2 100 9 S W 0.1 60 4 N W 0.1 15 1 1300 N E 0.1 15 1 0.2 60 4 * S E 0.2 60 4 0.3 100 9 S W 0.2 15 1 0.1 100 9 N W 0.1 15 1 145 Table D.15 continued. Hourly cloud coverage by sky quadrant at the Central Facility 27 June, 1995 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 1400 N E 0.2 15 1 0.2 60 4 S E 0.1 15 1 0.1 60 4 S W 0.2 15 1 0.2 60 4 N W 0.3 15 1 1500 N E 0.3 15 1 0.1 60 4 S E .0.1 15 1 S W 0.2 15 1 0.2 60 4 N W 0.3 15 1 Table D.16. Hourly overhead cloud amounts from 27 July, 1995. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 0700 0.6 015 1 0800 0.5 015 1 0900 0.1 015 1 0.5 100 9 1000 0.1 100 9 1300 0.1 015 1 0.1 100 9 1400 0.1 015 1 1500 0.1 015 1 146 D.2.6 Date: 6 July 1995 Table D.17. Hourly observations from 6 July, 1995 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s_ 1/deg) (kPa) (°C) (%) Coverage Type 0000 0.0/320 99.37 21 73 Scattered 0100 0.0/320 99.37 21 69 Clear 0200 0.0/320 99.41 20 78 Clear 0500 2.7/230 99.43 18 82 Clear 0600 0.0/240 99.52 20 77 Clear 0700 0.0/240 99.65 27 58 Scattered 0800 2.2/200 99.68 32 45 Scattered light haze 0900 2.7/190 99.72 34 39 Scattered light haze 1000 3.6/190 99.72 36 28 Scattered 1100 3.1/260 99.71 37 34 Scattered 1200 4.5/250 99.60 40 28 Scattered 1400 4.9/270 99.54 40 27 Scattered 1500 4.5/280 99.49 39 28 Scattered 147 Table D.18. Hourly cloud coverage by sky quadrant at the Central Facility 6 July, 1995 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 0000 N E 0.2 60 3 S E 0.2 60 3 S W 0.6 60 3 N W 0.4 60 3 0700 S W 0.1 60 4 N W 0.1 60 4 0800 N E 0.1 15 1 0900 N E 0.1 15 1 S E 0.1 15 1 S W 0.1 15 1 N W 0.1 15 1 1000 S E 0.1 15 1 S W 0.1 15 1 1100 N E 0.1 60 4 S E 0.1 15 1 S W 0.1 15 1 N W 0.1 15 1 1200 N E 0.1 15 1 S E 0.3 15 1 S W 0.2 15 1 N W 0.1 15 1 1400 N E 0.3 15 1 S E . 0.4 15 1 S W 0.3 15 1 N W 0.3 15 1 1500 N E 0.4 15 1 S E 0.3 15 1 S W 0.4 15 1 N W 0.2 15 1 148 Table D.19. Hourly overhead cloud amounts from 6 July 1995. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 0900 0.1 015 1 1100 0.1 060 4 1200 0.1 015 1 1300 1400 0.1 015 1 1500 0.3 015 1 D.2.7 Date: 9 July 1995 Table D.20. Hourly observations from 9 July, 1995 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s-Vdeg) (kPa) (°C) (%) Coverage Type 0500 0.0/280 99.08 22 79 Scattered 0600 0.0/240 99.10 23 75 Scattered 0700 0.0/060 99.19 27 65 Scattered 0800 0.0/070 99.25 30 53 Scattered 0900 0.0/070 99.25 33 45 Clear 1000 0.0/040 99.26 34 43 Clear 1100 0.0/070 99.28 36 41 Clear 1200 0.0/090 99.28 38 33 Clear 1300 0.0/080 99.24 38 33 Clear 1400 0.0/080 99.21 38 33 Clear 1500 0.0/060 99.20 38 37 Clear 149 Table D.21. Hourly cloud coverage by sky quadrant at the Central Facility 9 July, 1995 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 0500 N E 0.1 60 3 S E 0.4 60 3 S W 0.3 60 3 N W 0.1 60 3 0600 N E 0.2 60 3 S E 0.4 55 7 S W 0.3 55 7 N W 0.1 60 3 0700 S E 0.4 60 3 S W 0.2 60 3 N W 0.1 60 3 0800 S E 0.3 60 3 Table D.22. Hourly overhead cloud amounts from 9 July, 1995. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 0500 0.2 060 3 0600 0.1 060 3 0700 0.1 060 3 150 D.2.8 Date: 11 July 1995 Table D.23. Hourly observations from 11 July, 1995 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s_ 1/deg) (kPa) (°C) (%) Coverage Type 0000 2.7/180 99.02 26 72 Clear 0100 3.1/180 98.98 25 73 Clear 0200 1.8/120 98.97 24 78 Clear 0500 0.9/130 99.01 22 87 Clear 0600 1.8/140 99.02 23 86 Clear 0700 1.3/150 99.09 27 71 Scattered very light dew/haze 0800 4.4/175 97.74 28.7 56 Scattered light haze 0900 3.1/205 97.74 31.7 46 Scattered smoke 1000 2.2/260 99.12 42 29 Clear moderate-heavy smoke 1100 3.1/260 99.11 44 47 Clear smoke/haze 1200 3.1/260 99.07 45 26 Clear light haze/smoke 1300 1.8/220 99.03 45 24 Clear light haze/smoke 1400 4.0/180 98.95 43 24 Clear moderate smoke 1500 5.4/190 98.93 43 23 Clear moderate smoke Table D.24. Hourly cloud coverage by sky quadrant at the Central Facility 11 July, 1995 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 0700 N E 0.1 60 4 0800 N E 0.1 50 8 0900 N E 0.1 50 8 151 Table D.25. Hourly overhead cloud amounts from 11 July, 1995. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 0700 0.1 060 4 0800 0.1 050 8 0900 0.1 050 8 D.2.9 Date: 13 July 1995 Table D.26. Hourly observations from 13 July, 1995 at the Central Facility Winds Total Time Spd/Dir Press Temp R H Cloud Weather (LST) (m s_ 1/deg) (kPa) (°C) (%) Coverage Type 0600 1.3/170 990.1 27 73 Clear 0700 2.7/170 989.9 26 76 Clear 0800 2.2/190 989.9 27 75 Clear 1100 0.4/150 990.9 24 85 Clear 1200 0.4/140 991.3 24 85 Clear 1300 2.7/170 991.6 28 72 Scattered light haze 1400 4.0/190 991.6 33 56 Scattered Haze 1500 4.5/200 991.4 36 47 Clear light haze 1600 3.1/200 991.1 40 36 Scattered 1700 3.6/190 991.3 41 34 Scattered moderate smoke 1800 4.9/180 991.0 39 34 Scattered Haze/smoke 1900 4.9/180 990.7 39 34 Scattered Haze/smoke 2000 2.7/140 990.6 39 37 Scattered Haze 2100 5.4/120 990.5 38 35 Scattered light haze 152 Table D.27. Hourly cloud coverage by sky quadrant at the Central Facility 13 July, 1995 Cloud Observations, Whole Sky Cloud Types: Quadrant L o w M i d High Time Amt Height Type Amt Height Type Amt Height Type (LST) (km/10) (km/10) (km/10) 0700 N E 0.1 15 1 S E 0.1 60 4 S W 0.1 15 1 0800 S W 0.1 100 9 1000 S W 0.1 60 4 1100 S E 0.1 15 1 1200 N E 0.2 15 1 S E 0.2 15 1 S W 0.2 15 1 N W 0.1 15 1 1300 N E 0.2 15 1 S E 0.2 15 1 S W 0.2 15 1 N W 0.2 15 1 1400 N E 0.2 15 1 S E 0.2 15 1 S W .0.2 15 1 N W 0.2 15 1 1500 N E 0.2 15 1 S E 0.2 15 1 S W 0.2 15 1 N W 0.2 15 1 153 Table D.28. Hourly overhead cloud amounts from 13 July, 1995. Overhead Cloud Amount (30° Arc) Time (LST) Cloud Cover (%) Height (km/10) Type 1100 0.1 015 1200 0.2 015 1300 0.1 015 1400 0.1 015 1500 0.1 015 154 Appendix E . J F D Parameters Table E . l . J F D parameters used as input to the CuP model. B corresponds to Bowen ratio parameters. S corresponds to Solar Forcing parameters. Cut offs represent where the JFDs were truncated. Axes Slopes Standard Deviations Cut Offs Time (LST) B (K/m) S (K/m) B (m) S (K) B (m) S (K) 1 M a y 1994 0830 -5 .12X10- 2 2.83x10-3 2.934 0.286 5.868 0.572 1130 -3 .15X10- 2 3.09x10-3 4.541 0.317 9.081 0.635 1452 -2.60x10-2 3.33x10-3 0.475 0.304 0.949 0.607 1730 -4 .14X10- 3 -3.19x10-3 17.50 0.103 34.99 0.205 27 July 1994 0830 -1 .41X10- 2 4.40x10-3 84.505 2.055 169.01 4.110 1130 -6.53x10-3 3.97x10-3 14.618 0.445 29.236 0.890 1430 -9.30x10-3 3.94x10-3 18.862 0.460 37.723 0.920 1730 -3 .06X10- 4 3.88x10-3 21.734 0.276 43.468 0.552 28 July 1994 0830 -2.18x10-2 4.52x10-3 2.059 0.477 4.104 0.954 1135 -1.06x10-2 4.41x10-3 12.36 0.437 24.73 0.874 1430 -5.47x10-3 4.15x10-3 22.86 0.404 45.72 0.807 1730 4 .62X10- 5 4.06x10-3 109.1 0.115 218.2 0.231 31 July 1994 0830 -5.43x10-2 4.75x10-3 2.111 0.617 4.222 1.235 1130 -6.38x10-3 4.79x10-3 8.414 0.461 16.83 0.923 1430 -3.61x10-3 4.50x10-3 24.17 0.453 48.34 0.906 1730 1.68x10-3 4.49x10-3 22.29 0.315 44.58 0.630 27 June 1995 0830 -2 .16X10- 2 4.69x10-3 2.142 0.972 4.284 1.944 0910 -1.55x10-2 4.59x10-3 8.556 0.470 17.11 0.939 1128 -8.25x10-3 4.45x10-3 17.15 0.610 34.30 1.219 1429 -1.11x10-2 4.64x10-3 15.70 0.421 31.39 0.841 155 Table E . 1 continued. JFD parameters used as input to the CuP model. B corresponds to Bowen ratio parameters. S corresponds to Solar Forcing parameters. Cut offs represent where the JFDs were truncated. Axes Slopes Standard Deviations Cut Offs Time (LST) B (K/m) S (K/m) B (m) S (K) B (m) S (K) 6 July 1995 0829 -1.05x10-2 4.79x10-3 7.980 0.888 15.94 1.777 1128 -4 .85X10- 3 4.74x10-3 56.68 0.774 113.36 1.548 1431 -2.25x10-3 4.52x10-3 53.27 0.492 106.54 0.984 9 July 1995 0830 -2.24.x 10- 2 4.98x10-3 1.826 0.551 3.651 1.102 1130 -7.28x10-3 4.84x10-3 14.37 0.423 28.73 0.846 1431 -1.25x10-2 4.88x10-3 29.91 0.577 59.81 1.154 11 July 1995 0830 -2.17x10-2 4.99x10-3 5.229 0.925 10.46 1.851 1130 -9.36x10-3 4.73x10-3 15.36 0.798 30.73 1.597 1430 -3.80x10-3 4.56x10-3 60.53 0.472 121.1 0.943 13 July 1995 0830 6.53x10-2 5 .24X10- 3 0.140 0.557 0.279 1.114 1131 -1 .02X10- 1 5.09x10-3 1.744 0.611 3.491 1.221 1430 2 .10X10- 1 5.08x10-3 1.145 0.429 2.289 0.849 156 

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