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Parameterization of net radiation in urban and suburban environments Doerksen, Geoff N. 2004

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PARAMETERIZATION OF NET RADIATION IN U R B A N A N D S U B U R B A N ENVIRONMENTS by GEOFF N . DOERKSEN B.Sc, Simon Fraser University, 2001 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Earth and Ocean Sciences; Atmospheric Science Programme) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A April 2004 © Geoff N . Doerksen, 2004 Library Authorization In presenting this thesis in partial fulfillment 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. Name of Author (please print) Date (dd/mm/yyyy) ™e o f T h e f s i s : fer^pkVr^ o-A „eA- rrArrti^ Degree: f|Sf\. Year: £boY Department of Mtf*GSfh*r7c~ Sore^c<fl ^cfiy r>^(\ The University of British Coldmbia Vancouver, BC Canada ^^O^^C^S A B S T R A C T Radiation budgets are currently understudied in urban environments. It is especially difficult, almost impossible, to find an existing urban radiation site where the radiation budget is continually being monitored. This creates the need to model the radiative components in cities: such information is used for several applied purposes (solar energy, building and urban design) and as input to meteorological pre-processors used to calculate urban heat, mass and momentum fluxes, atmospheric stability and mixed layer depth, that in turn drive climate and air quality models. Recently field measurements of the component surface radiation budget fluxes have been gathered at several urban sites in different climates and with different surface structure and cover. Data collected in Basel, Lodz, Marseille, Miami, and Vancouver are used here to devise an urban radiation scheme that uses measurements of solar radiation and routine weather observations to estimate net radiation. The simplest approach to obtain net radiation (Q*) is to use linear regression relations between net radiation (Q*) and incoming solar radiation (Kvl) derived from data measured at the above urban, suburban and rural radiation sites. Multiple regression incorporating a cloud parameter shows a marked improvement over such simple linear regression at the study sites. The major limitation of these regression methods is that they are strictly daytime Q* schemes and cannot generate estimates during the night. An alternative is to parameterize each surface radiation budget component separately. Here this involved both tests of existing models and schemes and development of a new urban L t scheme. Several incoming longwave all-sky radiation schemes were tested at the study sites where the Maykut and Church all-sky L i scheme provides lower error and a smaller bias than Crawford and Duchon all-sky L i - , when both are combined with the Dilley and O'Brien clear-sky L- i parameterization. To estimate outgoing longwave radiation a correction term (CT), to account for the difference between the surface and air temperature, was evaluated at a densely-built urban site in Basel. A new urban outgoing longwave radiation scheme (termed LUST) was created based on the strong correlation found between the difference between the surface and air temperature (T s - T a) and solar radiation. The scheme, also evaluated at the densely-built i i urban site in Basel, uses measurements of air temperature and solar radiation to estimate outgoing longwave radiation. The LUST scheme generally performed better than the CT models at most sites with a reduction of RMSE by as much as 30% at the urban and suburban sites. Finally, two net radiation parameterization schemes, both including LUST, were tested. The Q* scheme where Li was modelled with a cloud parameter was found to give the best results at two suburban sites, while the scheme that modelled hi with cloud observations performed best at two heavily-built urban sites, an urban parking lot site and a rural grassland site, and error was similar at a third central city site. It is recommended that i f cloud observations are available that latter Q* scheme be used, however if they are not then use of the other Q* scheme is acceptable. m T A B L E O F CONTENTS ABSTRACT i i TABLE OF CONTENTS iv LIST OF TABLES vii LIST OF FIGURES viii LIST OF SYMBOLS AND ACRONYMS xi ACKNOWLEDGEMENTS xiv CHAPTER 1 INTRODUCTION 1 1.1 Introduction 1 1.2 Radiation Budget 2 1.3 Urban Radiation Budget 8 1.4 Radiation Models and Parameterizations 14 1.4.1 Incoming Longwave Radiation 14 1.4.2 Outgoing Longwave Radiation 18 1.4.3 Net Radiation 20 1.4.3.1 Linear Regression of Net and Solar Radiation 20 1.4.3.2 Parameterization of Net Radiation 23 1.5 LUMPS 24 1.6 Research Objectives 27 CHAPTER 2 METHODOLOGY 28 2.1 Introduction 28 iv 2.2 Climatology and Site Descriptions 28 2.2.1 Basel 29 2.2.2 Marseille 32 2.2.3 Lodz 34 2.2.4 Vancouver 35 2.2.5 Miami 36 2.3 Instrumentation 37 2.4 Data Resolution, Logging and Processing 39 2.5 Radiative Flux Source Area 40 CHAPTER 3 REGRESSION OF NET AND SOLAR RADIATION 47 3.1 Introduction 47 3.2 Basic Regression Model (BRM) 47 3.3 Hysteresis Regression Model (HRM) 52 3.4 Cloud Parameter Regression Model (CPRM) 58 3.5 Comparison of Regression Methods 59 CHAPTER 4 NET RADIATION PARAMETERIZATION SCHEME 60 4.1 Introduction 60 4.2 Parameterization of Incoming Longwave Radiation 60 4.2.1 Clear-Sky Model Results 60 4.2.2 Results for All-Sky Models that use Cloud Observations 62 4.2.3 All-Sky Model Results using a Cloud Parameter 65 4.2.4 All-Sky Model Comparison 66 4.3 Outgoing Longwave Radiation Parameterization Results 70 v 4.3.1 Analysis of the Correction Term 70 4.3.2 A New Outgoing Longwave Radiation Scheme: LUST Model 76 4.3.3 L T Model Results 83 4.4 Net Radiation Parameterization Scheme 91 CHAPTER 5 CONCLUSIONS 99 5.1 Summary of Conclusions 99 5.2 Recommendations for LUMPS 102 5.3 Future Research 103 REFERENCES 105 A l CLEAR SKY SOLAR RADIATION 112 A2 STATISTICAL METHODS 115 A3 SUM URBAN SURFACE TEMERATURE 116 v i LIST O F T A B L E S 1.1a Natural albedos. 4 1.1b Urban albedos. 4 1.2a Natural surface emissivities. 6 1.2b Artifical surface emissivity. 6 2.1 Study sites. 29 2.2 Radiative flux instrumentation. 38 2.3 Air temperature and relative humidity instrumentation. 39 2.4 Data resolution and averaging. 40 2.5 Radiative flux source areas. 41 3.1 Errors and regression coefficients for B R M . 48 3.2 Errors and regression coefficients for H R M . 53 3.3 Errors and regression coefficients for C P R M . 58 4.1 Incoming longwave radiation models tested. 61 4.2 Cloud observations. 63 4.3 Regression coefficients for Equations 4.1, 4.2 and 4.3. 74 4.4 Net radiation parameterization schemes. 91 4.5 Comparison of Q* estimates using four different net radiation 93 parameterization schemes at eight study sites. 4.6 Comparison of Q* estimates at bspa using Eq. 4.9 and Eq. 4.11. 97 A3.1 Surface temperature instrumentation at the bspr site. 118 A3.2 Total facet view factors at bspr. 121 vii LIST OF FIGURES 1.1 Flow chart of the structure of LUMPS. 2.1 The urban site bspr with the instrument tower extending from street level to well above the urban canyon. 2.2 The bspr tower extending out of the urban canyon. 2.3 Hemispherical image depicting the radiative source area of bspa. 2.4 An aerial photo of bspa showing the radiative source area. 2.5 The urban site bspa shown in an aerial photograph showing the FOV of downfacing radiometers. 2.6 An aerial photograph with the bspr site tower in the centre showing the FOV of downfacing radiometers. 2.7 The mars site in Marseille where the tower was constructed on top of a gravel roof, showing the FOV of downfacing radiometers. 2.8 An aerial view of the lodz site where the tower extended above the Institute roof, showing the FOV of downfacing radiometers. 2.9 An aerial photograph containing the vane suburban site showing FOV of downfacing radiometers. 2.10 An aerial view of the alls suburban site showing the FOV of downfacing radiometers. 3.1 Monthly bi coefficients for several sites showing the seasonality of the coefficient throughout the year. 3.2 Seasonality of the b 0 coefficient for several sites throughout the year. 3.3 Temporal variation of the hysteresis loop between net and solar radiation at Marseille for four clear days in June and July, 2001. 3.4 Incoming and outgoing longwave radiation fluxes during 4 days at the urban site in Marseille, mars. 3.5 Spatial variation of the hysteresis loop relationship between net and 56 solar radiation at four sites in Basel on July 5, 2002. 3.6 Incoming and outgoing longwave fluxes at four sites in Basel during 57 one clear day on July 5, 2002. 3.7 Root mean square error in W m"2 for three regression methods, 59 B R M , H R M and C P R M at 9 study sites. 4.1 Comparison of modelled and observed clear-sky L s l values. 61 4.2 Comparison of L v l a i i schemes combined with 7 clear-sky L s l models 64 applied at seven study sites. 4.3 Crawford and Duchon, 1999 (CAD) L i a u model tested at eight sites. 66 4.4a Comparison of observed versus predicted L-l using the M A Y L-iaii 68 scheme and cloud observations, and the C A D L - l a n scheme using the cloud parameter, tested at four urban sites. 4.4b Comparison of observed versus predicted L-l using the M A Y L-iaii 6 9 scheme with cloud observations, and the C A D L - l a i i scheme using the cloud parameter tested at one rural and two suburban sites. 4.5 Plot of the correction term CT = £ s 4 a T a 3 (T s -T a) versus incoming 72 solar radiation and net radiation, for 18 days in the summer of 2002 over a densely-built urban surface at bspr in Basel. 4.6 The form of the relation between the correction term (CT) and 73 incoming solar radiation, for a cloudless day on July 5, 2002 at bspr in Basel. 4.7 Correction term (CT) value during 18 nights in the summer of 2002 75 at bspr in Basel. 4.8 Observed 10-min average values of T s -T a and K.4- plotted on a 77 common time axis at bspr for 4 days in the summer of 2002 with very different solar radiation regimes. 4.9 Times series at bspr of T s - T a for three days of differing cloud 79 amounts. 4.10 Daily mi coefficients evaluated at bspr, plotted against daily 80 Ki totals for 193 days in 2002. i x 4.11 Daily ni2 coefficients evaluated at bspr correlated with a 81 daily clearness index, K - i D c i defined for 193 days in 2002. 4.12 RMSE for LT measured vs modelled using Equations 4.1,4.2 and 84 4.7 for seven study sites. 4.13a Modelled versus measured LT values at three urban sites. 88 4.13b Modelled versus measured L i values at three suburban sites. 89 4.13c Modelled versus measured LT values at the rural site. 90 4.14 R M S E for observed versus predicted Q* using the four different net 92 radiation parameterization schemes at eight study sites. 4.15a Measured versus modelled net radiation calculated using Equation 95 4.9 and Equation 4.11 applied to four urban sites. 4.15b Measured versus modelled net radiation calculated using Equation 96 4.9 and Equation 4.11 at two suburban and one rural site. A3.1 Three infrared thermometers (IRT) attached to the railing of the 118 North facing wall on the fourth storey of an apartment building at bspr. A3.2 Plan view of bspr site with the idealized configuration modelled by 120 S U M with a repeating array of street, building and courtyard elements, and the real plan view. A3.3 Comparison of Ts.suM and T s . L t taken during the IOP in Basel at 123 bspr. A3.4 Difference calculated by: T S . S U M - T S_ LT during the IOP in Basel at 123 bspr. x LIST OF SYMBOLS AND ACRONYMS BNT Brunt (1932) B R M Basic Regression Model BST Brutsaert(1975) C A D Crawford and Duchon (1999) CP cloud parameter C P R M Cloud Parameter Regression Model CSI Campbell Scientific, Inc. CT correction term [= £ s 4 a T a 3 (T s - Ta)] (W m"2) D diffuse shortwave radiation (W m"2) DIL Dilley and O'Brien (1998) ea vapour pressure E 0 extraterrestrial solar irradiance (W m" ) F view factor (%) FOV instrument field of view H R M Hysteresis Regression Model IDS Idso(1981) IOP Intense Observational Period I 0 solar constant (1367 W m"2) IRT infrared radiation thermometer JAC Jacobs (1978) K shortwave radiation (W m" ) incoming shortwave radiation (W m"2) K t outgoing shortwave radiation (W m") K4DCI daily clearness index daily solar radiation total (M J m"2 day"1) KSIDTC daily Ki0 total clear-sky modelled (M J m"2 day"1) KSIDTM daily Ki total measured (M J m"2 day"1) Ki0 clear-sky incoming shortwave radiation (W m" ) K * net shortwave radiation (W m"2) Kx clearness index hi incoming longwave radiation (W m"2) LT outgoing longwave radiation (W m" ) L ^ a l l all-sky incoming longwave radiation (W m" ) Li-clr clear-sky incoming longwave radiation (W m") L * net longwave radiation (W m"2) LST Local Standard Time LUMPS Local-scale Urban Meteorological Parameterization Scheme LUST Longwave Urban Surface Temperature model M A E mean absolute error M A Y Maykut and Church (1973) M B E mean bias error MSE mean standard error N fractional cloud cover PAR photosynthetically active radiation PRA Prata(1996) Q* net all-wave radiation (W m"2) Q E 2 latent heat flux density (W m") Q H sensible heat flux density (W m" ) AQs net storage heat flux (W m") r radius (m) R H relative humidity (%) RMSE root mean square error S direct-beam shortwave radiation (W m") SAT Satterlund(1979) SUG Sugita and Brutsaert (1993) SWB Swinbank(1963 T a air temperature (K or °C) Tsky sky temperature (K or °C) T s surface temperature (K or °C) u wind speed (m s"1) U B L urban boundary layer UHI urban heat island w precipitable water (kg m") Z S sensor height (m) a shortwave albedo a Stefan's constant (5.67 x IO"8 W m"2 K" 4) P heating coefficient £A infrared atmospheric emissivity £c!r infrared clear-sky emissivity infrared surface emissivity xiii A C K N O W L E D G E M E N T S Many people are to thank for the completion of this body of work and would not have been possible without their generous support. I am gratefully indebted to my supervisor, Dr. Tim Oke, for his constant support, constructive criticism and encouragement. He has always been available for discussion of ideas, answering questions and providing feedback. The lessons I have learned from him in the field, at school and in life I will always value. I would also like to thank my committee members, Dr. Andy Black, Dr. Ian McKendry and Dr. Phil Austin, who thoughtfully read through my thesis and provided valuable comments. Numerous people were responsible for providing data for use in the project. Thanks to Trevor Newton for providing the Miami dataset along with details of the site. Thanks to Sarah Roberts for providing the Marseille dataset and stimulating conversations in the lab. Thanks to Cindy Walsh for maintaining the Vancouver site and for her technical prowess when computer glitches were experienced. Thanks to both Dr. Brian Offerle and Dr. Sue Grimmond for providing the dataset and site detail of Lodz. Extended thanks go to the B U B B L E crew in Switzerland, especially Dr. Andreas Christen and Dr. Roland Vogt for their many contributions. Not only did they provide a well instrumented and coordinated IOP and unrestricted access to their facilities and data but they also were very gracious hosts and made us feel welcome in Basel. Many thanks to Andres Soux for providing and running S U M to calculate source areas and also for being available to answer questions and discuss ideas. I am grateful to Dr. James Voogt for discussing S U M and providing feedback on emissivity and surface temperatures and Phoebe Jackson who helped code several Matlab scripts. Funding for this research has been provided to Dr. T. R. Oke by Natural Sciences Engineering Research Council of Canada and the Canadian Foundation for Climate and Atmospheric Sciences. Personal funding was provided through University of British Columbia Teaching and Research Assistantships in the Department of Geography and Earth and Ocean Sciences. I must also thank Bi l l Bailey who as an inspiring professor and teacher guided me into climatology. I would especially like to thank my family, friends and Kris for their love and support. xiv C H A P T E R 1 INTRODUCTION 1.1 Introduction Knowledge of the radiation budget is vital to the understanding of the local climatology and has direct implications in the energy balance. Urbanization modifies the natural landscape and atmosphere through changes in surface cover and emissions of atmospheric pollution, subsequently changing the magnitude and dynamics of the radiation budget. Modern urban construction materials, such as metal, glass, concrete and asphalt in combination with the urban geometry of streets and buildings, and the polluted urban air combine to modify radiative exchanges. It is now widely accepted that urbanized areas possess a unique climatology and if we are to determine the effect of cities on such characteristics as air pollution dispersion, urban mixing depth, and meso-scale airflow it is necessary to study their radiation budget. Few urban radiation studies have been performed and it is even more difficult to find an existing urban radiation site where the radiation budget is continually being monitored. Typically radiation sites are located away from the city, often specifically in order to attain 'natural' measurements that are uncontaminated by urban influences. In contrast the focus of the present study is directly upon the urban radiation budget and how it is possible to arrive at estimates of radiation fluxes when minimal input information is available. 1 1.2 Radia t ion Budget Radiation from the Sun is the main driving force behind the climatology of the Earth's atmosphere and surface. The radiative exchanges between the surface and the atmosphere define the surface radiation budget. Net all-wave radiation (Q*) or just net radiation is the summation of the incoming and outgoing fluxes of short and longwave radiation to and from a surface. The complete radiation budget is equated as: Q* = K i - K t + L i - LT (Wrn 2 ) (1.1) where K.X is incoming shortwave radiation, KT is outgoing shortwave radiation, L-l is incoming longwave radiation and LT is outgoing longwave radiation flux density. These radiation terms all denote a radiative flux at a plane surface. The radiative flux is defined in units of Watts per unit area, or the energy transferred across a two dimensional surface in unit time, called a flux density. The net radiation of a surface is the net result of all of the incoming fluxes minus the outgoing fluxes. Solar or shortwave radiation (K) is defined as the portion of the electromagnetic spectrum in the range of 0.15 to 3.0 urn (Oke, 1987), i.e. it extends from ultraviolet to the near infrared. Solar radiation propagates through Earth's atmosphere and is either scattered, absorbed or transmitted. The portion of incoming solar radiation that is scattered and reflected makes up diffuse shortwave radiation (D). The portion of incoming solar radiation that arrives at Earth's surface without being absorbed or diffused is called the direct-beam shortwave radiation (S). Therefore, the total incoming shortwave radiation received by the surface is: 2 Ki = S + D (1.2) Outgoing solar radiation, KT is the solar flux density reflected by Earth's surface. The reflectivity of the surface integrated over the solar band is called the albedo, a, and hence is defined: The albedo of a surface is a unitless number between zero and unity. A n albedo of zero describes a surface that absorbs all incident radiation and an albedo of 1 represents a surface that reflects all the solar radiation that it receives. Earth's surface naturally exhibits a wide range of albedo values as shown in Table 1.1a. The albedo of a natural surface is influenced by many factors such as the surface type, moisture conditions, surface roughness and solar zenith angle (Barfield and Gerber, 1979). Also, the albedo of a natural surface can change from season to season depending on the condition of the vegetation type, vegetation cover and leaf emergence. a = Kt/Kl (1.3) 3 Table 1.1a Natural albedos. Surface Albedo Soil, dark, wet to light, dry 0 05- -0 40 Desert 0 20- -0 45 Grass, long to short 0 16- -0 26 Agriculture crops 0 18- -0 25 Tundra 0 15- -0 20 Orchards 0 15- -0 20 Forest, deciduous 0 15 --0 20 Forest, coniferous 0 05- -0 15 Snow, old 0 35- -0 70 Snow, fresh 0 75- -0 95 Ice, sea 0 30- -0 45 Ice, glacier 0 20- -0 40 Adapted from Oke (1987) and Stull (2000) Table 1.1b Urban albedos. Author Location Surface Albedo Oguntoyinbo (1970) Ibadan, Nigeria 0.12 Hess etal. (1978) Cracow, Poland 0.16 White etal. (1978) St Louis, Missouri U 0.13 Rouse and Bello (1979) Hamilton, Ontario U 0.13 Mayer and Noack (1980) Munich, Germany U 0.16 Steyn and Oke (1980) Vancouver, B C S 0.14 Aida (1982a) Tokyo, Japan U 0.10 Vukovich (1983) St Louis, Missouri U 0.13 Brest (1987) Hartford, Connecticut U 0.11 Brest (1987) Hartford, Connecticut S 0.13 Solerand Ruiz (1994) Barcelona U 0.23 Taha (1994) Los Angeles, downtown U 0.20 Newton (1999) Miami S 0.16 Offerle et al. (2003) Chicago S 0.18 Offerle et al. (2003) Los Angeles S 0.21 Offerle et al. (2003) Lodz, Poland U 0.08 Christen and Vogt (2003) Basel, Switzerland {bspr) U 0.11 Christen and Vogt (2003) Basel, Switzerland {alls) S 0.13 Snow covered: Bengtsson (1981) Lulea, Sweden S 0.20 Robinson and Kukla (1985) New York - New Jersey S <0.5 Kidder and Wu(1987) St Louis U 0.26 U = Urban and S = Suburban L o n g w a v e radiat ion is defined as encompass ing the 3 to 100 urn range (Oke, 1987) and has been g iven several names such as infrared, terrestrial, s k y and atmospheric radiat ion. Terrestr ial radiat ion denotes outgoing longwave radiat ion ( L T ) and sky and atmospheric radiat ion denotes i n c o m i n g longwave radiat ion (L-l). H o w e v e r , to keep the te rminology unambiguous, longwave radiat ion fluxes w i l l further be referred to s i m p l y as i n c o m i n g and outgoing. A l l bodies whose temperature is above absolute zero radiate energy. A body at a specific temperature that emits the m a x i m u m possible amount o f radiat ion is sa id to be a b lackbody . B o d i e s that radiate less than their fu l l potential are ca l led greybodies. The eff ic iency w i t h w h i c h bodies emit radiat ion is their surface emiss iv i ty ( £ s ) . A b lackbody has a surface emiss iv i ty o f unity. The emiss iv i ty o f greybodies is expressed as the radiat ion emit ted b y a surface compared to that emitted b y a b l ackbody at the same temperature. E m i s s i v i t y values range between zero and uni ty and a table o f typica l natural surface values is shown i n Table 1.2a. The source o f longwave radiat ion received at Ear th ' s surface is m a i n l y radiated f rom atmospheric water vapour, carbon d iox ide and ozone gas (Ineichen et al, 1984). C louds have a profound influence o n the longwave exchange because they act as almost fu l l radiators (Oke , 1987). Ne t longwave ( L * ) is defined as the difference between i n c o m i n g and outgoing longwave radiat ion: L * = L T - L - I (1.4) 5 Table 1.2a Natural surface emissivities. Surface Emissivity Soil, dark, wet to light, dry 0.98- 0 90 Desert 0.84- 0 91 Sandstone 0.98 Grass, long to short 0 .90- 0 95 Agriculture crops 0.90- 0 99 Forest, deciduous 0.97- 0 98 Forest, coniferous 0.97- 0 99 Cloud, cirrus 0.30 Cloud, alto 0.90 Cloud, low 1.0 Snow, old 0.82 Snow, fresh 0.99 Ice, sea 0.92- 0 97 Adapted from Oke (1987) and Stull (2000) Table 1.2b Artifical surface emissivities. Surface Emissivity Asphalt 0 95 Concrete 0 71 - 0 90 Gravel 0 92 Glass 0 87--0 94 Iron 0 13--0 28 Aluminum 0 01 - 0 05 Bricks 0 90--0 92 Stone 0 85--0 95 Wood 0 90 Plaster, white 0 91 Tar and Gravel, roof 0 92 Slate, roof 0 90 Tile, roof 0 90 Corrugated iron, roof 0 13 -0 28 Adapted from Oke (1987) and Stull (2000) Outgoing longwave radiation can be calculated through the application of the Stefan-Boltzmann Law: L T = £ S G T s 4 (1.5) where c is Stefan's constant (5.67 x 10"8 W m~2 K" 4), T s is the surface temperature (K) and £ s the emissivity of the surface. By analogy with Equation (1.5) it is reasonable to use an atmospheric emissivity (£A) and a sky temperature (T s k y ) , to calculate L i : L l = £ A a T s k y 4 (1.6) However, this equation is rarely used to calculate L i because it requires knowledge of the sky temperature and emissivity. To operationalize Equation (1.6) one would need vertical profiles of temperature, water vapour and ozone, cloud height and water amount, and information about other trace gases, aerosols and their optical properties (Niemela et al, 2001a). While temperature and humidity profiles can be obtained from radio soundings, these observations are not always available. Even more rare are detailed profile measurements of aerosol, ozone and cloud properties. Therefore, the application of ground based measurements, such as screen-level temperature and humidity, is more widely used. 7 1.3 Urban Radiation Budget In urban environments the radiation budget is altered by the modification of the surface and atmospheric properties. Several contributing factors alter the surface properties such as changes in albedo and emissivity of materials, geometric trapping, thermal inertia and the urban heat island (UHI). Atmospheric properties in the urban boundary layer ( U B L ) are mainly controlled by gaseous and particulate pollution, altered temperature structure, altered moisture structure and cloud modification through the influence of the city. It is widely accepted that incoming solar radiation in cities is attenuated when compared with their rural surroundings. Oke's 1988 review presents agreement among researchers that the average city (approximately one mill ion people) received 15 to 20% less incoming solar radiation than its unpolluted environs. These studies also acknowledge that the attenuation values are higher or lower depending on the different pollution conditions within a specific city. It was reported that large cities where photochemical pollutants dominate typically experience less than 10% attenuation. While in industrial cities, especially ones where particulates from coal-burning or industrial processing predominate, the consensus of opinion supports annual attenuations of greater than 10%. These cities observed winter monthly values greater than 20% and individual days up to 30%. Recent investigations have found extremely large attenuations with significant industrial aerosol or photochemical pollution (Arnfleld, 2003). Stanhill and Kalma (1995) detected a 33% decrease in incoming shortwave radiation in Hong Kong over a 35 year period which could not be explained by changes in cloud cover but suggest that an interactive effect of aerosol load on cloud optical depth 8 had some influence. In Mexico City an average of 22% reduction was observed by Jauregui and Luyando (1999) on clear days during the dry season with similar attenuation during the rainy season. They found solar dimming had an inverse relationship to wind speed and temperature. Attenuation reached its maximum of 25 - 35% during prevailing weak winds and high relative humidity. A study by Liepart (1997) in Germany attributed a decrease in solar radiation at an urban site in Hamburg to increased cloud cover thought to be triggered by the increasing emissions of water vapour and particulate matter from jet traffic. The surface albedo of cities ranges from 0.08 to 0.23 in the studies presented in Table L i b . The albedo of urban environments is consistently lower than most typical natural landscapes. This increased absorption of the city has been explained in part by models by Arnfield (1982), Aida (1982b), Kondo et al. (2001) and Sailor and Fan (2002). Aida (1982b) concluded that the urban irregularity, when H/W (height to width) ratio = 1, increases the surface absorption of solar radiation up to 20% compared with a flat surface of the same material. Kondo et al. (2001) found that albedo values decrease with increasing building height and decreasing uniformity of building height distribution. The combination of the trapping role of urban geometry coupled with the low albedo of some building materials used in roofs, walls and streets results in increased absorption. The surface albedo can drastically change when snow falls on a city. However the interesting thing to note after a snowfall is the urban-rural difference. While the snow on the rural landscape remains relatively untampered with, the snow in the city is spoiled through a number of influences. Factors such as the removal of snow from streets, soiling of snow by vehicles and pollutant deposits, and the urban heat island effect (Oke, 9 1988) all aid in the reduction of the albedo of fresh snow. In addition to these snow factors the urban geometry also determines where snow will accumulate. The vertical walls of buildings are typically free of snow and present a surface of high absorption in contrast to the snow covered surface. Todhunter and X u (1992) modelled net radiation over suburban snowpacks. They found that shortwave albedo varied considerably due to dry deposition of particulates and ground exposure resulting from snowplowing and snow shoveling operations. This made the assignment of an albedo to the surrounding suburban snowpack quite problematic (Todhunter and Xu, 1992). In a residential area in Lulea, Sweden Bengtsson (1981) found that old snow has albedos as low as 0.20-0.30. Robinson and Kukla (1984) reported a range of residential albedos from 0.50 at maximum snow cover to 0.15 in snow-free conditions along the New York - New Jersey border. Recent work has also been interested in urban effects on specific spectral bands of solar radiation. Jacovides et al. (2000) investigated the modification of the spectral composition of solar radiation by urban aerosols in Athens. They found attenuations of 27% in the ultraviolet band (300-400 nm), 17% in the visible band (400-700 nm) and 16% in the near-infrared band (700-1100 nm). An enhancement of the near-infrared diffuse component by 66% was observed along with an increase of 54% and 21% in the visible and ultraviolet bands respectively. The diffuse component accounted for more than 80%> of the total radiation field under a highly polluted atmosphere. These results agree with those of Sprigg and Reinsnyder (1972) and Wesely and Lipschutz (1976) who also found a decrease in the ratio of direct to diffuse radiation. The ratios of the direct to diffuse solar irradiances were found to depend strongly on the polluted atmospheric 10 conditions (Jacovides et al, 2000). Photosynthetically active radiation (PAR) is also attenuated in the presence of a polluted atmosphere. The entire visible region of the solar spectrum generally referred to as the PAR, with plant photochemistry being especially sensitive at wavelengths of 400-500 nm and 600-700 nm (McCree, 1972; Szeicz, 1974; and Rao, 1984). Jacovides et al. (1997) observed over an 18% reduction in PAR coupled with a 7% - 51% increase in diffuse PAR in Athens. These results have direct implications on many biological processes which use radiation that are spectrally sensitive such as the vision of animals and photosynthesis in plants. In the longwave region urbanization has been found to alter the infrared radiative properties of both the surface and the atmosphere. Longwave radiative exchanges are altered through unique surface emissivities brought about by building materials, the geometric complexity, the presence of a urban heat island that raises surface and atmospheric temperatures and a changed atmospheric gas and aerosol structure modifying radiative transmission and emission (Oke, 1988). Several researchers have found elevated values of incoming longwave radiation over a city. Oke and Fuggle (1972) measured incoming longwave radiation during nocturnal traverses across Montreal and reported values 2-25% greater than the surrounding rural areas. They concluded that the increases were directly correlated with the urban heat island intensity, namely the warmth of the city atmosphere rather than the effects of the polluted atmosphere. Comparable nocturnal results have been published by Aida and Yaji (1979) and Saito (1981) both in Tokyo, Suckling (1981) in Brandon, Manitoba, and Nunez et al. (2000) in Goteborg, Sweden. Rouse et al. (1973) found large daytime incoming longwave radiation differences in Hamilton, Ontario. They attributed the increase of L-l to particulate 11 pollution warmed by the absorption of solar radiation. Estournel et al. (1983) in a study in Toulouse, France also verified larger hi values through out the day and night. Surface emissivities can be tabulated for individual surfaces (Table 1.2b), however it is often difficult to determine the areal average value of a city due to the number of building materials and surfaces. Areal averages were estimated by Arnfield (1982) where he constructed a geometric urban radiation model incorporating the emissivity of individual surfaces. Results showed that the effect of canyon geometry is to increase the integrated urban emissivity relative to that of the individual surface materials. Kobayashi and Takamura (1994) also emphasized the need to assess the geometrical structure of the urban canyon. Using a Monte Carlo model, their results showed that neglecting the geometric effects caused significant errors in calculated L.T. Further it was found that calculations with area-weighing of the radiation emitted from flat homogeneous surfaces are not appropriate. Arnfield (1982) applied eight land use zones in Columbus, Ohio and found a relatively small range of emissivity values, from 0.937 to 0.961 in snow-free conditions, and 0.965 to 0.983 with snow. These urban surface emissivity values are slightly higher than rural values. Such elevated values in combination with a warmer urban surface tend to radiate more outgoing longwave radiation, therefore, cities usually have higher rates of longwave emission especially when there is an intense UHI. The overall net radiation budget of cities is remarkably similar to the budget in rural areas, the altered incoming and outgoing radiation fluxes tend to offset one another (Oke, 1988). The attenuation of incoming solar radiation from a polluted atmosphere is compensated by an increase of L-l due to a warmer urban boundary layer (UBL). 12 Similarly, larger L T through greater heat losses in the city counteracts smaller K T values brought on by lower albedo and Ki. Given the nature of radiative fluxes to offset one another there are minimal urban-rural net radiation differences. This view also is supported by Arnfield (1982) where he simulated urban-rural net radiation differences using his urban radiation model. He concluded that typical pollution and heat island effects on the incoming longwave and solar fluxes are such that the difference could be positive or negative but, in the absence of a snowcover, they tend to be small. Daytime net radiation observations show that urban-rural differences are small, while White et al. (1978) and Mayer and Noack (1980) found a smaller Q* in urban environments, Oke and McCaughey (1983), Cleugh and Oke (1986) and Newton (1999) found slightly larger Q* values for suburban neighbourhoods. Nocturnal studies performed by Oke and Fuggle (1972) and Mayer and Noack (1980) in an urban centre, and Oke and McCaughey (1983) and Cleugh and Oke (1986) in suburban areas commonly found a greater net radiation deficit. The consensus seems to be that urban net radiation for both daytime and nighttime are either slightly higher or lower than rural values. However, contrary to this opinion Adebayo (1990) found 8-20% higher urban net radiation in the tropical city Ibadan, Nigeria but this was based on only three dry season days and three wet season days. Very few studies have made Q* observations during snow events in urban environments. Xu and Buttle (1987) indicate that enhanced net radiation over suburban snowpacks resulting from building-snowpack interactions is a contributing cause of increased snowmelt rates found in suburban environments. They reported average net radiation totals over suburban snowpacks that were between 67 and 435% of open terrain values. Todhunter and X u (1992) devised a physically based model which simulated net 13 radiation fluxes over a suburban snowpack and compared it with measured net radiation at two suburban homes in Peterborough, Ontario. They state that determination of Q* over a suburban snowpack requires specification of the geometric relationship between the snowpack surface, and the building walls, sky and solar disk. 1.4 Radiation Models and Parameterizations 1.4.1 Incoming Longwave Radiation The emissivity of the atmosphere depends on both the vertical temperature profile and the vertical distribution of radiatively active constituents, which determine the infrared transmission and emission. The majority of incoming longwave radiation reaching the surface originates within a few hundred meters of the surface; therefore, the near-surface temperature profile is of primary importance in determining L-l (Niemela et al, 2001a). The most important atmospheric gas contributing to hi is water vapour as downwelling longwave flux in the atmospheric window (8-12 Jim) depends strongly on the water-vapour amount. Carbon dioxide is the second most important gas for L-l with O 3 , C H 4 , N2O and CFCs having a smaller influence. While a few are based on radiation transfer theory, most schemes for Li are parameterizations based on empirical relationships derived from observed radiation fluxes. One of the first of these was that of Angstrom (1915, 1936) who devised a relationship between screen-level air temperature (Ta) and vapour pressure (ea) in order to calculate clear-sky incoming longwave radiation L i c i r during clear sky conditions: L i c i r = c r T a 4 ( a - 6 10-cea) (1.7) 14 where a, b, c are empirical coefficients. Brunt (1932) presented a similar framework utilizing screen-level air temperature and vapour pressure: U c l r = aT a 4(a-Z>e a 1 / 2 ) (1.8) Swinbank (1963) devised an equation that employed only T a: L i c i r = 5.31xlO"13Ta6 (1.9) Brutsaert (1975) developed a parameterization based on the analytic solution of Schwarzchild's equation for a clear atmosphere: U c l r = 1 .24(e a /T a ) 1 / 7 oT a 4 (1.10) Satterlund (1979) similarly stated: U c l r =1.08[l -exp{-e a T a / 2 0 1 6 }]aT a 4 (1.11) Idso (1981) proposed an empirical formula where the emissivity of the atmosphere depends on ea and T a: 15 L i c i r = [0.7 + 5.95 x IO"5 ea exp(1500 / Ta)] rj T a 4 (1.12) Prata (1996) developed a new incoming longwave radiation formula that was tested using longwave radiation measurements, radiosonde profiles and an accurate radiative-transfer model. The formula depends on screen-level temperature and precipitable water (w) and is written as: U d r = [l - (1 +w)exp{-(1.2 + 3.0w) 1 / 2 }] o T a 4 (1.13) where w = 46.5 (ej T a) in kg m"2. Dilley and O'Brien (1998) also developed an L-l scheme which depends on the screen-level temperature and precipitable water: L l c i r = 59.38 + 113.7 (T a / 273.16)6 + 96.96 (w / 25) 1 / 2 (1.14) To assess all-sky conditions a cloud factor can be incorporated that is proportional to total cloudiness. Jacobs (1978) presented a linear all-sky downwelling longwave radiation scheme: L l a l l = (1 + 0.26 C) L i e - (1.15) where L^aii is the incoming longwave radiation flux density for all-sky conditions, and c is the total cloudiness in tenths. 16 Maykut and Church (1973) developed a widely used scheme which used radiation data from Alaska: Llaii = (1 + 0.22 c 2 7 5 ) L i c l r (1.16) As it is known that clouds at different heights have different emission rates, a model can be defined that applies the Bolz (1949) cloud correction term: Llaii = (1 + a c2) L i c l r (1.17) where a is a coefficient that depends on the type of cloud at a certain height. Sugita and Brutsaert (1993) also recognized that improvements could be made to all-sky L i modelling if cloud type was included in their scheme: U a l l = (1 + U C V) L i c i r (1.18) where u and v are constants that depend on cloud type. They tabulated these constants for several cloud types and found the best constants were determined to be u = 0.0496 and v = 2.45 when cloudiness data from visual sky observations were used. De Rooy and Holtslag (1999) developed a scheme that includes cloud fraction and differentiates between low, medium and high clouds: L i a „= £ a a T a 4 + c 2 N - c 3 ( N - N h ) (1.19) 17 where N is the total cloud cover, Nh is the fraction of low- and middle level cloud; and c 2 = 70 W m"2 and c 3 = 50 W m"2. Crawford and Duchon (1999) devised a scheme for calculating all-sky downwelling longwave radiation based on near-surface air temperature, humidity and pressure and solar observations. The scheme makes use of fractional cloudiness a term denoted as the cloud parameter (CP) which is the ratio of observed solar radiation to modelled clear-sky (K!0) radiation: CP = l - K s l / K i 0 (1.20) see Appendix 1 for calculation of K i 0 ; as calculated here measurements of atmospheric pressure are not needed. The scheme can be used in combination with a modelled clear-sky emissivity (£ c ir) and is presented as: Llall = [£clr + (1 " E c l r ) C P 2 ] G T a 4 (1.21) The application of this scheme is desirable when cloud observations are not available. 1.4.2 Outgoing Longwave Radiation The outgoing longwave radiation L i leaving the surface is dependent on the surface temperature and emissivity in accordance with the Stefan-Boltzmann law. However, it is a difficult task to obtain surface temperature at the local scale in an urban 18 environment. Since the surface temperature is not normally available it is desirable to approximate LT by: LT = e s a T a 4 + e s 4 a T a 3 (T s - T a) (1.22) where £ s = surface emissivity, T s = surface radiation temperature and T a = screen-level air temperature. Holtslag and van Ulden (1983) found a relationship between the correction term 4 o T a 3 (T s - T a) and measurements of incoming solar radiation, net radiation and sensible heat flux. For the comparison they used four days of data from a short grassy field in Cabauw, Netherlands. The air temperature was measured at 1.1 m and the surface radiation temperature was measured with an infrared radiation thermometer. They found that from the comparison between 4 a T a 3 (T s - T a) and K - l and Q*, no wind speed effects and no cloud cover effects could be detected. It was determined that a good estimation of the correction term in (1.22) can be obtained from Q*, giving: 4 a T a 3 ( T s - T a ) = c 3 Q * (1.23) From the limited amount of data they collected they found C3 = 0.12 for a grass surface. With (1.22) and (1.23) combined LT can be approximated by: LT = £ s a T a 4 + c 3 Q * (1.24) 19 Holtslag and van Ulden (1983) acknowledged that the surface coefficient C3 is specific to surface type and presented c 3 = 0.38 for bare soil and c 3 = 0.25 for Prairie grass. Therefore, application of this scheme in an urban environment would benefit from a re-evaluation of the coefficient within a city. Offerle et al. (2003) modified Holtslag and van Ulden (1983) and estimated the correction term using measurements of solar radiation and an albedo value instead of net radiation. 1.4.3 Net Radiat ion 1.4.3.1 L inea r Regression of Net Radia t ion and Solar Radiat ion As previously mentioned there are few urban radiation sites that collect all of the radiative components including net radiation. In order to assess the net radiation within urban areas a simple method exists to estimate net radiation using its main forcing term, measured solar radiation. A linear regression can be applied when solar radiation is plotted against net radiation such that: Q* = b0+b] ( l - a ) K * (1.25) where bo and b\ are empirical coefficients. This method was first developed by Monteith and Szeicz (1961) and relied on an albedo value for the surface. This equation can be operationalized to calculate daily values, however i f a diurnal albedo is applied it can be used to calculate hourly values. The equation was simplified to remove the albedo from the equation. When this is done a new constant was developed called by Monteith and Szeisz (1961) the heating coefficient (P). This approach attracted considerable attention 20 by several researchers including Ekern (1965) and Stanhill, Hofsetede, and Kalma (1966). Idso (1968) contested the notion of a heating coefficient as a result of inconsistent P values found when different reports were compared. After further study of the heating coefficient it was deemed neither statistically sound nor a descriptively helpful parameter. Idso (1971) said there was no compelling reason to believe that any single parameter would be able to do what researchers were hoping it would do. Along similar reasoning albedo was taken out of the equation to give: Q* = b0+biKi (1.26) There is now general agreement that the inclusion of albedo in the regression does not improve the standard errors, consequently regressions between Q* and K-l would prove more useful i f they did not require knowledge of the albedo (Jamieson, 1979). Idso, Baker and Blad (1969) acknowledged a general trend that shows net radiation to be greater in the morning than the afternoon on some days and eluded to a hysteresis loop within the regression. Even though the "heating coefficient" term was abandoned there still seems to be merit in trying to incorporate a new term to describe the effective hysteresis on the regression of net and solar radiation. A new term will be defined here as the hysteresis term (3Ki/3t) and will be included in a new equation: Q* = b0 + b\ Ki + b2 (dKl/dt) (1.27) 21 where bo, b\ and bi are empirical coefficients. Iziomon et al. (2000) recognized that the net radiation budget has a dependence on sky conditions and atmospheric turbidity and introduced a clearness index KT. They found the inclusion of both Ki and KT to be particularly helpful for locations where measurements of shortwave albedo are not available. They suggest: Q* = 5o + Z>i K l + Z>2KT (1.28) where bo, b\ and bi are empirical coefficients and K T = Ki/ E 0 . The extraterrestrial solar irradiance on a horizontal surface (EQ) is given by: E o - I 0 c o s ( Z ) (1.29) where IG is the solar constant (1367 W m"2) and Z is the zenith angle which is a function of time, date and latitude. Equation (1.28) includes a clearness term (KT) that is merely the transmissivity of the atmosphere. To improve on this method the cloud parameter (CP) in Eq (1.20), that takes into account the transmissivity of the atmosphere, can be incorporated into a regression equation to give: Q* = Z>o+6i Ksl + ^ C P (1.30) where bo, b\ and bi are empirical coefficients. 22 1.4.3.2 Parameterization of Net Radiation As the regression method does provide an estimate of net radiation, Idso (1971) stated that certain phenomena, such as the interaction of radiant, sensible and latent heat exchange at a surface, just do not lend themselves to such a simple analysis. He claims that only a detailed study of all facets of the various energy exchange process will be sufficient for our understanding of these phenomena. Holtslag and Van Ulden (1983) presented a model in which net radiation is parameterized into its individual components of incoming and outgoing short and longwave radiation. The model is based on several assumptions using routine weather measurements. Since the model uses routinely measured weather variables it is quite desirable and the authors note that the scheme can be expected to apply at various locations. The radiation scheme depends on air temperature T a at screen height, surface albedo, and total cloud cover N , n * = ( l - a ) K - l + c i T a 6 - o - T a 4 + c 2 N (1.31) ^ 1 +c 3 where c\, c 2 and c 3 are empirical coefficients with values of 5.31xl0~13 W m~2K~6, 60 W m"2 and 0.12 respectively. The first coefficient (c\) is adapted from Swinbank (1963) and is used to describe the relationship between screen-level air temperature and longwave radiation. The second coefficient (ci) acts as a multiplier coupled with total cloud cover and estimates the radiant flux density contributed by clouds. Finally c 3 replaces the heating coefficient term described in the linear regression method. The heating coefficient provides correlation between surface temperature and air temperature that allows an air temperature to be used to estimate the LT component of the radiation budget. Holtslag and van Ulden (1983) determined this coefficient by examining data 23 measured during four summer days over a short-grass surface in Cabauw, Netherlands. Equation (1.31) was tested using a full year of observations in the Netherlands and good agreement was found between measurements and estimates made with the scheme (Holtslag and Van Ulden, 1983). The model was designed for grass surfaces, however the authors expect it to be more widely applicable. Offerle et al. (2003) presented a net radiation scheme modified from Holtslag and van Ulden (1983) that estimated the correction term with solar radiation instead of Q*. While the modified scheme makes use of a grass surface coefficient (approximated from Holtslag and van Ulden, 1983) good results were attained when applied to urban and suburban sites, especially when a measured albedo value was used at the urban site. Unfortunately, this Q* scheme is not tested here because it was recently published relative to thesis submission. 1.5 L U M P S Local-scale Urban Meteorological Parameterization Scheme (LUMPS) is a parameterization scheme developed by Grimmond and Oke (2002). This scheme uses standard meteorological observations and basic knowledge of the surface to calculate urban heat fluxes. Currently, knowledge of the surface sensible heat flux and atmospheric stability is necessary as input to models to calculate air pollution dispersion, urban mixing depth, and meso-scale airflow. These input variables in cities are rarely observed and need to be parameterized by simple routinely measured data. The flow chart presented in Figure 1.1 shows the linkages in LUMPS between meteorological 24 observations, surface cover and morphometry, and the surface energy balance. L U M P S is formulated in the framework of the surface energy balance, Q * = Q H + Q E + A Q S (1.32) where Q * is the net-radiation, Q H is the sensible heat, Q E is the latent heat and AQs is the flux associated with the change in heat storage. A s seen in Figure 1.1, Q* is the precursor to L U M P S and drives the model. The L U M P S model requires that Q * is formulated using incoming solar radiation and standard weather observations such as air temperature (T a ), wind speed (u), and relative humidity (RH). The solar radiation data that L U M P S uses can either come from measurements or by estimation. This thesis, however, uses only measured solar radiation values so as to avoid error propagation that results when using multiple models. Several accepted methods of solar radiation modelling exist for clear skies, but difficulties arise when modelling clouds. Without further knowledge of cloud it is quite difficult to model solar radiation because solar radiation is strongly controlled by cloud cover. It should be emphasized that Q* can be calculated through either the energy balance or the radiation budget. Knowledge of either of these systems result in the same Q*, however L U M P S requires Q* to be calculated through the radiation budget so it can be used to calculate the rest of the energy balance terms. 25 Meteorological observations Ki ( T a ) e a , c F ) T a . P U Q* ^ AQs QH, QE L, u* ^ ^ (Albedo, aK Cover fraction, Emissivity, £SJ Fim, Fv, FR Cover fraction, Fvor F,r I Roughness, z0M, z0H, zd Frontal Area Index, XF Surface cover and morphometry (GIS) Figure 1.1 Flow chart of the structure of LUMPS. Quantities in parentheses are needed only if net all-wave radiation Q* or incoming shortwave radiation K \ are not measured: T a is air temperature, e., is actual vapor pressure, Cp is cloud fraction, P is pressure, U is wind speed, AQs is storage heat tlux, Q H is turbulent heat flux density, Q|. is latent heat flux density, L is Obukhov length, and u* is friction velocity. Source: Grimmond and Oke (2002). 26 1.6 Research objectives The main objective of this thesis is to present and validate methods of estimating urban net radiation using solar radiation and standard weather measurements. The motivation behind this approach is mainly derived by both the need for an urban net radiation estimation scheme and as input to the LUMPS. The research objectives are to: • review the nature of the urban radiation budget based on previous observational and modelling studies • review available Q* parameterization schemes and suggest possible modifications • gather and document suitable Q* data sets for development and testing of schemes • apply the Q* data to validate models • recommend appropriate Q* scheme(s) and input values. 27 C H A P T E R 2 M E T H O D O L O G Y 2.1 Introduction This chapter outlines the instrumentation, climatology and description of the study sites used in this project. It also highlights the importance of radiative flux source area analysis when selecting a study site that is deemed to be representative of its surroundings. 2.2 Climatology and Site Descriptions It is quite rare to find urban sites where radiation components are being monitored. However, this study draws on several sites located within urban and suburban environments. Nine study sites were chosen from Basel C H , Marseille FR, Lodz PL, Vancouver C A N , and Miami USA at which both short- and longwave radiative components were measured (Table 2.1). The sites in Marseille and Lodz were located in the urban core while the sites in Vancouver and Miami were situated in a suburban neighbourhood. The study in Basel was a large multi-institutional project that included an intense radiation campaign. The magnitude of this urban radiation campaign is rare and provided three urban sites, one suburban site and several rural or 'reference' sites. 28 Table 2.1 Study sites. Site Code City-Area Type Observational Period Latitude Longitude Elevation masl (m) Land - Use bier Basel - rural 01-Aug-01 to 47.59N 275 Rural grassland Lange Erlen 31-Jul-02 7.65E alls Basel - suburban 11-Jun-02to 47.55N 277 Low density residential Allschwil 10-Jul-02 7.56E miam Miami - suburban 17-May-95to 25.73N 2.4 (airport) Low density residential Dade County 21-Jun-95 80.37W vane Vancouver - suburban 01-Sep-02to 49.25N 69 Low density residential/ Sunset 16-Jul-03 123.07W commercial bmes Basel - urban 30-Jun-02 to 47.56N 255 (si)* Medium to high density mixed Messe 09-Jul-02 7.60E 282 (rl)* commercial/industrial bspa Basel - urban 01-Aug-01 to 47.56N 278 Medium to high density mixed Spalenring 31-Jul-02 7.58E residential/commercial bspr Basel - urban 12-Dec-01 to 47.57N 255 Medium to high density mixed Sperrstrasse 12-Jul-02 7.60E residential/commercial lodz Lodz- urban 01-Jan-01 to 51.76N 205 Medium to high density mixed Lipowa 01-Jan-02 19.45E residential/industrial mars Marseille - urban 22-Jun-01 to 43.29N 92 High density commercial/ Cours d'Appel 12-Jul-01 5.38E residential Notes: * si = street level, rl = roof level + see also Figures 2.3 to 2.10 2.2.1 Basel The city of Basel is located in northeastern Switzerland where the borders of France, Germany and Switzerland meet. At this point the Rhine River turns from a westward direction to north at the transition to the Upper Rhine Valley. The city lies in open terrain surrounded by the hills of the Black Forest (Germany) in the northeast, the Vosges mountains (France) in the northwest and Jura mountains (Switzerland) in the south. The topography of the area controls the mesoscale flow over the city, which is dominated by an easterly wind along the Rhine Valley turning to the north at the northern 29 edge of the city (Feigenwinter, 1999). The area has predominately a warm temperate climate with more precipitation in the summer months than in the winter. A large multi-institutional project called the Basel UrBan Boundary Layer Experiment (BUBBLE) was established in Basel to examine turbulence, dispersion, and radiation and other energy fluxes within the city centre. Several sites were established for the project including three at urban, one suburban and several rural reference locations. Two large towers were erected in the heavily built-up area of the city; bspa, where a mast was installed on the roof of the Institute of Meteorology, and bspr, a 32 m tower built in a narrow street canyon. Figure 2.1 and 2.2 show the tower at bspr in the urban canyon. The heavily built-up area is predominately made up of neighbourhood blocks with rows of 3 to 4 storey attached buildings around the outside of the blocks with courtyards in their interior. The buildings are a mixture of commercial and residential structures. Roofs comprise a mixture of types including flat roofs with tar and gravel and pitched roofs with clay tiles. The streets are made of concrete. Most blocks contain vegetation and light industrial / commercial buildings in the inner courtyard. The vegetation consists of gardens and deciduous trees. A third urban site, bmes, was located on the roof of a parking structure 500 m southeast of the bspr site. An existing lamp post was used as an instrument platform at 2.2 m. The concrete structure was closed to the public during the measurement period. 30 Figure 2.1 The urban site, bspr is visible in this photograph with the instrument tower extending from street level to well above the urban canyon. On either side of the canyon are 3 - 4 storey residential buildings. The structure of the neighbourhood block can be seen with a row of buildings around the outside of the block and an inner courtyard made up of vegetation and light industrial buildings. [Photo by Matthias Roth, 2002]. The suburban site, alls, was predominately made up of single detached and 2-3 storey row houses. The buildings are made of plaster or stucco with clay tile roofs. Directly below the instrument tower is a garage with a flat, gravel roof. Most of the homes have backyards with trees, shrubs and gardens. One rural site was established, bier, located in the valley of the Wiese River just northeast of the city, having an open grassland surface. 31 Figure 2.2 The bspr tower extending out of the urban canyon. At the base of the tower is a trailer housing the data acquisition system. 2.2.2 Marseille The city of Marseille is the second largest city in France with one million occupants. It is in the Provence region of southern France and is situated on the northern coast of the Mediterranean Sea. Marseille is located in the Rhone delta at the south end of the Rhone Valley, a long north-south rift between the Cevenees Mountains and the foothills of the French Alps. The area experiences a Mediterranean climate with its characteristic wet, mild winters and extremely dry, hot summers. During the summer both the lack of 32 precipitation and elevated temperatures are brought on by the presence of a high pressure cell. This sub-tropical high pressure cell moves toward France during the summer advecting dry continental tropical air. The Mediterranean Sea maintains relative warmth in the winter creating a low-pressure trough and a corresponding convergence zone, resulting in frontal and cyclonic disturbances (Roberts, 2003). Locally Marseille is influenced on a diurnal basis by a strong sea-land breeze system. At night, the land breeze results in a northwest flow toward the sea while during the day a cooler breeze blows on-shore from the west. Marseille also experiences the Mistral, a localized drainage flow responsible for a strong northerly flow down the Rhone Valley towards the Mediterranean Sea. In the wake of the Alps ridge, a dynamic low pressure region is created and results in a cool, dry wind that predominantly occurs in the winter months (Guenard et al, 2003). A large multi-institutional European air quality study called ESCOMPTE (Experience sur Site pour COntraindre les Modeles de Pollution atmospherique et de Transport d'Emissions) took place in Marseille June 5 - July 15, 2001. A tower was installed on the top of a building in the heavily built-up city centre. The area contains little vegetation (approx. 16% plan area) mainly as trees in courtyards and street boulevards. The buildings around the tower are comprised of predominately limestone and granite administrative, residential, and commercial buildings with clay tile or pebble-topped roofs (Roberts, 2003). 33 2.2.3 L o d z Lodz, located in central Poland, is the second most populated city in the country. It is situated on the northwestern edge of the Lodz highlands on the watershed of the Vistula and Oder rivers. The town boundaries span 214 square kilometers with relatively flat terrain that has a slight southeast inclination with only 55 m elevation gain. The area has no water bodies and the closest mountain range is over two hundred kilometers to the south. Lodz experiences a warm temperate climate with both maritime and continental influences. The combined effects of continental air masses from the east mixing with maritime air masses from the west results in highly variable local weather patterns. The winters are relatively cold with a continuous snow cover on the ground of 10 - 20 cm, while the summers are warm and receive more precipitation than the winter. The urban site, lodz, is located in an area of medium to high density mixed industrial / residential use. Most of the buildings in the area were constructed 100 years ago during the boom of the textile industry (Klysik and Fortuniak, 1999). The buildings surrounding the site are quite large, about 15 -20 m high, and are constructed of brick, cement and stone. The majority of buildings around the instrument tower have tar roofs, a few have concrete / cement and clay tiles. The instrument tower was installed on top of the Institute roof. It should be noted that this black tar roof comprises a large portion of the radiation source area of the instruments on the mast. The vegetation interspersed amongst the building elements and streets is predominately grass and deciduous trees. 34 2.2.4 Vancouver Vancouver, British Columbia is situated at the mouth of the Fraser River that lies in the Fraser Valley extending from the Straight of Georgia in the west to the Fraser Canyon in the east. Greater Vancouver is bounded by the Coastal Mountains to the north and the Cascade Mountain Range to the southeast. The climate of the Lower Fraser Valley is characterized by wet, mild winters and dry, warm summers. The large-scale flow is predominately from the west and has embedded disturbances or cyclones which are best developed in winter (Roth, 1988). In the summer, a sub-tropical high pressure cell extends northward and generally induces light winds and cloudless skies with occasional weak frontal disturbances from the north. More locally, both land-sea and mountain-valley circulations are present (Steyn and Faulkner, 1986). The effect of the land-sea breeze is to cause mainly westerly winds during the daytime and weaker easterly flow during the night (Roth, 1988). The suburban site, vane, is located in southeast Vancouver at a transformer station operated by the British Columbia Hydro and Power Authority. The Hydro compound is comprised of a flat gravel surface with an open electrical transformer lattice structure and a small building in the centre. A 28 m tower extends out of the southwest corner of the Hydro compound. The compound is surrounded by a 20 to 30 m wide strip of grass. The surrounding neighbourhood is mixed commercial / residential with 1 - 2 storey detached buildings and houses. The commercial buildings predominately have a flat gravel roof with concrete parking lots while the residential houses have tar shingles with a front or backyard comprised of grasses, gardens, trees and shrubs. 35 2.2.5 Miami The city of Miami is located at the southeastern edge of the Florida peninsula approximately 50 km north of the southern end. The area bounded by the swamps of the Everglades to the south and west, and by the Atlantic Ocean to the east. The area is relatively flat with many lakes and canals with no natural topography features over 2 m in elevation in the greater Miami region. The natural vegetation of the area is predominantly marsh grass with palm, ficus and fruit trees and bushes in less wet regions. Southern Florida is designated as belonging to the tropical savanna region, sometimes called the wet and dry tropics because of the hot-wet climate in the summer and the hot-dry climate in the winter. Precipitation is highly concentrated in the summer months and is typically caused by local thunderstorms and thunderstorms induced by the convergence of hot humid air from the Atlantic Ocean and equally hot and humid air from the Gulf of Mexico. Westerly trade winds bring warm, humid, near-surface air to the region with temporal inversions above 1-2 km that weaken vertical uplift especially in the winter (Newton, 1999). A study area was established in western Miami with two towers, 700m apart, to measure the upwelling and downwelling radiative fluxes. The main tower was the location of the turbulence instrumentation, which measured the downwelling radiative components. The other site, located 700 m upwind of the main tower, measured the upwelling radiation within a suburban radiative flux source area. From here on in, both sites will be considered one location with both upwelling and downwelling radiant fluxes. The suburban site, miam, is located in the backyard of a residential single-story house. While the backyard is not regularly irrigated it remains green. The backyard also 3 6 contains several large 2 - 8 m leafy trees and 3 lightly coloured aluminum garden sheds. The three residential houses in the immediate area of the tower have white stucco walls with reddish-brown roofs made of tar and paper shingles and ceramic tiles. 2.3 Instrumentation At each site downwelling and upwelling short and longwave radiative components were measured. The up-facing radiometers were sited such that there were no horizontal obstructions and were representative of the incoming radiation from the atmosphere and sky. In most cases the down-facing radiometers were mounted directly below the up-facing radiometer, with the exception of the Miami suburban site. The down-facing radiometers captured the outgoing radiation from the urban, suburban or rural surface. The overall net radiation budget at all sites was calculated from the measured short- and longwave components. Table 2.2 details the radiation instrumentation and measurement heights. Corresponding standard meteorological measurements were also taken at each site, including air temperature and relative humidity, shown in Table 2.3. 37 Table 2.2 Radiative flux instrumentation. Site Instrument Manufacturer Variables Measurement Measured Height (m) bier CNR1 Radiometer Kipp & Zonen alls CNR1 Radiometer Kipp & Zonen miam C M 5 Pyranometer Epply PIR Pyrgeometer Epply C M 5 Pyranometer Epply PIR Pyrgeometer Epply vane CNR1 Radiometer Kipp & Zonen bmes CNR1 Radiometer Kipp & Zonen bspa CM11 Pyranometer Kipp & Zonen PIR Pyrgeometer Epply bspr CNR1 Radiometer Kipp & Zonen CM11 Pyranometer Kipp & Zonen C G 2 Pyrgeometer Kipp & Zonen lodz CNR1 Rad iometer 1 Kipp & Zonen m a r s CNR1 Radiometer* Kipp & Zonen K l , K T , L 4 , L T 2.0 K I , K T , L I , L T 15.1 K t L t Ki Li K l . K t U , L t 10.0 10.0 2.5 2.5 K i , K t , L i , L t 27.8 K l , K T , L l L T 2.2 above roof 32.9 32.9 K 4 , K T , L l , L T 31.5 K i . K T 3.2 L i . L t 3.2 K 4 , K T , L l , L T 37 K l , K T , L l , L T 34.6 or 43.9 Q * was calculated by summing all of the incoming radiative components minus the outgoing radiative components. 1 Heating was applied to the C N R during cold nights. ''The tower mast was raised or lower depending on the wind conditions. Table 2.3 A i r temperature and relative humidity instrumentation. Site Instrument Variables Measured Measurement Height (m) bier Temperature / Hum. Sensor 1 T a , RH 2.0 alls Temperature / Hum. Sensor 1 T a , RH 15.0 miam HMP35C Vaisala 2 T a , RH 40.74 vane HMP35C Vaisala 2 Ta, RH 20.1 bmes Temperature / Hum. Sensor 1 T a , RH 2.8 above roof bspa PT100 Psychrometer T a , RH 32.9 bspr PT100 Psychrometer T a , RH 31.2 PT100 Psychrometer T a , RH 2.6 lodz Rotronics 10OMPH T a , RH 37 mars HMP35C Vaisala 2 T a , RH 28.5 or 37.9 ' not ventilated 2 with radiation shield 2.4 Data Resolution, Logging and Processing The study sites utilize different data acquisition systems in regards to sampling, averaging and downloading of the data. Table 2.4 outlines the sampling rates and averaging times of the radiometers, temperature and relative humidity sensors. The instruments were sampled at a given rate and averaged by the data logger to 10 min averages in Basel, 15 min averages in Lodz, Marseille and Vancouver, and 1 hour averages in Miami. Each of the sites used a slightly different logging system, typically a CSI 21X or 23X logger housed on-site which provided the sampling and averaging protocols. These measurements were then downloaded via an on-site computer system, a mobile computer system or an automated data communication line that regularly transferred the data and stored it as a secure data file. Quality control of data was 39 conducted either by hand or with automated computer programs. Analysis of the data was performed in Matlab 6.0 and Excel. Table 2.4 Data resolution and averaging. Site bier alls miam vane bmes bspa bspr lodz mars Sample K 1 , K T , L A , L T 0.1 0.1 0.067 0.2 0.1 0.1 0.1 0.2 0.2 Rate (Hz) T a and RH 0.1 0.1 0.067 0.2 0.1 0.1 0.1 0.2 0.2 Averaging Times (min) 10 10 60 15 10 10 10 15 15 2.5 Radiative Flux Source Area During the direct measurement of a surface radiative flux, a specific portion of the surface called the source area mainly influences the sensing instrument (Schmid et al, 1991). The contributions of individual surface elements within the zone of influence are combined to produce a composite influence of the source area. Therefore, determination of the source area is important for radiative flux measurements when comparing sites of differing surface types and geometric densities. Reifsnyder (1967) devised a way of calculating the source area or "field of view" (FOV) of an instrument using geometry that obeys Lambert's cosine law. The method addresses the issue of determining the "field of view" of an inverted radiometer. If the radiometer is oriented parallel to a level ground surface it is exposed to radiation from the entire surface extending to infinity in all directions. The portion of the surface directly below the sensor provides the bulk of the radiation influence. Given this, Reifsnyder defines the view factor, F, for a circular surface disc of radius, r, as the ratio of radiation received from the disc to the amount received from the remaining ring surrounding the disc and extending to infinity. The view factor, F, is given by: 40 F = r 2 / ( r 2 + z s 2 ) (2.1) where z s is height of the sensor above the surface, r is the radius of the source area and F is the proportion of the measured flux for which that area is responsible. Therefore, to determine the upwelling radiative flux source area the equation can be rearranged to give: r = z s ( l / F - i y 0 - 5 (2.2) The radiative flux source areas for the study sites were calculated for the down-facing radiometers and presented in Table 2.5. Table 2.5 Radiative flux source areas. Site bier alls miam vane bmes bspa bspr (upper) bspr (lower) lodz mars (down) mars (up) Radiometer Height (m) 2.0 15.1 10 27.8 2.2 32.9 31.5 3.2 37 34.6 43.9 View Factor (%) Radius (m) 8.7 65.8 43.6 121.2 9.6 143.4 137.3 13.9 161.3 150.8 191.4 95 Plan Source Area (m2) 239 13603 5966 46108 289 64577 59198 611 81675 71423 114977 View Factor (%) Radius (m) 19.9 150.2 99.5 276.6 21.9 327.4 313.4 31.8 368.1 344.3 436.8 99 Plan Source Area (m2) 1243 70879 31086 240245 1505 336478 308451 3183 425567 372149 599093 Figure 2.3 is shown to demonstrate that the portion of the surface directly below a down-facing radiometer provides the bulk of the radiation influence. The hemispherical photograph taken from the sensor location closely resembles what the down-facing 41 radiometer would 'see'. It can be seen that the Institute roof directly below the tower has a large radiation influence. It is also evident that the inner courtyard has a major radiation influence, mainly from vegetated surfaces and surrounding walls and roofs of the neighbouring buildings. Streets are not clearly visible by the sensor at this site, while the bspr site had a major radiation influence by the street directly below the tower. Presented as a comparison, Figure 2.4 is an aerial photograph of the bspa site, with the area within the red circle depicts 95% of the source area. It is interesting to view these figures together as they both show the source area of the radiometer. However, the hemispherical photograph more closely depicts the fractional area that can be 'seen' by the radiometer. The aerial photograph is relatively undistorted and does not represent what the radiometer 'sees'. Therefore, one must be careful when making fractional area assessments from aerial photographs, especially in urban areas. For example, the hemispherical photograph of bspa displays a very small street fractional area, while the aerial photograph shows a greater proportion of street surfaces. Because of the urban geometry most of the street surfaces are not visible by the radiometer. Four of the urban study sites are shown in Figures 2.5 to 2.8 and two of the suburban sites are shown in Figures 2.9 and 2.10. These figures each have the 95% and 99% upwelling radiative flux source area on them. 42 s J3 u ** "° H •= | 1 e u s . s « « ** *" s a * g •2 s a ! i * J= -S 2 4 a rt •S ° £ a M IT) 5 8 SOX -O 5 S I 0 • 3 w IB O S ? a 1 ^ — V 4» .2 ~ E - o < ** M fa ^ Q s a " M U E h O fa C3 "9 43 -5 CV 11 J, * « n •s * - I a £ » 5 8 • f i u — S 3 - O Oil CB 2 s» 0 £ a * 1 — IB es B •c a I* ° u? es 9\ CB « 5 — fl •£ " o g CQ 3 . 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B ju o a B B w O V rt fc" m ** « P] « u - fa * • U DI B .5 S B - ° S a o * - oi •- SI a a w i •§ = O a u * 93 i t ! * cn o 2 rt C3 oi S I ^ V 1 r i £ £ a .11 fa •< .2 2 e.2 ^ 8 2 | 3 -a S ON o 3 O 9s K u 4 6 CHAPTER 3 REGRESSION OF NET AND SOLAR RADIATION 3.1 Introduction Several researchers have found net radiation to be linearly correlated with solar radiation and have used more readily available values of K>1 to estimate net radiation in absence of Q* measurements. Three regression models are presented in this chapter that utilize K i , air temperature (T a) and relative humidity (RH) to estimate daytime Q*. Previous studies over non-urban surfaces have shown a range in slopes and intercept coefficients in K i VS . Q* regressions. These probably indicate the effects of different surfaces and atmospheric conditions, hence it is interesting to investigate the case of cities that have their own distinct surfaces and atmospheric characteristics. 3.2 Basic Regression M o d e l ( B R M ) The simplest form of regression between net and solar radiation is presented in Eq. 1.26. Studies show this regression to have a high R 2 , upwards of 0.95. This high correlation is one of the main reasons why K-l is being used to estimate Q* in a linear manner. One should not be too surprised by this high correlation, because K i is the dominant component in the daytime radiation budget and dictates the overall net radiation. Most studies that have applied this basic regression model have been applied over rural and agricultural landscapes while very few studies have been performed in cities. Twenty-three sets of empirical results for the regression of Q* over grass exist, including those proposed by Shaw (1956) for Iowa; Clothier et al. (1982) for New Zealand; Hu and Lim (1983) for Malaysia; Monteith and Szeicz (1961) for England and 47 2 others give regression coefficients of b, =0.66 and b 0 = -28 W m"z (Linacre, 1992). More recently, Iziomon et al. (2000) working over a grass surface at three sites near Freiburg, Germany at different altitudes found average values of bj = 0.60 and bo = -26.3 W m"2, for the three sites over a four-year period. Impens and Lemeur (1969) published results for oats, bean, sunflower and corn crops and the average over these agricultural surfaces was found to be bi = 0.68 and bo = -28 W m"2. Table 3.1 shows the bi and bo coefficients and the associated errors with the B R M for rural, suburban and urban sites over a number of different time periods. Observations of K i and Q* were used to determine the bi and bo coefficients where only daytime values were used in the regression model, i.e. K i > 0. Measured Q* and modelled Q* values were used to calculate the statistical errors and correlation coefficient presented in Table 3.1. Table 3.1 Errors and regression coefficients for BRM (Q* = b 0 + b]Ki, Eq. 1.26) at several sites, where R = rural, S = suburban and U = urban. bier alls miam vane bmes bspa bspr3* bspr31* lodz mars R S S S U U U U U U MBE (W m"2) 0 0 0 0 0 0 0 0 0 0 MSE (W m"2) 1136 944 909 1018 1327 770 559 924 908 292 RMSE (W m"2) 34 31 30 32 36 28 24 30 30 17 MAE (W m"2) 26 25 23 27 29 24 19 25 25 14 R 2 0.96 0.98 0.98 0.97 0.96 0.98, 0.99 0.98 0.97 1.00 N 28638 2824 524 14226 1054 27833 16802 15816 17699 1305 b 0 -27.04 -46.89 -28.50 -29.96 -65.41 -37.75 -31.25 -42.13 -32.74 -85.90 b, 0.67 0.73 0.74 0.75 0.58 0.77 0.82 0.76 0.79 0.78 * Note: bspr3 is where measurements were taken at 3.2 m on the tower and bspr31 at 31.5 m. The rural site bier in Basel has a low bi value of 0.67. The suburban sites alls, miam and vane have similar bi values of 0.73, 0.74 and 0.75. The b\ values at the urban sites were found to be higher than both the rural and suburban sites giving 0.76, 0.77, 48 0.78 and 0.79 for bspr31, bspa, mars and lodz respectively. An interesting comparison can be made at the bspr site between two sets of measurements taken at different heights on the tower. When B R M is applied to both sets of data, in the street canyon and above the canyon, two different regression lines result with a bi value of 0.82 at the height of 3.2 m, and 0.76 at 31.5 m on the tower. The in-canyon data give a higher bi value due to the fact that the sky view factor at 3.2 m on the tower is approximately 0.53 and the down-facing radiometer senses a large portion of pavement. Conversely, at 31.5 m on the tower the sky view factor is much greater, close to 1.0 and senses the composite of the underlying neighbourhood, which includes roofs, walls, streets and vegetation. The trend of the bo coefficient is more difficult to explain as it is both a function of the radiative processes at the surface including its thermal properties and structure and radiative processes in the atmosphere mainly due to cloud cover. The bo coefficient is defined by the net longwave budget because it is the Q* value at sunrise / sunset when K-l goes to zero. A comparison between the bo values at two different sites mars and miam can be made to partially explain the nature of the coefficient. The entire observational period in Marseille was relatively cloudless including ten completely clear days in the 20 day dataset. The Marseille site is also situated within a densely-built urban matrix with relatively little vegetation and a high percentage of roofs, walls and road surfaces contained within the source area of the sensors. Therefore, having a cloudless atmosphere contributing a relatively low incoming longwave radiation flux, plus a warm urban surface emitting a relatively high outgoing longwave flux, this site possesses a large negative bo value of -86 W m~2. The suburban site in Miami on the other hand, with a very warm and humid sub-tropical atmosphere, had many cloudy days in the 49 observational period and the surface has a much greater percentage of vegetation. This combination results in a higher incoming longwave flux and lower outgoing longwave flux giving a relatively low negative bo value of -28 W m"2. In order to assess the seasonality of the regression coefficients, monthly values were calculated at the sites where sufficient data were collected. Figure 3.1 shows the bi coefficient at rural, suburban and urban sites throughout the year. The rural site bier shows a noticeable trend towards a higher bi value in the summer months approaching 0.70 and quite a lower winter value in January and December of 0.3 to 0.4. The suburban and urban sites exhibit less monthly variation than the rural site, however they follow a similar trend with a lower bi value in the winter months and a higher value in the summer. Figure 3.1 Monthly h, coefficients for several sites showing the seasonality of the coefficient throughout the year. 50 The monthly bo coefficients are plotted in Figure 3.2 for several of the sites. As noted, the bo coefficient is the intercept on the y-axis of the regression i.e. where K-l = 0 and Q* = L * at sunset and sunrise. The data were subject to the filter of KX > 0, so nighttime values are not included in the regression analysis, and the intercept is for times very close to but not actually at sunrise / sunset. Thus bo is not the average net radiation at night but rather the net radiation near sunset and sunrise. The coefficient bo is subject to monthly variability mainly due to the fluctuating nature of the clouds in the atmosphere. The suburban site vane shows a rather smooth curve where bo is almost a very small negative value in the winter and becomes more negative into the summer. This is in keeping with the bi-modal cloud climatology of the location: cloudy in winter, much less cloud in summer. The other sites in Basel and Lodz, however, show a more random variation in monthly bo values. A l l of the sites in Basel are in-phase with each other, with the rural site having a less negative value than the urban sites. It stands to reason that the Basel sites are all in-phase because they are broadly subject to similar incoming longwave radiation. 51 Month Figure 3.2 Seasonality of the b0 coefficient for several sites throughout the year. 3.3 Hysteresis Regression Model (HRM) The notion of adding a hysteresis term to the basic regression method in order to explain the diurnal variations of net radiation and improve the standard errors of the B R M is explored here. Idso, Baker and Blad (1969) alluded to a hysteresis effect when they plotted net all-wave versus solar radiation in their study over bare soil and short grass sod in Minnesota. The hysteresis term will be denoted here as dKl/dt as included in the new regression Eq. 1.27. The coefficients for Eq. 1.27 and the errors associated with the H R M approach are tabulated in Table 3.2. Little improvement has been attained over the B R M relation by including the hysteresis term. For example, the suburban site alls has an improved RMSE of 30.7 to 29.9 W m"2, while the urban site bspr31 result remained relatively unchanged the RMSE only going from 30.4 to 30.2 W m"2. 52 Table 3.2 Errors and regression coefficients for HRM (Q* = b 0 + b, Ki + b2 dKi/dt, Eq. 1.27) at several sites, where R = rural, S = suburban and U = urban. bier alls miam vane bmes bspa bspr3 bspr31 lodz mars R S S S U U U U U U MBE (W m"2) 0 0 0 0 0 0 0 0 0 0 MSE (W m"2) 1141 893 908 982 1316 771 552 910 898 281 RMSE (W m"2) 34 30 30 31 36 28 24 30 30 17 MAE (W m"2) 26 24 22 26 29 24 19 25 25 13 R 2 0.96 0.98 0.98 0.97 0.96 0.98 0.97 0.98 0.97 1.00 N 28268 2822 524 14139 1050 27527 16531 15785 17681 1299 bo -27.42 -46.92 -28.50 -30.16 -65.50 -38.15 -31.64 -42.19 -32.77 -85.93 bi 0.67 0.73 0.74 0.76 0.58 0.77 0.82 0.76 0.79 0.78 b 2 0.04 0.13 -0.01 0.13 0.05 0.03 0.06 0.08 0.06 0.08 The hysteresis loop relation between net and solar radiation varies both temporally and spatially, some days exhibit a wider hysteresis loop than others. Four clear days were examined at the urban site in Marseille (Figure 3.3). Day 184 exhibits the widest hysteresis loop with the morning having a higher Q* on the rising limb of the loop and the afternoon having a lower Q* on the falling limb. Other researchers (Monteith and Szeicz, 1961) found similar results, with lower Q* in the afternoon and have attributed it to greater afternoon surface temperatures, along with relatively constant longwave emission from the atmosphere. However, not every day exhibits this type of idealized hysteresis loop relation. On Day 182 the hysteresis loop crosses over at 0800LST, such that Q* is lower before noon and higher after noon, until the loop crosses back at 1700LST. Day 179 has quite a wide loop in the early morning between 0500 and 0600LST and Day 192 doesn't have a loop at all. Stanhill et al. (1966) presented one such cycle for the radiation balance above an orange grove on a clear day at Rehovot, Israel and found a crossover similar to the Day 182 result, midway in the cycle. They attributed this hysteresis cycle directly to the 'heating coefficient' of the surface (see Chapter 1 for more details on the heating coefficient). 53 0 200 400 600 800 1000 0 200 400 600 800 1000 K l Measured (W m"2) Figure 3.3 Temporal variation of the hysteresis loop between net and solar radiation at Marseille for four clear days in June and July, 2001. Idso, Baker and Blad (1969) disputed the link between the hysteresis effect and the 'heating coefficient' in their study over bare soil and grass sod. Their data constituted 3 clear days in St Paul, Minnesota and in fact they found net radiation was greater in the afternoon than in the morning, in seeming contradiction to the higher surface temperatures expected in the afternoon. They concluded that the daily cycles of the net and solar radiation appear to be more intimately connected with the conditions of the atmosphere than with the surfaces in question. Furthermore, they state that it is the atmospheric emission which determines the gross nature of the curves, however they do admit the surface can exert a substantial effect. It is also thought that atmospheric pollution and/or high cirrus clouds can be responsible for variations in incoming longwave radiation. Days that have been classified by observers as cloudless can in fact 54 have a polluted atmosphere, especially in urban centres. Hall (1968) was able to link very large variations in sky radiation to high-level cirrus clouds that may be undetectable by a ground-based observer. Of the 20 days of data collected in Marseille 10 days were 'clear', however these days contained occasions that were quite hazy or smoggy. Figure 3.4 shows the temporal variability of both the surface and atmospheric longwave radiation during the four days of the hysteresis loops. Day 179 shows the most temporal variation with 2 spikes at 07:00 and 14:30 LST of over 20 W m"2 above the background level. The atmospheric radiation appears to exhibit more temporal variation than the surface radiation. The L t signature follows relatively the same pattern on each day, with the exception of a spike at 15:00 LST on Day 179, that appears to be related to an L i peak. 9 12 15 Time LST (hours) 21 24 Figure 3.4 Incoming and outgoing longwave radiation fluxes during 4 days at the urban site in Marseille, mars. 55 To illustrate how the hysteresis loop differs from one surface to another, Figure 3.5 shows four different surfaces, within a 4 km radius of each other, plotted during one clear day in Basel. The suburban site alls and the concrete parking lot bmes, possess the widest hysteresis loops, while the urban site bsprSl shows a relatively narrower loop and the rural site bier has no loop at all. Plotting the longwave radiation fluxes at the four sites in Figure 3.6 reveals that the outgoing longwave flux is responsible for the width of the hysteresis loop on this clear day. Because the four sites are subject to cloudless skies they experience a very similar Li regime and it is the L T variation at each site that is defining the hysteresis loop. Ki Measured (W m"2) Figure 3.5 Spatial variation of the hysteresis loop relationship between net and solar radiation at four sites in Basel on July 5, 2002. 56 12 15 Time LST (hours) 24 Figure 3.6 Incoming and outgoing longwave fluxes at four sites in Basel during one clear day on July 5, 2002. Comparing the longwave fluxes for the surfaces shows that the concrete parking lot bmes has the highest average longwave loss and the rural site bier has the lowest loss. The suburban site alls has a relatively low longwave loss at night, however it has quite a high loss during the day, giving rise to a hysteresis loop that is widest around midday. An analysis of these sites during cloudy conditions reveals that the hysteresis loop is also affected by variations in L-l. Therefore, it's evident that both incoming and outgoing longwave radiation play an important role in determining the quality of the hysteresis loop on any given day. The H R M may be relevant for net radiation estimation on a daily basis because it allows for the hourly variation of Q* to manifest itself within the hysteresis loop. 57 However, when the H R M is applied to a larger set of data averaging tends to suppress the hourly variation within the hysteresis term and does little to improve the statistical errors over the B R M method. 3.4 Cloud Parameter Regression Model (CPRM) Iziomon et al. (2000) incorporated a clearness index term into the basic regression model of Equation 1.28. The clearness term they included is given by K - i / E 0 where E 0 is the extraterrestrial irradiance. They justified adding the clearness term because of its ability to express sky conditions and atmospheric turbidity, both of which affect the net radiation budget at the surface. The clearness term, however, is merely the transmissivity of the atmosphere since E 0 is the solar irradiance at the top of the stratosphere before it travels through the atmosphere. To improve this method the Davies et al. (1975) solar radiation model can be used to define a new term, called the cloud parameter (CP) that takes into account the transmissivity of the atmosphere by the inclusion of air temperature (Ta) and relative humidity (RH) measurements. The cloud parameter is used in place of the clearness index in the regression Equation 1.30. The coefficients and errors for C P R M are tabulated in Table 3.3. Table 3.3 Errors and regression coefficients for CPRM (Q* = b0 + b, K l + b2 CP. Eq 1.30) at several sites, where R = rural, S = suburban and U = urban. bier alls miam vane bmes bspa bspr3 bspr31 lodz mars R S S S U U U U U U MBE (W m"2) 0 0 0 0 0 0 0 0 0 0 MSE (W m"2) 664 687 870 527 933 355 574 433 889 195 RMSE (W m"2) 26 26 30 23 31 19 24 21 30 14 MAE (W m"2) 17 21 21 17 22 14 19 16 24 11 R 2 0.98 0.98 0.98 0.99 0.97 0.99 0.99 0.99 0.97 1.00 N 20473 2425 420 10532 919 20136 12518 12169 13528 1099 bo 4.14 -8.00 -1.57 -9.87 -32.78 -8.12 -26.98 -9.96 -29.70 -47.96 b, 0.76 0.76 0.76 0.79 0.63 0.82 0.84 0.81 0.81 0.79 b 2 -91.36 -66.34 -51.16 -40.06 -73.39 -65.95 -21.81 -68.94 -14.06 -51.30 58 3.5 Comparison of Regression Methods The C P R M approach requires both T a and RH measurements, however it allows for a better assessment of atmospheric turbidity and contribution to the surface net radiation budget by clouds. Results from the C P R M show a marked improvement over both B R M and H R M for many of the sites, as shown in Figure 3.7. The C P R M shows improvements of over 2 0 % in the RMSE at the rural site bier, the suburban site vane and urban site bspa and bsprSl. However, only small improvements of less than 5 % were seen at the suburban site miam and urban site lodz. It is unknown why the three regression methods performed similarly at these two sites. 40 S i t e s Figure 3.7 Root Mean Square Error in W m"2 for three regression methods, BRM, HRM and CPRM at 9 study sites. 59 CHAPTER 4 NET RADIATION PARAMETERIZATION SCHEME 4.1 Introduction In this chapter net radiation is segregated into its constituent parts and both the upwelling and downwelling radiative components are parameterized. Several incoming longwave radiation schemes are presented and a new outgoing longwave radiation scheme is formulated. Both longwave schemes are tested against data from the urban, suburban and rural study sites already introduced. The hi and L,T models that perform best are combined with the solar radiation component to form an all-sky net radiation scheme. Final testing of the combined scheme is conducted using data from a densely-built urban site. 4.2 Parameterization of Incoming Longwave Radiation This section is divided into three parts, each relating to tests of a different incoming longwave radiation scheme. The schemes are to model clear-sky incoming longwave radiation (Lsl cir), and all-sky incoming longwave radiation (L^au) one of which uses cloud observations the other a defined cloud parameter. 4.2.1 Clear-sky model results Observations from the four urban, three suburban and one rural site (Table 2.1) were used to test the seven clear-sky incoming longwave models listed in Table 4.1. On the basis of visual inspection of daily solar radiation records cloudless days were defined. Acceptance required that the entire day was cloud free. hic\r values estimated using each 60 of the 7 models were compared with measured values of L i c i r at each site. Figure 4.1 shows the Root-Mean Square Error (RMSE) for each model and site during cloud-free conditions. Table 4.1 L i models tested. Code Author Equation Clear-sky L i models BNT Brunt, 1932 1.8 S W B Swinbank, 1963 1.9 BST Brutsaert, 1975 1.10 SAT Satterlund, 1979 1.11 IDS Idso, 1981 1.12 P R A Prata, 1996 1.13 DIL Dilley and O'Brien, 1998 1.14 All-sky L i models (a) Using cloud observations: J A C Jacobs, 1978 MAY Maykut and Church, 1973 S U G Sugita and Brutsaert, 1993 1.15 1.16 1.18 (b) Using cloud parameter: CAD Crawford and Duchon, 1999 1.21 BNTT BST SV\fi SAT IDS Model and Site Figure 4.1 Comparison of modelled and observed clear-sky L i values, d is the number of clear days tested. 61 Overall the PRA and DIL L i c i r models performed the best for most of the rural, suburban and urban sites, with R M S E between 11 and 32 W m"2. The DIL model performed better than PRA at all four urban sites, while they performed similarly at the rural and suburban sites. Most of the L-t c i r models performed poorly at mars. The BNT model also performed consistently well for all sites, with R M S E below 25 W m" . While DIL provides the best estimates at the urban sites tested here, it is a relatively new scheme and PRA is more widely used. Offerle et al. (2003) used PRA to estimate L4cij. in their urban net radiation study. They based their selection of PRA on the longwave model comparison by Niemela et al. (2001a) and tests by Newton (1999) at a suburban site. 4.2.2 Results for all-sky models that use cloud observations The incoming longwave all-sky flux was modelled through the application of the three L i a i i equations by Jacobs, 1978 (JAC), Maykut and Church, 1973 (MAY) and Sugita and Brutsaert, 1993 (SUG) as outlined in Eq 1.15, Eq 1.16 and Eq 1.18 respectively. Cloud observations were obtained from the closest local meteorological station (Table 4.2). A l l cloud observations were reported in eighths (octas) or tenths of the sky covered and the time to which they refer is linearly interpolated in-between the observational times. For example, the nighttime values in Basel were linearly interpolated between the 19:00 LST observation and 07:00 LST the next day. The three Li-aii equations were combined with the 7 L-i-cir models resulting in a possible 21 combinations of all-sky L - l schemes. These combined schemes are able to estimate L - l during clear or cloudy conditions (i.e. all-sky) with inputs of cloud coverage, air 62 temperature, and relative humidity. The R M S E for these L - l schemes are reported in Figure 4.2. Table 4.2 Cloud observations. Radiation C l o u d site Number of daily Observat ion Distance site observat ions t imes between sites bier Binningen 3 7am, 12pm, 7pm 8 km alls Binningen 3 7am, 12pm, 7pm 2 km miam Miami Int. Airport 24 hourly 10 km bmes Binningen 3 7am, 12pm, 7pm 5 km bspa Binningen 3 7am, 12pm, 7pm 2 km bspr Binningen 3 7am, 12pm, 7pm 3 km mars Marignane 24 hourly 21 km Note: Cloud observations are linearly interpolated in-between observation times. The JAC all-sky model performed well when combined with the DIL clear scheme; the R M S E was less than 40 W m"2 for all study sites. The M A Y all-sky model performed consistently well with most of the clear sky L - l models. However, DIL slightly outperformed the PRA scheme and resulted in R M S E of less than 30 W m"2 at all sites. The SUG model results varied from site-to-site, giving a range of errors. For example, the SUG and PRA combination worked well for miam with a R M S E of 15 W m"2, but poorly for bier with a RMSE of 41 W m"2. It is evident that the three all-sky L - l models in combination with the suite of clear-sky L - l models result in a large range of errors and results for each site. The all-sky L - l models are site specific, because the longwave emission depends in part on the cloud climatology (types, frequencies and height of cloud in the atmosphere) of each site. These all-sky models L - l use a single-layer cloud cover observation that doesn't differentiate between cloud type or height. However, it is well known that clouds have a strong influence on L - l . Clouds of differing types and heights have unique effects on ground based L - l measurements. 63 (a) Jacobs, 1978 L i a l l model (JAC) 30 70 60 % 50 3 40 LU CO 30 --20 •-10 --bfl-B N T B S T S W B S A T IDS Model and Site P R A DIL abler a alls • m/am Mbmes dbspa Mbspr • mars (b) Maykut and Church, 1973 Li a „ model (MAY) B N T B S T S W B S A T IDS Model and Site P R A DH (c) Sugita and Brutsaert, 1993 Li a n model (SUG) SWB SAT IDS Model and Site Figure 4.2 Comparison of hXM schemes combined with 7 clear-sky L i models applied at seven study sites. For example, a low stratus cloud produces a greater emittance and hence greater irradiance at the ground than a high cirrus type cloud. Several researchers, Bolz (1949), Sellers (1965) and Sugita and Brutsaert (1993) recognized this and developed empirical schemes that assign specific coefficients to different cloud types and heights. Sugita and Brutsaert (1993) found an improvement of 5 W m"2 if cloud type was used in addition to amount of cloud cover. Unfortunately, information on cloud type and height isn't always available. Therefore, the ability to utilize more readily available single-layer cloud observations is desirable. However, as mentioned, one of the drawbacks of this method is that these Lslan models tend to be site specific in the sense that they are "tuned" to certain atmospheric conditions. Here it is concluded that the M A Y all-sky L-l model gives the most consistent results for the urban, suburban and rural sites, and the lowest error when compared with JAC and SUG. 4.2.3 All-sky model results using a cloud parameter Crawford and Duchon, 1999 (CAD) devised a scheme for calculating downwelling longwave radiation in all-sky conditions based on observations of air temperature, humidity, pressure and solar radiation. As calculated here the scheme does not require measurements of atmospheric pressure. The scheme makes use of fractional cloudiness, denoted by the cloud parameter (CP), defined in Equation 1.21 as the ratio of observed solar radiation to the modelled clear-sky solar radiation. CP is completely independent of visual cloud observations and has been deemed an appropriate way to determine cloud if K-l measurements are available (Offerle et al, 2003). Equation 1.21 65 was applied to eight of the study sites using the 7 clear-sky Li models. Nighttime values of CP were linearly interpolated between the sunset value and the sunrise value the next day. The predicted versus observed RMSE is displayed in Figure 4.3. 80 70 60 50 40 or 30 U 20 y 10 •Hi abler a alls • m/am • vane nbmes mbspa Dbspr BNT BST SWB SAT IDS Model and Site PRA DIL Figure 4.3 Crawford and Duchon, 1999 (CAD) LiM model. The C A D all-sky Li scheme combined with the seven clear-sky Li models resulted in a RMSE of less than 40 W m~2 at 96% of the site / model combinations and less than 30 W m"2 for almost 80% of them. PRA and DIL had the lowest errors and their performance is equally good at urban, suburban and rural sites. The RMSE associated with DIL was below 30 W m"2 for all sites and it performed better than PRA at mars. 4.2.4 All-sky model comparison The use of the cloud parameter approach is appealing because it does not require cloud observations and the parameter can be generated with the same resolution as radiation measurements. Standard cloud observations are usually restricted to airports or 66 other first order weather stations which may well be distant from where the radiation is measured. Further, cloud observations are usually not more frequent than hourly and often even less frequent. The CAD scheme determines the ratio of actual to modelled clear-sky Kl, so anything in the optical path of the solar beam is included in the cloud parameter. For example, any solar attenuation by atmospheric pollution will appear to increase the fractional cloudiness and be incorporated into the cloud parameter. This is likely to be problematic in highly industrialized and polluted cities. The radiative properties affecting solar attenuation by pollution are different to those possessed by clouds. However, this may be offset by the fact that urban areas experience increased L-l due to a warmer atmosphere (Oke and Fuggle, 1972). Marseille has a polluted atmosphere and the scheme performs relatively well there using DIL, with RMSE of 25 W m" . Figure 4.4 is a comparison between modelled and measured values for two L i a i i schemes: the MAY (Eq. 1.16) and CAD (Eq. 1.21) schemes. The CAD scheme under-estimates L-l at most sites, especially at the rural site bier, and it moderately under-estimates at the suburban and urban sites. The CAD scheme shows little variability in modelled hi values at mars, so that low hi is over-, and high L-i- is under-estimated. The MAY scheme gives a better estimate of hi, however, whereas the data lie closer to the 1:1 line than the CAD scheme, there is a greater spread of measured versus modelled values at most of the sites, except mars, where the scatter is less than CAD. Overall, the MAY scheme provides lower error and a smaller bias than CAD. While CAD tested with slightly greater error it is appealing because it doesn't require cloud observations. Both MAY and CAD are included in the final net radiation schemes. 67 L i Measured (W m"2) Figure 4.4a Comparison of observed versus predicted L l using (a) the MAY scheme and cloud observations, and (b) the CAD scheme using the cloud parameter. Both (a) and (b) use the DLL L i d r model. 68 Figure 4.4b Comparison of observed versus predicted L.X using (a) the M A Y L^aii scheme with cloud observations, and (b) the CAD h-l^i scheme using the cloud parameter. Both (a) and (b) use the DIL L - l d r model. 69 4.3 Outgoing Longwave Radiation Parameterization Results This section presents two methods of estimating outgoing longwave radiation: the correction term (CT) method (Holtslag and van Ulden, 1983) and a newly developed Longwave Urban Surface Temperature (LUST) scheme. Both schemes use empirical coefficients evaluated at a densely-built urban site, bspr, and are tested at urban, suburban and rural study sites. 4.3.1 Analysis of the Correction Term Since the surface temperature is not normally available LT can be approximate by the sum of £s a T a 4 and a correction term (Holtslag and van Ulden, 1983). The correction term £s 4 rj T a 3 (Ts -Ta) in Eq. 1.22, to account for the difference between surface and air temperature, was evaluated for a densely-built urban surface at the urban canyon site bspr in Basel. Measurements taken from the down-facing pyrgeometer at 31.5 m were used to calculate an average urban surface temperature (Ts) for the canyon, surrounding roof and courtyard area. The surface temperature was calculated using the Stefan-Boltzmann law, estimates of surface emissivity and measurements of outgoing longwave radiation. It is difficult to determine an average urban emissivity given the complex geometry and materials of the urban surface where each facet has a unique emissivity (Table 1.2b). Arnfield (1982) employed the principles of radiation geometry and the Lambertian assumption to construct a numerical model of radiation exchanges in synthetic urban roof and canyon systems approximating a range of urban morphometries. Local scale urban emissivities were determined using typical emissivities of canyon, roof 70 and street facets. Here an emissivity of 0.96 was assigned based on the model estimates of Arnfield (1982) for a similar structure to that in Basel. The air temperature (Ta) used in the evaluation of the correction term (CT) was measured at 17.5 m on the tower, a height equivalent to 1.5 m above the mean roof level. The air temperature sensor, attached to a boom extended away from the tower, is removed from any roof influence and is at a height free of urban canyon shading. In order to obtain a suitable parameterization of the correction term CT was regressed separately upon K.4 and Q*. Both these radiation fluxes were taken from the top of the tower at 31.5 m. Scatterplots using 18 days during the IOP in the summer of 2002 (Figure 4.5) show that good estimates of CT can be obtained using either K-l or Q* with a simple linear form: CT = £ s 4 a T a 3 (T s -T a) = c 3 Q* + c 4 (4.1) and CT = £ s 4 G T a 3 (T s -T a) = C 3 K i + C 4 (4.2) where c 3 is the slope and c 4 is the intercept of the regression. 71 120 -| 100 -^ 80 -'e ^ 60 -H U 40 -20 --150 50 250 450 650 850 Kl (W m"2) 120 -, 100 -E ^ 60 -H U 40.* -150 50 250 450 650 850 Q * (W m - 2) Figure 4.5 Plot of the correction term CT = ^  4 a T a 3 (T s -Ta) versus incoming solar radiation (top) and net radiation (bottom), for 18 days in the summer of 2002 over a densely-built urban surface at bspr in Basel. 72 A daily hysteresis loop is also evident in the correction term. A plot of a single clear day highlights the nature of such a hysteresis loop (Figure 4.6). As the surface heats up the difference between T s and T a increases (i.e. a larger CT term). This is particularly strong in the afternoon when the surface is at its hottest due to solar heating. The lag is due to the large thermal inertia of the urban fabric. 100 90 80 70 'a 60 50 H U 40 30 20 10 0 200 400 600 K l (W m"2) 800 1000 Figure 4.6 The form of the relation between the correction term (CT) and incoming solar radiation, for a cloudless day on July 5, 2002 at bspr in Basel. Time is reported in solar time. A hysteresis term can be incorporated into Equation (4.2) to give: CT = £ s 4 a T a 3 ( T s -T a) = c 3 K l + c 4 + C 5 dK-l/dt (4.3) The regression coefficients for Equations 4.1, 4.2 and 4.3 are given in Table 4.3. Addition of the hysteresis term improves explanation, but only slightly. 73 Table 4.3 Regression coefficients for Equations 4.1,4.2 and 4.3. Equation N c 3 c 4 c 5 R2 4.1 (Q*) 2578 0.086 22.36 0.76 4.2 (Kl) 2578 0.069 16.62 0.79 4.3 (Kl, dKl/dt) 2578 0.069 16.61 -0.061 0.79 Holtslag and van Ulden (1982) found a relationship between CT and Q*, in which C 3 ~ 0.12 and c 4 was zero, over a grass surface in Cabauw during four summer days in 1977. The urban C 3 coefficient evaluated at bspr ( C 3 = 0.086) is smaller, and the intercept at bspr (22.4 W m"2) is much higher than the Holtslag and van Ulden (1982) grass surface values. The positive intercept is due to the urban surface being warmer than the air temperature, both day and night, during the summer IOP whereas typical rural nocturnal conditions show an inversion. Holtslag and van Ulden were able to parameterize the C 3 coefficient based on surface thermal properties. The derivation relied on an intercept of zero in Equation 4.1. Since the urban intercept was found to be non-zero, simple parameterization of C 3 was not pursued. Offerle et al. (2003) estimated CT using an approach modified from Holtslag and van Ulden (1983). In their urban net radiation study CT is estimated by a rural C 3 coefficient (approximated from Holtslag and van Ulden, 1983), measurements of incoming solar radiation and a surface albedo. Equations 4.2 and 4.3 are suitable during the day when solar radiation is greater than zero, however at night (i.e. when K-l = 0), the correction term is only described by the c 4 intercept value. Figure 4.7 shows the measured nighttime CT values during the Basel IOP. 74 Figure 4.7 Correction term (CT) value during 18 nights in the summer of 2002 at bspr in Basel. An attempt was made to describe the correction term at night using a linear or sinusoidal relation. However, it was found that estimating CT by simple linear regression or a sinusoidal equation did little to reduce errors compared to keeping CT constant throughout the night (i.e. CT = c 4 at night). Root-mean squared errors were improved by less than 0.1 W rn 2 . Therefore, CT is held constant at night in the formulation of the outgoing longwave radiation model proposed here. 75 4.3.2 A new Outgoing Longwave radiation scheme: LUST Model A new outgoing longwave radiation scheme was created called the Longwave Urban Surface Temperature (LUST) model. The scheme is based on the correlation between the difference between the surface and air temperature (T s - T a) and solar radiation. Hence it uses measurements of air temperature and solar radiation to estimate outgoing longwave radiation. The relation underlying the scheme was developed using observations in 2002 at the densely-built urban site bspr. The difference (T s -T a) was evaluated using an average T s calculated using measurements from the down-facing pygeometer at 31.5 m, and the T a was measured at 17.5 m. The evaluation of this scheme was conducted using data for the 193 days between Ol-Jan-02 and 12-M-02. The short-term relation between T s -T a and solar radiation proves to be surprisingly close in an urban environment. The diurnal trend of T s -T a looks remarkably like the solar radiation curve when plotted on a common time axis (Figure 4.8). The author is not aware that this close correspondence has been noticed before. It may be particularly well displayed in cities because the energetics of the surface temperature is driven by sensible rather than latent heat and the thermal inertia of the system is large. 76 Day 189 £ 3 . T -T s a /.* I / / / L\ / ' % **. **»•***, 600' 1000 300 400 ^ 200 12 16 20 Time (hours) Day 191 T -T s a 1000 800 600^ 400 : 8 12 Time (hours) 16 20 24° 200 Day 190 . T -T s a 1 1 — KA | . J i j k 1 / v-.-~v > Lf ' il A \ * i \ v . . . . 1000 800 600 i ! 400 " 200 8 12 16 Time (hours) Day 192 20 8 12 16 Time (hours) Figure 4.8 Observed 10-min average values of T s -Ta and k i plotted on a common time axis at bspr for 4 days in the summer of 2002 with very different solar radiation regimes. Time reported in LST. This close relation between K\i and T s -T a is noticeable even at small time scales. Day 189 is predominately cloudless with only small Ki attenuation, due to cloud, at around 17:00 LST. The T s -T a data closely follow the Ki curve, including the corresponding dip at 17:00 LST, although the T s -T a trend appears to temporally lag behind Ki, throughout the day. Even short-term changes in Ki where spikes in solar radiation directly affect the T s -T a difference. For example, on Day 192 the Ki spike to about 900 W m"2 just before 12:00 LST corresponds with an elevated T s -T a value shortly thereafter. Similarly, on Day 190 the drop in Ki from about 700 to 50 W m"2 at 16:00 LST corresponds to a sudden drop in T s -T a from 10 to 1 °C. The LUST scheme uses 77 these relations to develop a method of predicting an average T s given T a and K - i measurements. The scheme, therefore, is well suited to estimating L.T on a local scale when solar input is available. A further analysis of the T s -T a relation reveals several characteristics. Figure 4.9 displays the diurnal relation on three summer days at bspr with very different daily solar radiation totals, K4 d t . On July 5, 2002 a cloudless day with a large K 4 d t (29.5 M J m"2 day"1) the T s -T a difference is large. The maximum of 13 °C occurs just after solar noon. The rising limb of the trend is concave up while the falling limb is convex down (Figure 4.9b). The time series loop, that is created when the trend is reversed after solar noon, highlights that the T s -T a difference in the afternoon is higher than that of the morning. A well defined loop is present on July 5, 2002 because the surface is warmer than the air in the afternoon (larger T s -T a difference) while in the morning the surface temperature is closer to the air temperature (smaller T s -T a difference). This may relate to the large thermal inertia of urban construction materials. On a partially cloudy day, July 4, 2002 with K - t D T = 15.6 M J m"2 day"1, the loop is wider while the T s -T a and the absolute values are smaller (maximum of 9 °C). A day with a small K i D T (4.8 M J m"2 day"1), July 2, 2002 shows almost no loop, and small T s -T a values that are almost constant throughout the day. Based on these three days it can be seen that knowledge of KSIDT may prove useful in estimating the T s -T a difference. 78 July 4, 2002 (c) K l Tota l : 15.6 MJm" 2 d a y 1 (d) ft SN rf° o , oPO ' ' M P SN Figure 4.9 Times series at bspr of T s - T a for three days of differing cloud amounts. In each case the left panel shows T s - T a for the entire day and the right one shows the loop in T s - T a when the time series is reversed after solar noon (x = sunrise to solar noon, circle = solar noon to sunset). SR = sunrise, SS = sunset and SN = solar noon. 79 Multiple regression was performed between T s -T a on K-l and dK.-1/dt at bspr, giving a relation of the form: T s -T a = mi Kl + m 2 3Kl/dt + b (4.4) The regression coefficients mi and m 2 can be parameterized on a daily basis. To accomplish this the data were subdivided into daily subsets and regression was performed on each subset in order to define daily regression coefficients. This yielded unique mi, ni2 and b values for each day in the dataset. These single day mi coefficients can be predicted using the daily K-l total with good correlation for larger daily K - l totals and relatively poorer correlation for KI-DT below 10 M J m"2 day"1 (Figure 4.10). The trend shows a positive slope of 0.0001 and an intercept of 0.0089. 0.020 -| £ 0.015 - V* £ 0.000 -I 1 , , , , , Q 0 5 10 15 20 25 30 K l daily total (M J rn^day"1) Figure 4.10 Daily mi coefficients (in Eq. 4.4) evaluated at bspr, plotted against daily K J totals for 193 days in 2002. 80 A daily clearness index, K-LDCI is defined to parameterize the m2 coefficient: K-i-DCi — KVIDTM / K4-DTC (4.5) where K^DTM = daily K l total measured and K-IDTC = daily K i - total for cloudless skies, calculated by integrating Davies et al. (1975) clear-sky K l model values (see Appendix 1) over the complete day. The daily clearness index, a number between zero and unity, is an assessment of how clear the day is. The m 2 coefficient plotted against K4-DCI (Figure 4.11) shows the hysteresis term (3Kl/3t) is only important on predominantly clear days, more specifically when Ksl D ci > 0.9. Therefore, the hysteresis term can be neglected on days when the K-l daily total is less than 90% its clear sky equivalent. The hysteresis term was not included in the LUST scheme because it did little to reduce overall error. 6 u 0.02 0 .a -0.02 g -0.04 u E -0.06 Q -0.08 0.2 0.4 0.6 0.8 • * Figure 4.11 Daily m 2 coefficients (in Eq. 4.4) evaluated at bspr correlated with a daily clearness index, KJ^DO (Eq. 4.5), defined for 193 days in 2002. This shows that the hysteresis term (dKX/dt) is only important when a large proportion of the day is near cloud-free ( K i D a > 0.9). 81 The intercept, b, is the T s -T a difference at night (in °C). This term was not found to be individually correlated to K-IDCI, K J , D T M , wind speed, cloud cover, daily average T a or relative humidity. It is thought that the intercept value relates to a combination of these variables. The surface at bspr in the summer tends to be warmer than the air at night while only a few winter days produced a negative T s -T a . For the purposes of the LUST scheme the intercept is kept constant and is determined by averaging the daily intercept values. The LUST scheme to estimate an average T s is: T s = ( 0.0001 K i D T M + 0.0098 ) Ki + T a + 2.5 (4.6) Hence to estimate the outgoing longwave radiation: LT = es a [( 0.0001 KiDTM + 0.0098 ) Ki + T a + 2.5 ] 4 (4.7) 82 4.3.3 L T Model Results The outgoing longwave radiation was calculated with Equations 4.1, 4.2, 4.3 and 4.7 using air temperature and solar radiation measurements for seven of the study sites. A surface emissivity was assigned to each site based on surface type where urban £ s = 0.96, suburban £ s = 0.95 (taken from Arnfield, 1982) and rural £ s = 0.94 (short grass, taken from Oke, 1988). The air temperature was measured at the height stated in Table 2.3. Equation 4.1 was implemented using measurements of Q*, however, the final formulation of the scheme does not use them because Q* is factored out of the equation and solved for. The CT models perform relatively well at sites where Eq. 4.2 had lower error than Eq. 4.1 (Figure 4.12). The urban site bspa, a site with a similar 2D radiation source area to that of bspr, had the lowest error (RMSE of 8 W m"2). At both suburban sites, miam and vane, the models also perform well, with R M S E of less than 10 W m"2. At the suburban site alls the error was slightly higher with a RMSE of 12 W m"2, and at the rural site bier it was low (RMSE of 9 W m"2). Only at the densely-built urban site mars did the models perform relatively poorly (RMSE of 28 W m"2 and L T over-estimated). 83 35 bier alls miam vane bmes bspa mars Site Figure 4.12 RMSE for LT measured vs modelled using Equations 4.1, 4.2 and 4.7 for seven study sites. Overall, the LUST scheme performs better than the CT models at most sites. The LUST model improves errors at the urban site bspa (RMSE of 7 W m"2), both suburban sites alls and vane (RMSE of 10 and 6 W m"2) and has similar error at the rural site bier. The LUST scheme performs slightly worse at the suburban site miam, and worst at the urban site mars (RMSE increased by 2 W m"2). The addition of the hysteresis term ( C5 dKl/dt) in Eq. 4.3 did little to reduce error, and even introduces greater error at miam. The hysteresis loop between CT vs Kl and CT vs Q* is well developed on clear days. However with clouds present the loop is poorly defined and its inclusion does little to improve estimation of LT. The miam site experienced cloudy conditions on most days and gives the poorest improvement in the LT estimate when the hysteresis term is included. It is recommended that the hysteresis 84 term not be included in the L,T scheme, or that it is only applied on clear days or portions of clear days. Figure 4.13 shows scatter plots of the individual measured versus modelled LT values, using Equations 4.1, 4.2 and 4.7 at the seven study sites. At night, when LT values are lower, L t is consistently over-estimated at most sites using the CT method. At night the CT value is simply a constant (c4). This coefficient is likely to be site specific but no differentiation between sites was recognized here. The site alls shows consistent under-estimation around midday and during the afternoon. At mars and miam all schemes over-estimate during both the day and night. The LUST scheme generally produces results that lie closer to the 1:1 line during both daytime and nighttime, especially at both the suburban sites alls and vane and the rural site bier. Estimation of high L i is greatly improved at alls using LUST. Whereas estimation of high L t is worse at bspa with good improvement during low and mid L t values. The central city site mars again exhibited the worst model performance, with a consistent over-estimation, of approximately 40 W m"2. The reason for the poor performance at mars is thought to be the large proportion of red clay roofing tiles seen within the 2D radiative flux source area of the pyrgeometer. These tiles become extremely hot during the day, and very cool during the night (Roberts 2003), creating a large range of T s - T a values both positive and negative. The tiles experienced a diurnal temperature range of over 35 °C on some roof facets. At night the tiles are typically cooler than the surrounding air, giving negative b intercept values (or a small c 4 intercept value). Since CT and LUST schemes use an intercept value evaluated at the bspr site this 85 results in an offset when applied to mars, thereby skewing the L t results. Also at mars strong winds, such as the Mistral, affect the T s - T a regime. Therefore, at this urban site, regarded as somewhat of an anomaly because of these conditions, the combination of an anomalously large range of roof temperatures in the hot dry summer and strong wind regime are believed to be responsible for poor model performance. It would prove interesting to see if a long term dataset from mars would yield similar results or if model performance would improve with data from other seasons in the year. Results from the rural site bier indicate that its very different surface conditions affect model performance. Separate linear trends can be seen in the population of measured versus modelled L.T values (Figure 4.13c). Closer examination reveals that these trend lines in the data relate to a different day. This is thought to be controlled by surface conditions. The rural grass surface varies over time more than an urban surface. This site was subject to seasonal changes, as the plant cover varied from bare soil to grass (ranging from 10 - 120 cm in height) and similarly it experienced a wide range of surface moisture and snow cover conditions. Such changes are less at urban sites where the built components are relatively invariant in character. Earlier it was noted that plotting measured versus modelled LT for a single day reveals an interesting phase lag, similar to a hysteresis loop. The loop is well developed at the suburban and urban sites, but poorly defined at the rural site. At the bmes parking lot site (Figure 4.13a), the bottom portions of two loops can be seen at 370 W m 2 just below the 1:1 line. The loop changes direction at sunrise and solar noon and shows that L t is more over-estimated in the morning and less over-estimated in the afternoon and night. These loops are caused by the temporal lag between T s - T a and K - l , a result of the 86 thermal inertia of building materials. Neither the CT nor LUST schemes accounts for this lag. Future versions of the LUST scheme will attempt to incorporate this feature. The development of this section started with the testing of the Holtslag and van Ulden (1983) CT method where it was found that the rural coefficients contained in the scheme were not appropriate for application in urban environments. Therefore, the CT method was re-evaluated at a densely-built urban site where new urban coefficients were found including the T s - T a vs K - l relation and development of the LUST scheme. The LUST scheme is, therefore, a genuinely urban scheme and shows promise. 87 88 89 4.4 Net Radiation Parameterization Scheme Based on the analysis of the solar models and the L,T and L - l results four complete all-sky net radiation parameterization schemes were formulated (Table 4.4) and tested. Table 4.4 Net radiation parameterization schemes . Incoming shortwave radiation Outgoing shortwave radiation Incoming longwave radiation Outgoing longwave radiation Net radiation scheme + Kl - K t + Ll - L t = Q * Eq 1.14 Eq 1.16 (cloud) Eq 4.2 (CT) Eq 4.8 Measured Values Assigned Albedo Eq 1.14 Eq 1.16 (cloud) Eq 1.14 Eq 1.21 (CP) Eq 4.7 (LUST) Eq 4.2 (CT) Eq 4.9 Eq 4.10 Eq 1.14 Eq 1.21 (CP) Eq 4.7 (LUST) Eq 4.11 1 The net radiation schemes are driven by solar radiation, air temperature, relative humidity measurements and / or cloud observations. An albedo was assigned to each site based on published values. Assigned albedo values used in the schemes are 0.2 for rural grassland, bier (Oke, 1987), 0.15 for suburban, alls, miam and vane (Oke, 1988), 0.14 for urban, bspa, bspr, and mars (Oke, 1988) and 0.35 for light concrete, bmes (Stull, 2000). The regression coefficients in Eq. 4.2 and Eq. 4.7 as evaluated at bspr, were applied to all study sites in the final net radiation schemes, including the rural site. It may not be appropriate to apply urban coefficients to a rural site, however it is done to provide a comparison between surface classes. 91 bier alls miam vane bmes bspa bspr mars Figure 4.14 RMSE for observed versus predicted Q* using the four different net radiation parameterization schemes at eight study sites. Two distinct sets of results emerge: those using cloud observations (Eq. 4.8 and 4.9) and those using the cloud parameter (Eq. 4.10 and 4.11) to calculate L i . The lowest error occurs when cloud observations are applied to bier, bmes, bspa, and bspr and the cloud parameter is applied to alls, miam, vane and mars (Figure 4.14 and Table 4.5). The incoming longwave radiation seems to account for greater variation in error in the Q* schemes than the outgoing longwave radiation. If cloud observations are used, Eq. 4.9 ( L t estimated using LUST) produces the best Q* results when applied to bier, alls, vane, bspa and bspr while only slightly better results are attained when Eq. 4.8 (LT estimated by CT method) is applied to miam, bmes and mars. When the CP method is used, Eq. 4.11 ( L t estimated by LUST) provides better Q* estimates when employed at bier, alls, vane, bspa and bspr with only slightly better results when Eq. 4.10 ( L t estimated by CT method) is employed at miam, bmes and mars. Table 4.5 Comparison of Q* estimates using four different net radiation parameterization schemes at eight study sites. Site Eq.4.8 Eq. 4.9 Eq. 4.10 Eq. 4.11 bier RMSE 29 28 33 31 R 2 0.97 0.97 0.96 0.96 n 49443 49381 49375 49313 alls RMSE 24 23 23 22 R 2 0.99 0.99 0.99 0.99 n 4320 4320 4256 4256 miam RMSE 33 33 27 27 R 2 0.98 0.98 0.98 0.98 n 840 840 827 827 vane RMSE 36 33 R 2 0.96 0.96 n 27069 27049 bmes RMSE 28 29 30 31 R 2 0.98 0.97 0.97 0.97 n 1417 1417 1353 1353 bspa RMSE 25 24 31 29 R 2 0.98 0.98 0.97 0.97 n 47551 47374 47483 47306 bspr RMSE 24 • 23 28 25 R 2 0.98 0.98 0.98 0.98 n 30498 30498 30402 30402 mars RMSE 13 13 12 13 R 2 1.00 1.00 1.00 1.00 n 1920 1920 1861 1861 Note: RMSE reported in W m"2. Figure 4.15 shows scatter plots of measured versus modelled net radiation at 7 sites, employing Equations 4.9 and 4.11. The best model performance, using both equations is found at mars, where the R M S E is 13 W m"2. This is somewhat surprising given the poor L t estimation at this site. Therefore over-estimation in L l (negative flux) must be offset by an over-estimation in a positive flux in another part of the Q* scheme. 93 Either L-l- is over-estimated at the site or the assigned albedo is too low. Good model performance is also seen at the urban sites bspa and bspr where Eq. 4.9 gives R M S E of 24 and 23 W m"2, respectively, when cloud observations are used, and out performs Eq. 4.11 that uses the cloud parameter. At both sites Eq. 4.11 results in an under-estimation of net radiation at midday while Eq. 4.9 results in a close fit at bspr and slightly under-estimates at bspa. The suburban site alls shows a good fit for both Q* schemes where Eq.4.11 produces results (RMSE of 22 W m"2) that show less deviation than Eq. 4.9 (RMSE of 23 W m"2). At this site, despite the better model performance, Eq. 4.11 under-estimates throughout the day while Eq. 4.9 has less bias. The suburban site miam is one of the few sites where better performance results from using the CP approach rather than using cloud observations. At the other suburban site vane, Eq 4.9 was not applied because cloud observations were not obtained, therefore only the CP method was evaluated at this site. Error was high at this site where Eq. 4.11 performed poorly (RMSE of 33 W m"2). The parking lot site bmes experienced relatively high error with Eq. 4.11 slightly out performing Eq. 4.9, and Q* was over-estimated during the night and under-estimated at the time of the peak net radiation flux. The rural site bier exhibits poor model performance, where Q* is under-estimated on most days throughout the day and night. Some days however result in a large over-estimation between net radiation values of -50 to 150 W nT2. It is thought that the changing nature of this rural surface results in poor estimates and because the site was tested with urban coefficients. 94 Figure 4.15a Measured versus modelled net radiation calculated using (a) Equation 4.9, and (b) Equation 4.11 applied to four urban sites. 95 . (b) alls 800 -200 0 200 400 600 800 Q* Measured (W m'z) Figure 4.15b Measured versus modelled net radiation calculated using (a) Equation 4.9, and (b) Equation 4.11 at two suburban and one rural site. It is unclear why Eq 4.9 performs better at some sites than Eq 4.11, and vice-versa. Analysis in section 4.2 reveals that at all sites modelled L - l has a lower RMSE using cloud observations in M A Y (Eq 1.16) compared to the cloud parameter in C A D (Eq 1.21). It follows that Eq 4.9 is likely to provide a better Q* estimate than Eq 4.11 at all sites. However, any model error due to using Eq 1.21 must be offset by over- or under-estimation in other parts of the Q* scheme, namely in the assignment of albedo or in the estimation of hi. The two most promising schemes (Eq 4.9 and 4.11) were assessed with greater temporal detail at bspa (Table 4.6). The site bspa was selected for the detailed 96 assessment because it is independent from the LT scheme evaluated at bspr, and the bspa site provided a year long urban dataset which allows for a seasonal analysis of the Q* schemes. Table 4.6 Comparison of Q* estimates at bspa using Eq. 4.9 and Eq. 4.11. Equat ion 4.9 Equat ion 4.11 N Bias RMSE N Bias RMSE Winter, day 4119 -5.0 22.3 4119 -18.6 27.5 Winter, night 5517 -3.3 22.5 5517 -17.0 29.2 Spring, day 7763 -11.3 26.1 7763 -23.2 33.1 Spring, night 5158 5.7 22.8 5158 -7.9 20.2 Summer, day 7573 -14.0 27.7 7573 -25.6 34.2 Summer, night 4935 2.9 22.9 4935 -10.7 21.7 Autumn, day 4159 -6.3 23.6 4159 -20.7 27.9 Autumn, night 5774 -2.4 23.2 5774 -17.3 28.6 All, day 23834 -10.2 25.5 23825 -22.8 31.7 All, night 21556 0.6 22.8 21508 -13.4 25.5 Bias = (predicted - observed) / N. Units of Bias and RMSE are W m"2. Day is when K i is greater than 5 W m"2 and night is K i = 0 W m"2. There appears to be a distinct difference in error at bspa between daytime and nighttime evaluations; night values have lower errors. Equation 4.9 gives the lowest error at this site, but it consistently under-estimates daytime Q* with a bias of -5 to -14 W m~2 during the seasons. The summer poses the highest error in the daytime with a large bias. Nighttime Q* estimates have relatively consistent error throughout the seasons with a smaller bias resulting in under-estimation in the winter and autumn and over-estimation in the spring and summer. Eq. 4.11 consistently under-estimates net radiation during 2 2 both the day and night with a bias ranging from -7.9 W m" (spring, night) to -25.6 W m" (summer, day). 97 Overall, between these two schemes better results are experienced when cloud observations are used. At seven sites tested Eq 4.9 experiences a R M S E below 33 W m"2 at three sites and lower than 24 W m"2 at four sites. If cloud observations are not available then Eq. 4.11 is a desirable Q* scheme. This scheme was tested at eight sites and provides estimates with R M S E of less than 33 W m"2 at six sites and less than 25 W m"2 at two sites. Recommendations for an urban net radiation scheme would be the employment of Eq. 4.9 if cloud observations are available and Eq. 4.11 if not. Offerle et al. (2003) found similar error, to those presented here, when their Q* scheme was tested at an urban site, using a known albedo, and two suburban sites, using assigned albedos. They found the best results at the urban site where daytime R M S E ranged from 20 to 22 W m"2 (for summer and winter, respectively) and nighttime R M S E was 25 to 28 W m"2. Ways to reduce error in Q* estimation would be to use a known albedo rather than generic values from the literature. If an incorrect albedo value is assigned to a surface error can be large, especially if the assigned albedo is largely different from the true albedo of the surface. Lastly, further research into the cloud parameter is likely to prove useful in L i - modelling. A great source of error in L-l estimation is the uncertainty of cloud cover. In this thesis the CP was taken to be a single layer that does not differentiate between high, medium and low cloud, known to have different rates of Ll emission. There may be merit in developing a CP method that incorporates this knowledge. 98 CHAPTER 5 CONCLUSIONS This thesis has focused on formulating an urban net radiation parameterization scheme with inputs of solar radiation measurements, standard meteorological observations and basic knowledge of the surface. The motivation for the scheme is driven by the requirements of L U M P S , an urban pre-processor scheme incorporating several parameterizations to permit calculation of urban heat, mass and momentum fluxes and atmospheric stability. The approach here is to parameterize each component of the surface radiation budget. This involved both tests of existing models and schemes and development of a new urban LT scheme. The restriction that the parameterization of net radiation should only require the input of solar radiation and standard weather measurements provides both a challenge and key insights into the radiative exchange at the urban surface-atmosphere interface. 5.1 Summary of Conclusions Measured net radiation was regressed on measured incoming solar radiation at several urban, suburban and rural radiation study sites as a first approach to the estimation of Q* using K l and easily attainable weather observations. The simplest form of the regression, B R M , produced distinct slope and intercept values for urban, suburban and rural areas. The slope values were found to change through the year, with a maximum in summer and a minimum in winter, and the intercept value was more negative in summer than in winter. The H R M attempted to incorporate a daily hysteresis loop that was 99 observed at some urban and suburban sites on cloudless days. However, when the H R M is applied to a larger data set averaging tends to suppress the hourly variation of the hysteresis term and hence the scheme does little to improve the statistical error over the B R M . A new regression method, C P R M that was tried includes a cloud parameter calculated from solar radiation, air temperature and relative humidity measurements. The method shows marked improvement over B R M and H R M , reducing R M S E by over 20% at several sites. However, the major limitation of the regression methods is that they are strictly daytime Q* schemes and cannot generate estimates during the night. • Several incoming longwave all-sky radiation schemes were tested at the urban, suburban and rural study sites. The two most successful schemes were the M A Y L-iaii and C A D Lslaii schemes when both included the DIL L - i c i r parameterization. The M A Y scheme, which requires the input of air temperature, relative humidity and single-layer cloud observations, gave a R M S E of 27 W nT or less from test at seven sites. The C A D scheme, which requires air temperature, relative humidity, and solar radiation measurements, had R M S E of less than 30 W m 2 based on tests for eight sites. Overall, the M A Y scheme provides lower error and a smaller bias than C A D . • For outgoing longwave radiation a correction term (CT) to account for the difference between the surface temperature, that is wanted but hardly ever measured at standard climate stations, and the air temperature that is always easily available was evaluated at a densely-built urban site in Basel. The CT was found to be highly correlated with measurements of K - i and Q*, such that a linear equation provides a good estimate of CT. The term was found to be positive at 100 almost all times, day and night, during the evaluation period, and was relatively constant during the night. • A new urban outgoing longwave radiation scheme (termed LUST) was created based on the correlation between the difference between the surface and near-surface air temperature (T s - T a) and solar radiation. The diurnal trend of T s -T a remarkably tracks variations of the solar radiation regime, which is very apparent when they are plotted with a common time axis. The scheme, also evaluated at the densely-built urban site in Basel, uses measurements of air temperature and solar radiation to estimate outgoing longwave radiation. • Two CT models and the LUST scheme to estimate outgoing longwave radiation, were tested at three urban, three suburban and one rural site. The CT models performed relatively well although the urban sites experienced both the lowest error (RMSE of 8 W m"2) and the highest error (RMSE of 28 W m"2). Overall, the LUST scheme performed better than the CT models at most sites. The LUST model improved R M S E by as much as 30% at the urban and suburban sites with the exception of central Marseille, where error increased by 14%. Also, the LUST scheme provided a better midday estimation of L t at the suburban sites. No improvement by using LUST was detected at the rural site. • Two final net radiation parameterization schemes were formulated and tested at the four urban, three suburban sites and the one rural site. Both Q* schemes used the LUST scheme to estimate the L t component. The Q* scheme where L - l was modelled with M A Y + DIL was found to give the best results at four sites (including a dry parking lot roof, rural grassland and two heavily built-up sites) 101 whereas the scheme that modelled L-l with C A D + DIL perfomed best at two suburban sites, and error was similar at another central city site. It is unclear why these two Q* schemes perform better at certain sites, however, since one utilizes cloud observations and the other a cloud parameter, they can be considered complementary. A detailed analysis of both schemes at a densely built-up site for eight months gave better results utilizing cloud observations (Eq. 4.9) Error was lowest in the winter and autumn. The model bias tended to be negative by day and close to zero during the night. Overall, better results are experienced when cloud observations are used. However, if they are not available the use of the cloud parameter (Eq. 4.11) is acceptable. 5.2 Recommendations for LUMPS The linear regression of net and solar radiation provides a simple method of estimating daytime net radiation using solar radiation measurements. The C P R M method that incorporates a cloud parameter, yields Q* estimates with a R M S E <31 W m"2. This method, however, is strictly a daytime scheme only, an undesirable limitation for LUMPS. Net radiation parameterization methods, provide both daytime and nighttime estimates of Q* and both upwelling and downwelling radiative components are parameterized. This method calculates incoming longwave radiation using one of several available schemes and outgoing longwave using the LUST scheme developed here. Two approaches to the incoming longwave part of the Q* scheme can be used: either using cloud observations (Eq. 4.9) or a cloud parameter (Eq. 4.11). Overall, 102 better results are found when cloud observations are used. At seven sites tests using Eq 4.9 all perform better than a R M S E of 33 W r n 2 and four sites had R M S E < 24 W m"2. If cloud observations are not available Eq. 4.11 is an acceptable scheme for Q*. This scheme was tested at eight sites and also provides estimates with R M S E < 33 W m"2 at six sites and < 25 W m"2 at two sites. Hence, it is recommended that a net radiation scheme to drive LUMPS can employ Eq. 4.9 if cloud observations are available and Eq. 4.11 if they are not. Since both schemes are quite sensitive to albedo the use of a measured albedo for the site is superior, however if it is not known Table L i b provides a suitable list of natural and urban albedos. 5.3 Future Research The approach of this thesis has been to parameterize each radiative component of the surface radiation budget in order to formulate an urban net radiation parameterization scheme. This approach reveals several interesting relations of relevance to modelling incoming and outgoing longwave radiation. Several researchers note that knowledge of cloud type and height can improve hi estimation over the use of a single-layer cloud observation. However, observations of cloud type and height are often not available and there is a need for a simple parameterization of such cloud properties based on readily available measurements. The approach of combining both single-layer cloud observations and a cloud parameter may have merit. The cloud parameter could be correlated with known cloud types to provide a method of classifying cloud type based on a generalization of the opacity of each cloud type. This combined with cloud cover observations might 103 be useful to better estimate the L - l coming from a cloud layer, rather than making the simple assumption that all clouds have a similar radiation influence. Further development of the LUST scheme also may have merit. LUST provides good estimates of LT at most sites tested here, however, it greatly over-estimates L t when the surface is cooler than the air, a temperature regime consistently seen at night in Marseille for one hot dry summer month. It would be of interest to see if this temperature regime persists throughout the year, and how it affects the T s - T a relation; and / or to see if this circumstance is common at other urban sites. 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Snow Conf, 43, 173-184. I l l APPENDIX 1 C L E A R SKY SOLAR RADIATION Clear-sky incoming solar radiation (K-l0) can be estimated as the sum of both the total transmission of the direct solar beam (S) and diffuse solar radiation (D), as given by Davies et al, 1975, S = Io COS Z <t>wa <)>da <|>ws <|>rs <>ds ( A l . 1) D = Io cos Z (|)wa (|)da (1- <t>wS fas (bds) / 2 (A1.2) where the average solar constant (Io) is the solar irradiance at the top of the atmosphere, here taken to be Io = 1367 W m"2 (Niemela et al., 2001). The cosine of the solar zenith angle (Z) is given by, cos Z = sin <j> sin 8 + cos ^cos 8 cos h (A1.3) where <p = latitude of the location, 8 = solar declination angle and h = hour angle. The solar declination angle is a function of the day of the year which can be approximated by, 8 = -23.4 cos [360 (YD +10) / 365] (A1.4) 112 where Y D = year date or day of the year. The hour angle is given by, h= 15 (12-0 (A1.5) where t is the local apparent solar time using a 24 hour clock. The transmission of solar energy through the atmosphere is due to (|)rs = dry air or Rayleigh scattering, = water vapour absorption, ^ = water vapour scattering, (j>da = dust absorption and (j>dS = dust scattering estimated by, c^ va = 1 - 0.077 (w m ) 0 3 (A 1.6) 4>ws = 1 - 0.0225 w m (A1.7) <!>* = 0.972 - 0.08262 m + 0.00933 m 2 - 0.00095 m 3 + 0.0000437 m 4 (A 1.8) <]>da <t>ds = 0.95m (A 1.9) The optical air mass (m) that incorporates the effect of atmospheric refraction at high zenith angles is given by Kasten (1966) as, m = [cos Z + 0.15 (93.885 - Z) " 1 2 5 3 ] ( A L I O ) If atmospheric soundings are not available precipitable water content (w) can be estimated at screen level (si) using water vapour pressure, ea, [in Pa] and an air temperature, T a [in K] , 113 w si = 0.493 e a / T a ( A l . l l ) where ea is estimated by ea = R H exp (26.23 - 5416 / T a), using relative humidity (RH) and air temperature. The calculated w si can then be adjusted by an empirical relation derived from atmospheric soundings (Venalainen, 1994), w = 0.71104 w s i - 0.032003 [in cm] (A1.12) The final formulation of Ki0 is the sum of the direct and diffuse solar radiation giving, K-io = Io cos Z (|)wa (|)da (<^s <t>rs t>ds + 1) / 2 ( A l . 13) 114 APPENDIX 2 STATISTICAL METHODS Summary of Statistics 1 " Mean Bias Error : M B E = — V (y{ -y{) n t i 1 1 " Mean Squared Error: M S E = — Y V y j - y ; ) 2 1 " Root Mean Squared Error : RMSE = — V (y ; - y ; ) ' 1 n Mean Absolute Error: M A E = — V l ^ - y j n 2 Z(yi-yi)2-Z(yi-yi) Correlation Coefficient: R 2 = i = 1 i=l where, y ; = observed y ; = predicted 1 n 115 APPENDIX 3 SUM URBAN S U R F A C E T E M E R A T U R E Urban Surface Temperature Cities present an almost limitless array of surface materials and surface configurations (Soux et al, 2004). Individually the materials and configurations of surface facets combine to form their own surface temperature. It is problematic to measure the surface temperature of each of these facets and integrate the measurements across an entire city to determine an average surface temperature. A typical city block is comprised of several building elements complete with roof, wall, street and vegetated facets. Conversely at the local scale, an area approximately 104 - 108 m 2 , there is undoubtedly no one surface temperature that can be measured that is representative. Sampling the surface temperature of a finite number of facets and weighting each according to its abundance in the FOV, can provide a measurement of surface temperature. Furthermore, a model can be employed to determine the fractional area of each facet as 'seen' by a sensor at a given height. This mean urban surface temperature as 'seen' by a sensor is comparable to the hemispherical radiometric temperature described in Norman and Becker (1995). Surface-sensor-Sun Urban Model (SUM) The Surface-sensor-Sun Urban Model (SUM) is designed to calculate what a remote sensor 'sees' of an urban surface. S U M takes into account latitude, date and time to calculate the solar geometry; building and street configuration to calculate building morphometry; and height and location of a sensor. S U M can predict the view factors of 116 the roof, wall and ground facets that are sensed from any given point above the surface and whether they are sunlit or shaded at any location and time of the day (Soux et al, 2004). Furthermore, the model can be used along with known facet temperatures to calculate the average temperature of the system. On the local scale an average surface temperature can be calculated, comparable to a surface temperature calculated by an inverted pyrgeometer at height above the urban surface. Surface Temperature Instrumentation at bspr The bspr site in Basel, located in the heavily built-up part of the city, was the site of a 32 m tower providing measurements above and below the urban canopy. At this site the urban canyon was well instrumented with infrared thermometers (IRT) using the tower and balconies as mounting platforms for several of the instruments (Figure A3.1). The LRTs were positioned so as to allow surface temperature measurements of the north wall, south wall and floor of the urban canyon. Roofs were outfitted with infrared radiation pyrometers on a flat roof, a piked roof facing north-northwest and a piked roof facing south-southeast. The surface temperature instrumentation used is outlined in Table A3.1. Air temperature measured from the tower was used to approximate the surface temperature of the vegetation. 117 Figure A3.1 Three infrared thermometers (IRT) attached to the railing of the North facing wall on the fourth storey of an apartment building at bspr. These 15" FOV IRTs sense the radiative temperature of the North facing wall and the street below. Table A3.1 Surface temperature instrumentation at the bspr site. Instrument Model F a c e t Everest Infrared Thermometer 4000A South wall upper half South wall lower half North wall upper half North wall lower half Canyon floor north side Canyon floor south side Infrared Radiation Pyrometer KT15 Flat gravel roof Piked roof SSE Piked roof NNW 118 S U M Results S U M was applied at the densely-built urban site, bspr, in Basel. S U M allows the user to specify the grid size and thus the resolution at which individual buildings or other surface facets can be 'seen' by the sensor. The model was applied at the local scale with a grid size of 275m by 275m, an area approximately equal to the 95% 2D radiation source area of the inverted pygeometer. The array of S U M contains a building-street-building-alley combination in both the x- and y-directions (Soux et al, 2004). Figure A3.2a shows a graphical representation, to scale, of the S U M array applied at bspr. The alley input parameter was used to simulate the courtyard fractional area, because courtyards comprise a much greater area than alleys in Basel. The sensor location in the array, having x, y and z coordinates, was placed at the height of 31.5 m such that the modelled sensor location coincided with the real location of the down-facing radiometer. Figure A3.2b shows the real configuration of the buildings at the bspr site using three dimensional surface data. 119 o Z Q Figure A3.2 Plan view of bspr site with (a) the idealized configuration modelled by SUM with a repeating array of street, building and courtyard elements, and (b) the real plan view modified from Peter Keller, University of Basel, with the 95% 2D radiative source area contained within the black circle. The tower is positioned in the middle of a street element shown as a T in (a) and as a square in (b). After specifying the array dimensions for each element, S U M was used to calculate the view factors (VF) of street, courtyard, roof, and north, south, east, and west wall facets as 'seen' by the sensor at the height of 31.5 m (Table A3.2). These VFs were then multiplied by the facet surface temperature and summed to get the average surface temperature within the array. The facet surface temperatures used in the calculation were determined in various ways. The three roof measurements (flat gravel roof, piked slate SSE roof and piked slate N N W roof) were averaged and used as a single surface temperature for all roofs in the S U M array. This was justified on the basis that there is a mix of flat and piked, gravel and slate roofs within the array. The courtyard was estimated to contain 95% roof and 5% vegetated surfaces and temperatures were weighted accordingly. The north and south street IRT temperatures were averaged to give the street temperature, the top and bottom south wall IRTs were averaged for the south wall temperature and the top and bottom north wall IRTs were averaged for the north wall temperature. The east and west walls, having a very small view factor, were both assigned a temperature averaged from the north and south walls. Table A3.2 Total facet view factors at bspr. Facet (%) Total (%) Wall south 9.15 north 6.60 east 1.37 west 1.68 Total 15.93 Street 26.97 Courtyard 10.71 Roof 46.39 Total 100.00 121 In order to provide a comparison, the average surface temperature was calculated by employing the Stefan-Boltzmann Law. Longwave measurements from the down-facing pyrgeometer at 31.5 m were used with an assigned urban surface emissivity. An emissivity of 0.96 was assigned to the urban surface based on values in Arnfield (1982). The reflection of longwave radiation was calculated using measurements from the up-facing pyrgeometer and the surface emissivity and subtracted from the upwelling signal before calculating the radiation temperature. In the summer of 2002, 18 days of measurements taken during the Intense Observational Period (IOP) in Basel were used to calculate both versions of surface temperature (Figure A3.3). The average urban surface temperature calculated with S U M (TS-SUM) is highly correlated with the surface temperature calculated from measurements of upwelling longwave radiation (T s.Lt)- The two surface temperatures have an approximately linear relation with an R 2 of 0.98 and a slope of 0.81. 122 10 15 20 25 30 35 40 45 50 T s - SUM (°C) Figure A3.3 Comparison of TS_SUM and T s . L t taken during the I O P in Basel at bspr. The difference between TS_SUM and of T S _ L T varies between -1 to 7 °C (Figure A3.4) and shows predominantly positive differences about solar noon, and close to zero throughout the night. Thus, the surface temperatures are in good agreement during the night, however during the day TS.SUM is as much as 7 °C more than T S _ L T - It is likely that the wide diurnal range in roof surface temperature is largely responsible for the bias. S U M finds 56.6% of the field-of-view of the pygeometer is occupied by roof surfaces. The measured surface temperature of the flat roof has an extreme range in temperature from 5 to 60 °C. Figures A3.3 and A3.4 show that TS-SUM is being influenced by these extreme temperatures. Figure A3.3 shows quite clearly that TS„STJM is over-estimated during the day. This may be due to the combined errors arising from inadequate sampling of the very variable daytime roof temperatures and over-simplification of the urban morphometry in S U M . One of the limitations of S U M is that it only simulates flat roofs and doesn't take into account piked roofs that may be partially shaded during the day. S U M considers all roofs within the array to be sunlit for the entire day. 124 

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