Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Validation of an urban canyon radiation model for nocturnal long-wave radiative fluxes and the effect.. Voogt, James Adrian 1989-08-24

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
831-UBC_1989_A6_7 V66.pdf [ 11.51MB ]
Metadata
JSON: 831-1.0097570.json
JSON-LD: 831-1.0097570-ld.json
RDF/XML (Pretty): 831-1.0097570-rdf.xml
RDF/JSON: 831-1.0097570-rdf.json
Turtle: 831-1.0097570-turtle.txt
N-Triples: 831-1.0097570-rdf-ntriples.txt
Original Record: 831-1.0097570-source.json
Full Text
831-1.0097570-fulltext.txt
Citation
831-1.0097570.ris

Full Text

VALIDATION OF AN URBAN CANYON RADIATION MODEL FOR NOCTURNAL LONG-WAVE RADIATIVE FLUXES AND THE EFFECT OF SURFACE GEOMETRY ON COOLING IN URBAN CANYONS By JAMES ADRIAN VOOGT B.Sc, Queen's University, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Geography) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1989 © James Adrian Voogt, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of t^gC^rfyPU-V The University of British Columbia Vancouver, Canada Date S£PT~- 4? . . DE-6 (2/88) 11 ABSTRACT The urban canyon radiation model of Arnfield (1976, 1982) is validated using measurements of long-wave fluxes taken within a scale urban canyon constructed from concrete building blocks. A custom-designed traversing system allowed miniature radiometers to be automatically moved around the perimeter of a canyon cross-section thereby providing for the validation of individual model grid-points. Measured model input consists of surface temperatures obtained using fine wire themocouples, incident long-wave radiation at the canyon top, and emissivity of canyon materials. Tests were conducted to establish the expected accuracy and precision of the input data. Surface temperature data were filtered to remove a noise component. A probable error analysis of all measured model input and validation data is made. Sensitivity tests of the model to variations in input data are presented. Surface temperature is the dominant control under the conditions tested. Model-calculated view-factors are shown to be in error for adjacent corner points and are replaced with view-factors calculated using equations derived from the Nusselt Unit Sphere method (Steyn, pers. comm.) Validation results for a range of canyon height-to-width ratios, meteorological conditions and model parameters are presented. Excellent agreement between modelled and measured fluxes is obtained for points on the canyon floor and top. The agreement for fluxes at points on the canyon walls is generally good but is shown to suffer from errors in sensor orientation relative to the canyon walls. Use of the Unsworth and Monteith (1975) radiance distribution improves model performance statistics for incident and net long-wave radiation. Four different estimates of surface temperature are used as model input in place of the measured values to investigate the differences in the model output. Surface temperature-based estimates are found to be superior to those based upon air temperature. The use of unmodified screen-level air temperatures measured at Vancouver Airport produces the poorest agreement. The temporal and spatial variation of in-canyon temperatures and radiation are presented for three canyon height-to-width ratios. The canyon geometry is shown to significantly reduce the surface cooling on the canyon floor compared to an open site under ideal radiative cooling conditions. Results are compared to previous results from scale models (Oke, 1981) and field studies (Oke and Maxwell, 1975; Hogstrdm et al ., 1978). . Atmospheric controls of incident long-wave radiation, wind speed and direction are also shown to affect the observed cooling. IV TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS ACKNOWLEDGEMENT CHAPTER 1. INTRODUCTION 1 1.1 RESEARCH OBJECTIVES1.2 APPLICATIONS/SIGNIFICANCE OF THE RESEARCH 2 1.3 APPROACHES TO THE STUDY OF THE EFFECTS OF URBAN 4 SURFACE GEOMETRY ON THE CLIMATE WITHIN URBAN AREAS 1.3.1 Observational Studies 4 1.3.2 Scale Modelling 6 1.3.3 Mathematical Models 8 1 .4 RESEARCH METHODOLOGY 10 CHAPTER 2. THE CANYON MODEL INSTRUMENTATION, AND 13 TESTS 2.1 INTRODUCTION 12.2 SIMULATION METHODOLOGY 13 2.3 THE CANYON MODEL 5 2.3.1 General Description 12.3.2 Site 16 2.3.3 Materials 8 I I iv X xi v XX xxi v V 2.3.4 Construction Technique 18 2.3.5 Canyon Height and Width 20 2.3.6 Canyon Length 22 2.4 CANYON INSTRUMENTATION 3 2.4.1 Surface Temperature 22.4.2 Radiation 25 2.4.3 The Canyon Traversing System 32 2.5 OTHER VARIABLES MEASURED 36 2.6 TESTS 37 2.6.1 Surface Emissivity 32.6.2 Surface Temperature Tests. 40 2.6.3 Radiometer Distance Above Facet 43 2.6.4 Traverse System 44 CHAPTER 3. THE ARNFIELD MODEL 53 3.1 INTRODUCTION 53.2 MODEL FRAMEWORK 4 3.3 MODEL IMPLEMENTATION 57 3.4 MODIFICATION TO THE ARNFIELD MODEL 59 3.4.1 Canyon Height and Width 61 3.4.2 View-Factors 63.4.3 Additional Grid-Points 65 3.5 SENSITIVITY TESTS 7 3.5.1 View-Factors/Grid-Points 63.5.2 Surface Temperature 73 3.5.3 Radiation 85 3.5.4 Emissivity 7 vi 3.5.5 Radiance Distribution 91 CHAPTER 4. MODEL VALIDATION 94 4.1 INTRODUCTION 94.2 MODEL VALIDATION STATISTICS 95 4.3 MODEL VALIDATION USING DATA COLLECTED IN 'POINT' 96 MODE 4.4 MODEL VALIDATION USING AUTOMATICALLY COLLECTED 101 DATA 4.4.1 August 1/2 104.4.2 August 3/4 8 4.4.3 August 10/11 112 4.4.4 August 12/13 6 4.5 SUMMARY OF VALIDATION RESULTS 120 CHAPTER 5. MODEL RESULTS USING DIFFERENT ESTIMATES OF 123 SURFACE TEMPERATURE 5.1 INTRODUCTION 125.2 AIR TEMPERATURE 5 5.2.1 Results: Average Canyon Air Temperature 126 5.2.2 Results: Airport Air Temperature 130 5.3 AVERAGE OR MID-POINT SURFACE TEMPERATURE 130 5.3.1 Results: Facet Mid-Point Temperature 133 5.3.2 Results: Average Facet Temperature 138 5.4 SUMMARY 141 Vll CHAPTER 6. CANYON TEMPERATURES, RADIATION, AND COOLING 151 6.1 INTRODUCTION 156.2 SURFACE TEMPERATURE DISTRIBUTIONS 151 6.2.1 The Diurnal Variation of Surface Heating and 151 Cooling in the Model Canyons 6.2.2 Temperature Distributions on Canyon Facets 156 6.2.3 Cooling of Canyon Facets Following Sunset 160 6.3 AIR TEMPERATURES 165 6.3.1 Average Canyon Air Temperatures 166.3.2 Spatial Distribution of Canyon Air Temperatures 168 6.4 LONG-WAVE RADIATION 171 6.5 SUMMARY OF RESULTS: TEMPORAL AND SPATIAL VARIATION 176 OF IN-CANYON TEMPERATURES AND RADIATION 6.6 CANYON VERSUS OPEN SITE SURFACE COOLING 179 6.6.1 Canyon and Open Surface Cooling: Surface 181 Geometry Controls 6.6.2 Canyon and Open Surface Cooling: Atmospheric 195 Controls 6.7 SUMMARY OF RESULTS: CANYON AND OPEN SURFACE COOLING 197 CHAPTER 7. CONCLUSIONS 199 7.1 ACHIEVEMENT OF THE RESEARCH OBJECTIVES 199 7.2 RECOMMENDATIONS AND FUTURE RESEARCH 200 REFERENCES 203 Vlll APPENDIX A. SPECIFICATION OF SENSOR TRAVERSING SPEED AND 211 DELAY INTERVAL A.1 INTRODUCTION 21A.2 CANYON WALLS 4 A.3 CANYON TOP AND FLOOR 217 A.4 DELAY INTERVAL 220 A. 5 CONCLUSIONS 1 APPENDIX B. DATA PROCEDURES 222 B. 1 DESCRIPTION OF RECORDED DATA 22B.2 ASSIGNMENT OF TRAVERSED DATA TO GRID-POINTS 222 B.3 SIGNAL FILTERING THE SURFACE TEMPERATURE 223 B.3.1 Methods Used 225 B.4 EXTRAPOLATION OF ADDITIONAL SURFACE TEMPERATURES 235 ON CANYON WALLS APPENDIX C. CALIBRATION OF THE BARNES PRT-4A INFRARED 240 THERMOMETER APPENDIX D. ERRORS 243 D.1 INTRODUCTIOND.2 SURFACE TEMPERATURE ERRORS 24 4 D.3 EMI SSIVITY ERRORS 247 D.4 RADIATION ERRORS 24 9. D.4.1 Lict Errors 249 D.4.2 L*0 Errors 250 D.4.3 L* Errors 1 ix D.4.4 LD Errors APPENDIX E. MODEL INPUT APPENDIX F. ADDITIONAL VALIDATION DATA SETS F. 1 August 2/3 F. 2 August 8/9 F. 3 August 1 1/12 F. 4 August 14/15 F. 5 August 22/23 F. 6 August 23/24 APPENDIX G. STATISTICAL INDICIES OF MODEL PERFORMANCE G.1 SUMMARY UNIVARIATE STATISTICS G.2 COEFFICIENTS OF LEAST-SQUARES LINEAR REGRESSION G.3 MEASURES OF ERROR G.4 INDICATORS OF CORRELATION X LIST OF TABLES Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 3.1 Table 3.2 Table 3.3 Table 3.5 Table 3.6 Table 3.7 Table 3.8 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Canyon H/W, Dimensions, and Number of Grid- 24 Points. Comparison of Miniature and Full-Size Net 26 Radiometer Specifications. Emissivity of Canyon Surfaces. 39 Surface Temperature Precision. 40 Summary of Fixed Versus Traversed Radiometer 49 Tests. Components of the Radiation Budget Calcul- 54 ated in the Arnfield Model with Options and Required Input Fluxes. Arnfield Model Fortran Subroutines. 57 Approximate Compile and Execution Times for 58 the Arnfield Model Using an Isotropic Rad iance Distribution. Test 1 of Model Sensitivity to the Number of 68 Model Grid-Points. Test 2 of Model Sensitivity to the Number of 68 Model Grid-Points. Test 1: View-factor Comparison. 69 Comparison of View-factor Calculations: 72 Wall A/Floor. Model Performance Statistics: Point Mode 100 Validation Set. July 19/20, July 21/22 1988. Model Performance Statistics: August 1/2, 107 Individual Validation Points, Isotropic and Unsworth and Monteith Radiance Distribution. Model Performance Statistics: August 1/2, 108 Hourly Averaged Points, Isotropic and Unsworth and Monteith Radiance Distribution. Model Performance Statistics: August 3/4, 109 Hourly Averaged Points, Unsworth and Monteith Radiance Distribution. XI Table 4.5 Comparison of RMSE and d Statistics Calcul ated From Hourly Averaged Data Using Iso tropic and the Unsworth and Monteith (1975) Radiance Distributions. Table 4.6 Model Performance Statistics: Aug. 10/11 Hourly Averaged Points, Unsworth and Monteith Radiance Distribution. Table 4.7 Model Performance Statistics: Aug. 12/13, Hourly Averaged Points, Unsworth and Monteith Radiance Distribution. Table 5.1 Summary of Average Differences by Facet Incurred as a Result of Using Temperature Approximations (Aug. 1/2, H/W=2.0). Table 5.2 Summary of Average L0 Differences by Facet Incurred as a Result of Using Temperature Approximations (Aug. 1/2, H/W=2.0). Table 5.3 Summary of Average L* Differences by Facet Incurred as a Result of Using Temperature Approximations (Aug. 1/2, H/w=2.0). Table 5.4 Summary of Average L^ Differences by Facet Incurred as a Result of Using Temperature Approximations (Aug. 3/4, H/W=1.0). 1 1 1 Table 5.5 Table 5.6 Table 5.7 Table 5.8 Table 6.1 Table A.1 Table A.2 Summary of Average LQ Differences by Facet Incurred as a Result of Using Temperature Approximations (Aug. 3/4, H/W=1.0). Summary of Average L* Differences by Facet Incurred as a Result of Using Temperature Approximations (Aug. 3/4, H/W=1.0). Percentage Difference of Fluxes Leaving the Canyon Top for Various Surface Temperature Approximation Schemes.(Aug. 1/2 1988 H/W=2.0) Percentage Difference of Fluxes Leaving the Canyon Top for Various Surface Temperature Approximation Schemes.(Aug. 3/4 1988 H/W=1.0) Daily Average Meteorological Conditions 0600-1800 (PDT) August, 1988. True and Measured Radiation For a Sensor Traversed Across a Canyon Wall. Attenuation and Lag Time of Canyon Floor/Top Data for Various Traverse Times. 1 16 120 141 142 143 144 145 1 46 147 1 48 180 215 219 xii Table A.3 Table D.1 Table D.2a Table D.2b Table D.3a Table D.3b Table D.4 Table D.5 Table D.6a Table D.6b Table D.6c Table E.1 Table F.1 Table F.2 Table F.3 Table F.4 Table F.5 Adjustment Completed to a Step Change in Radiation Using a Miniature Net Radiometer. Error Summary: Surface Temperature. Error Summary: Emissivity (Ts, Tk, Tr). Probable Error Analysis: Emissivity. Error Summary: L^ct. Probable Error Analysis: Ljct. Error Summary: L*0. Error Summary L* (Traversed). Error Summary L0 (Traversed). Probable Error Analysis: LQ. Typical Probable Errors: Lc. Model Input for Nocturnal Model Runs. Model Performance Statistics: August 2/3, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Model Performance Statistics: August 8/9, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Model Performance Statistics: August 11/12, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Model Performance Statistics: August 14/15, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Model Performance Statistics: August 22/23, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. 221 245 248 248 249 250 251 252 253 254 255 257 258 259 260 261 262 Xlll Table F.6 Model Performance Statistics: August 23/24, 263 Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. xiv LIST OF FIGURES Figure 1.1 Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6a Figure 2.6b Figure 2.7 Figure 2.8 Figure 2.9 Figure 2.10 Simplified diagram of an urban canyon. 1 Map of study location. 17 The hollow, two-cell concrete block. 19 Increase in wall view-factor (\//w) for a 21 point located mid-way up the opposite can yon wall at mid-canyon for increasing lengths of wall. Radius of the area seen by a radiometer 27 necessary to achieve a given view-factor (<//) for different instrument heights above the surface. The 'end effect' for view-factors of a tra- 29 versed canyon facet as a traversed radio meter approaches the end of the facet. Obstruction of \ps by a miniature radio- 30 meter located above a canyon surface. Same as for Fig. 2.6a but using a full- 31 size net radiometer. Generalized drawing of the Canyon Traversing 33 System (CTS). The CTS as mounted in the model canyon. 35 Surface temperature validation. 42 Change in long-wave radiation measured as 46 the instrument rotates to and from the can-yon top. Figure 2. 1 1 Tests meter between a for Lo at f ixed point and traversed radio-8 on the West wall. 47 Figure 2. 12 Tests meter between a for L0 at fixed point and traversed radio-3 on the West wall. 48 Figure 2. 13 Tests meter between a for L* at fixed point and traversed radio-7 on the canyon floor. 50 Figure 2. 14 Tests meter between a for L* at fixed point and traversed radio-4 on the canyon floor. 51 Figure 3.1 The canyon coordinate system. 55 XV Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 4.1 Default and actual grid pattern used in the 60 Arnfield model and scale canyon. View-factor of a parallel wall element and 63 a perpendicular wall element. Test 1 of model sensitivity. 70 Model control run. 75 Sensitivity of modelled fluxes to surface 77 temperature changes at point 5 on the West wall. Sensitivity of modelled fluxes to surface 78 temperature changes at point 1 on the West wall. Sensitivity of modelled fluxes to surface 80 temperature changes at point 11 on the West wall. Sensitivity of modelled fluxes to surface 81 temperature changes at point 5 on the can yon floor. Sensitivity of modelled fluxes to surface 82 temperature changes at point 1 on the can yon floor. Sensitivity of modelled fluxes to equal 84 surface temperature changes at all points. Sensitivity of modelled fluxes to Lict. 86 Sensitivity of modelled fluxes to e. Surface 89 temperature distribution used is typical for the early evening. . Sensitivity of modelled fluxes to e. Surface 90 temperature distribution used is typical for the late evening. Sensitivity of modelled fluxes to the rad- 92 iance distribution used. Scatterplots of modelled and measured long- 98 wave fluxes from the 'point tests'. The isotropic radiance distribution is used for modelled L^. xvi Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 5.1 Figure 5.2 Figure 5.3 Scatterplots of modelled and measured long wave fluxes from the 'point tests'. The Unsworth and Monteith (1975) radiance distri bution is used for modelled L^. Scatterplots of modelled and measured long wave fluxes from Aug. 1/2 1988, H/W=2.0 using the complete data set. The isotropic radiance distribution is used for modelled Scatterplots of modelled and measured long wave fluxes from Aug. 1/2 1988, H/W=2.0 using the complete data set. The Unsworth and Monteith (1975) radiance distribution is used for modelled Lj. Scatterplots of hourly averaged validation data by grid-point for Aug. 1/2 1988, H/W=2.0. The isotropic radiance distribution is used for modelled L^. Scatterplots of hourly averaged validation data by grid-point for Aug. 1/2 1988, H/W=2.0. The Unsworth and Monteith (1975) radiance distribution is used for modelled Lj Scatterplots of hourly averaged validation data by grid-point for Aug. 3/4 1988, H/W=1.0. The Unsworth and Monteith (1975) radiance distribution is used for modelled Scatterplots of hourly averaged validation data by grid-point for Aug. 10/11 1988, H/W=0.67. The Unsworth and Monteith (1975) radiance distribution is used for modelled Scatterplots of hourly averaged validation data by grid-point for Aug. 12/13 1988, H/W=1.33l The Unsworth and Monteith (1975) radiance distribution is used for modelled Modelled long-wave flux differences ob tained using the average canyon air temp erature in place of measured surface temp erature. Data is from Aug. 1/2 1988, H/W=2.0. As per Fig. 5.1 for Aug. 3/4 1988, H/W=1.0. Modelled long-wave flux differences ob tained using the airport air temperature in place of measured surface temperature. Data is from Aug. 1/2 1988, H/W=2.0. 99 103 104 105 1 06 1 10 1 13 1 17 127 128 131 Figure 5.4 As per Fig. 5.3 for Aug. 3/4 1988, H/W=1.0, 1 32 XVI] Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.B Figure 6.9 Figure 6.10 Modelled long-wave flux differences ob- 134 tained using the mid-point facet temperature in place of measured surface temperature. Data is from Aug. 1/2 1988, H/W=2.0. As per Fig. 5.5 for Aug. 3/4 1988, H/W=1.0. 135 Modelled long-wave flux differences ob- 139 tained using the average facet temperature in place of measured surface temperature. Data is from Aug. 1/2 1988, H/W=2.0. As per Fig. 5.7 for Aug. 3/4 1988, H/W=1.0. 140 Diurnal variation of selected surface temp- 153 eratures in a canyon with H/W=1.0, Aug. 3/4. Spatial and temporal variation of surface 157 temperature distributions in canyons with H/W=2.0, H/W=1.0 and H/W=0.41. Cooling of selected points on canyon facets; 162 H/W=2.0 canyon, August 1/2. (a) West wall, (b) East wall, (c) Floor. Cooling of selected points on canyon facets; 163 H/W=1.0 canyon, August 3/4. (a) West wall, (b) East wall, (c) Floor. Cooling of selected points on canyon facets; 164 H/W=0.41 canyon, August 22/23. (a) West wall, (b) East wall, (c) Floor. Average canyon air temperature and air temp- 166 eratures recorded at Vancouver International Airport for (a) Aug. 1/2, (b) Aug. 3/4, (c) Aug. 22/23. Average canyon air temperature and air temp- 167 eratures recorded at Vancouver International Airport for (a) Aug. 2/3, (b) Aug. 10/11, (c) Aug. 11/12. Spatial and temporal variations of air temp- 169 erature above canyon facets in (top) a canyon with H/W=2.0, (middle) H/W=1.0 canyon, and (bottom) 0.41 canyon. Spatial and temporal variations of modelled 172 radiative fluxes in an H/W=2.0 canyon. Spatial and temporal variations of modelled 173 .^radiative fluxes in an H/W=1.0 canyon. XVII] Figure 6.11 Figure 6.12 Figure 6.13 Figure 6.14 Figure 6.15 Figure 6.16 Figure 6.17 Figure 6.18 Figure 6.19 Figure 6.20 Figure 6.21 Figure A.1 Figure A.2 Figure A.3 Figure B.1a Figure B.lb Spatial and temporal variations of model led radiative fluxes in an H/W=0.41 canyon. Bottom: Comparison of canyon and open site cooling overlaid with L*Q« Lict (top) and wind speed (u), (middle) are also presented. Data from Aug. 1/2, H/W=2.0 As per Figure 6.12. canyon H/W=1.33. As per Figure 6.12. canyon H/W=1.0. As per Figure 6.12. canyon H/W=1.0. As per Figure 6.12. canyon H/W=0.67. As per Figure 6.12. canyon H/W=0.41. Data from Aug. 14/15, Data from Aug. 3/4, Data from Aug. 8/9, Data from Aug. 11/12, Data from Aug. 20/21, Cooling of urban and rural surfaces observed from (a) scale models, (b) the cities of Montreal (H/W=3.29), Vancouver (H/W=1.50) and Uppsala (H/W=0.76). Temporal changes of heat island intensity generated using (a) a scale model and (b) observed intensities from Montreal, Vancouver and Uppsala. Temporal development of the temperature difference between the mid-point of the canyon floor and the open concrete. Surface temperature differences between the canyon and open sites at eight hours after sunset for the five H/W tested. Modelled distributions of , Lo and L* over canyon facets. Oct. 10, 1987. Sensor response to a ramp change in LQ or L* over a wall. Sensor response to a sinusoidal change in L0 or L*. Surface temperatures, evening of Aug. 1/2. Surface temperatures, evening of Aug. 25/26 XIX Figure B.2 Power spectrum of rescaled and detrended data for points 1 to 5 on the West wall on Aug. 1/2. Figure B.3 Detrended surface temperature of point 1 on the West wall; Aug. 1/2. Figure B.4 Power spectrum of rescaled and detrended surface temperature shown in Figure B.3. Figure B.5 Transfer function of a low-pass filter with a stop frequency (SF) of 0.03 for different truncations of the Fourier series. Figure B.6 Filtered surface temperature on Aug. 1/2 using various low-pass filters. Figure B.7 Power spectral density of surface temper ature (point 1 on the West wall) for Aug. 1/2 Figure B.8 Filter function derived from an optimal fil ter compared to a low-pass filter using 105 terms and a stop frequency of 0.015. Figure B.9 Filtered surface temperature using an 'optimal' low-pass filter. Figure C.1 Calibration curve for Barnes Model PRT-4A Infrared Thermometer. XX LIST OF SYMBOLS B Rate of change of actual radiation with time C Constant CTS Canyon traversing system C(f) Measured signal E Absolute error H/W Height-to-width ratio IF Canyon facet number IP Grid-point number on facet 10 Instrument output K Degrees Kelvin L Lag Lp Angular'distribution of sky-derived long-wave radiation L^ Incident long-wave radiation on a surface L0 Outgoing long-wave radiation from a surface L* Net long-wave radiation of a surface L*D Net long-wave radiation of the open surface Lict Incident long-wave radiation at the plane of the canyon top MAE Mean absolute error MBE Mean bias error N(f) Noise frequencies 0 Observed mean P Predicted mean Pe Probable error Pc Power -spectral density XXI Q Radiation (measured) Q* Net radiation QA Advected flux, actual radiation (Appendix 1) Latent heat flux QF Anthropogenic heat flux QQ Subsurface heat flux QH Sensible heat flux AQS Change of storage heat flux R Roof width RMSE Root mean square error RMSEs Systematic portion of the root mean square error RMSEu Unsystematic portion of the root mean square error RSTOP Convergence criterion for canyon multiple reflection routine SF Stop frequency S(f) Signal frequencies Ta Air temperature Tc Cavity temperature Radiative temperature of the sky Tr Apparent surface temperature measured by an infrared thermometer Ts Surface temperature UM Unsworth and Monteith (1975) radiance distribution for sky-derived long-wave radiation a Intercept of least squares regression line b Slope of least squares regression, slope of the UM radiance distribution, total length of plane element for view-factor calculations (Chapter 3.) c Intercept of the UM radiance distribution xxii d Index of agreement e Exponential f Frequency h Height n Number of data Coefficient of determination s0 Observed standard deviation Sp Predicted standard deviation t Time x Along-canyon axis, origin is at canyon mid-length y Distance aross canyon floor from wall A, distance from plane element for view-factor calculations y' Distance across canyon top from wall A z Distance up Wall A, measured from floor z' Distance up Wall B, measured from floor Z Summation a Attenuation factor of sensor response 0 Angle 6 Differential e Emissivity u Thermal admittance * 3.1415927 a Stefan Boltzmann Constant (5.67 x 10~8 W m~2 K"4) T Time constant i/>s Sky view-factor XX111 Azimuthal angle from North Angular frequency of oscillation Degrees Celcius XXIV ACKNOWLEDGEMENTS This thesis represents the culmination of work conducted over the past three years. The successful completion of this project could not have been obtained without the assistance of a large number of people, each of whom has played an important role. To my supervisors, Dr. T.R. Oke and Dr. D.G. Steyn I owe many thanks to the support they have shown throughout. They were always available to answer my questions and their help is gratefully acknowledged. Dr. R.J. Cole also took a keen interest in the project and provided useful comments. Dr. A.J. Arnfield provided the numerical model which was validated and assisted in the initial installation of the model at U.B.C. His on-going support has been most helpful. Mr. J. Skapski and Mr. H. Kozlow designed and constructed the canyon traversing system, without which this work would not have been possible. They are to be highly commended for this feat of engineering and their patience in dealing with the many trying problems which were encountered in the design and construction phases. Miss. S. Tewnion and Mr. G. Frickska performed admirably as field assistants during the data collection period and G. Friska also helped during the design and testing period. Many thanks go to my fellow graduate students, especially Dr. S. Grimmond and Dr. H. Cleugh who helped with the instrumentation in 1987 and 1988, Dr. H.P. Schmidt and M. Roth for providing assistance with my attempts at Fourier Analysis, and S. Robeson and J. Schmok who, as my initial office-mates, broadened my academic horizons. Also deserving of credit are my family and S. Jenks for their encouragement and support during the project. The financial assistance of the Natural Sciences and Engineering Research Council (NSERC) in the form of a scholarship is gratefully acknowledged. The project was funded by NSERC grants to Dr. Oke. The field site was made available by the Canadian Department of Transport. 1 CHAPTER 1. INTRODUCTION 1.1 RESEARCH OBJECTIVES The primary aim of this research is the validation of a numerical model (Arnfield, 1976, 1982) which estimates radiative fluxes within urban canyons. An urban canyon is composed of the principal surface elements (facets) which exist between two buildings, the building walls (canyon walls) and ground (canyon floor) (Figure 1). The canyon floor is often a street system consisting of roads, sidewalks and vegetative cover which differ in their proportions with location in the urban area. A canyon-air volume is contained by the canyon facets and is bounded at the top by an imaginary horizontal plane at roof-level and at the ends by vertical planes at the end of the buildings. Canyon - air volume Figure 1.1 Simplified diagram of an urban canyon. From Oke (1978). 2 Urban canyons (plus the intervening roofs) are the basic combination of vertical and horizontal surfaces in urban areas which, together can be used to represent the true city surface. Validation of this model for the estimation of urban surface albedos has been recently completed by Arnfield (1988). The model validation herein encompasses various ratios of building height to canyon width (H/W) for a single canyon orientation, but is restricted to nocturnal long-wave fluxes. This work will further define the ability of the model to estimate long-wave fluxes. The second objective is to test the effect of using various approximations to the full model input data. These tests are of practical use because data at the scale and resolution used for model validation are not normally available. A third objective is to examine the effects of urban surface geometry upon the cooling of urban areas, especially, the in-canyon spatial and temporal variations of long-wave radiation and air and surface temperatures. 1.2 APPLICATIONS/SIGNIFICANCE GF THE RESEARCH Model validation is, by itself, a very important part of the scientific process of experimentation (Flueck, 1978; Idso, 1987). Too often in the discipline of urban climatology validation studies have not kept pace with new modelling endeavours, resulting in a situation where many untried models exist, and their usefulness as predictive tools is thereby 3 limited. This research utilizes a measurement programme tailored specifically for model validation. It allows validation of model predictions for individual grid-points within the canyon over short time periods, and for both spatially and temporally averaged data. The availability of a complete and accurate data set for model input, makes it possible to test approximation schemes which may be used in place of the full model input data. This is an improvement upon model sensitivity analyses which cannot be done without first having correctly measured the true model input conditions. One of the objectives of urban climatology is to have findings applied to the process of urban planning and design (Oke, 1984). Urban surface geometry is one parameter of urban design which has been shown to have various climatic impacts upon the objects and organisms located within the urban geometry. Oke (1988) describes urban geometries defined only by the parameters H/W and building density which are best suited to maximize shelter, pollutant dispersion, urban warmth, and solar access. The present work provides further insight into the reduction of cooling in urban areas arising from altered surface geometry (H/W) under different weather conditions. While the focus of this research is upon microscale canyon processes, the knowledge of conditions within urban canyons aids in the research of processes occurring at larger scales in the atmospheric boundary layer over urban areas. Of particular importance is the ability to accurately model the long-wave fluxes leaving the urban canyons which form the lower boundary 4 conditions of the atmosphere above. Thus, this research can contribute to the understanding of processes occurring at the meso-scale. 1.3 APPROACHES TO THE STUDY OF THE EFFECTS OF URBAN SURFACE GEOMETRY ON THE CLIMATE WITHIN URBAN AREAS This section briefly reviews the three major approaches which have been used to investigate the effects of urban surface geometry on the climate within urban areas. Examples are reviewed and the approaches evaluated with respect to their suitability towards achieving the present objectives. The research methodology adopted is outlined in Section 1.4. 1.3.1 Observational Studies Methods of observation in urban climatology have been reviewed by Oke (1984) who developed a two-tier classification system based upon two sets of controls underlying the urban climate; turbulent boundary layers and urban morphological units. The major distinction lies between the urban canopy layer (UCL), dominated by the individual roughness elements and their surface properties, and the urban boundary layer (UBL) which represents the integrated effects of the UCL within a turbulent layer combining the surface and mixed layers (Oke, 1976, 1984). 5 Observational studies have been based upon either intensive • measurement in a single urban canyon or observations taken from a number of urban canyons with different properties. Examples of the first type include: the albedo of a canyon system (Nunez, 1975), the long-wave radiative flux divergence and nocturnal cooling within a canyon (Nunez and Oke 1976), and the energy balance of an urban canyon (Nunez and Oke 1977), all based upon measurements obtained in a single canyon in Vancouver, B.C. A recent study by Nakamura and Oke (1988) focussed upon the temporal development of wind, temperature and stability conditions in an urban canyon. Research using measurements from a range of canyons include the vast number of urban heat island studies which include measurements of air and/or surface temperatures within the urban canopy layer. Two recent examples which have focussed upon the role of the urban surface geometry in modifiying the observed air and surface temperatures in urban canyons are Barring et. al . (1985) in Malmo, Sweden and Yamashita et al. (1986) in the Tama River Basin (Tokyo suburbs) in Japan. The microclimate of sidewalk surfaces within a range of urban canyons has also been examined (Tuller, 1973). The use of a single canyon means the results are only strictly applicable to that site, and caution must be exercised when trying to generalize. The general relationships which have been demonstrated between surface geometry and air and surface temperature must be carefully analyzed with respect to the conditions under which they were gathered and the presence of 6 other influencing factors, nevertheless, observational studies have been useful. 1.3.2 Scale Modelling Scale modelling can overcome some of the limitations imposed by the natural variability inherent in field observations (e.g. canyon dimensions and properties and weather). Logistical constraints involved in instrumenting and using ''real' urban canyons may also be avoided. For the case of surface geometry effects upon the canyon temperature and radiative balance, use of a scaled model allows a range of surface geometries to be tested under different condition, a flexibility not usually available in field studies. For the results of a scale model to apply to the real world however, the model must meet certain scaling criteria for the variables of interest. For this reason, scale modelling within canyons has concentrated upon radiative transfer processes in which the turbulent fluxes can be neglected. Several examples of scale modelling of canyon processes exist. Oke (1981) used a scale model built of plywood and enclosed by a polyethylene vtent'"to represent rural and urban surfaces of varying geometry in a study of the nocturnal radiative cooling. Simulation conditions were restricted to calm and cloudless nights during which anthropogenic heat release was of negligible importance. Comparison of model results with field observations showed good agreement. Changing the geometry of the 7 urban model by altering the height to width ratio (H/W), resulted in a slowing of the rate of temperature decrease as H/W increased. Higher H/W ratios also led to an increase of the time taken for the urban heat island intensity to reach a maximum. The importance of the sky-view factor (^s) in decreasing the flux of net long-wave radiation at the floor of the canyon and thus on cooling was noted. Results of a thermal admittance experiment paralleled field observations, with the concrete city generating a large heat island. In a similar study, Johnson and Watson (1987) used scale modelling techniques to validate a simple numerical model developed to approximate the cooling or heating of a typical urban surface under conditions when radiative heat transfer is the dominant heat transfer mechanism. Their model was simply two sheets of plywood glued together and instrumented with thermocouples on each surface and between the layers. The plywood sheet, representing the floor of the canyon, was then placed on the open top of a chest freezer, whose walls take on the role of the canyon walls, and the bottom of which served as the night sky (radiative sink). The freezer sides and bottom were also instrumented with thermocouples. Comparison of modelled and observed temperatures exhibited good agreement. Aida (1982) used concrete blocks to.represent the urban system in order to study the effect of surface geometry on the formation of heat islands through the differential absorption of short-wave radiation. The model was constructed outdoors and measurements were taken during clear meteorological conditions 8 in different seasons. A limited number of simple surface geometries were examined. The conclusions indicated that the surface geometry alone could account for an anomolous absorption of solar radiation, with the major control being the ratio of relative canyon area to the entire model area. Deeper canyons, (those with a greater H/W ratio), exhibited smaller values of albedo per canyon top area. Diurnal and seasonal variations of the albedo were observed in relation to the zenith angle of the Sun. The results from this study have recently been used (Arnfield, 1988) in a validation of the albedo estimates produced by the Arnfield (1976, 1982) model. 1.3.3 Mathematical Models Due to the considerable resources needed for full-scale observational studies and the problem of similtude associated with scale modelling, the use of statistical and numerical models has increasingly become the methodology of choice for many urban climatologists. The use of mathematical models makes it possible to test different boundary conditions and allow the parameters of interest to vary. This is otherwise difficult or impossible to achieve. Extensive reviews of urban climate modelling have been undertaken by Bornstein (1986), Bornstein and Oke (1981), Landsberg (1981), and Oke (1974, 1979). Todhunter and Terjung (1988) have recently presented an in-depth comparison of three urban climate models and their ability to 9 model the effects of urban geometry upon the surface energy budget. Urban climate models may be subdivided into two main classes following the differentiation of the boundary layer over cities by Oke (1976) into the urban canopy layer (UCL) and the urban boundary layer (UBL). Those models which describe the climate of the urban canyon are one type of UCL model and are the subject of interest here. Canyon models evaluate terms of the surface energy balance, which, in the absence of advection, may be written: QF + K* + L* = Q* + Qp = QH + QE + QG + AQg (1.1) where the first two terms make up the surface radiation balance (Q*) including the net short-wave (K*) and net-longwave radiation (L*). QF is the anthropogenic heat flux, QH and QE are the turbulent fluxes of sensible and latent heat respectively, QG is the subsurface heat flux, and AQS is the change of energy storage by the system. The models vary in their complexity and emphasis; some concentrate solely upon radiative parameters (eg. Arnfield (1976, 1982), while others include all terms. The canyon radiation models are based upon the relatively straight forward principles of radiation geometry, multiple reflections, surface properties and the measurement or modelling of incident radiative fluxes. The canyon models are important because they provide results for use in larger scale models of the urban 10 boundary layer and resolve microscale variations of the energy balance. They also allow the development of planning and building design strategies which incorporate climatic aspects. Canyon models have been developed by: Aida and Gotoh (1982), Arnfield (1976, 1982), Bruhl and Zdunkowski (1983), Nunez (1975), Sievers and Zdunkowski (1985), Terjung and Louie (1973, 1974), Terjung and O'Rourke (1980a,b, 1981), Verseghy (1987), and Zdunkowski and Bruhl (1983). The model developed by Sievers and Zdunkowski (1986) incorporates energy balance parameters in a two-dimensional numerical simulation scheme to compute the air flow over urban surfaces and represents the state-of-the-art urban climate model. 1.4 RESEARCH METHODOLOGY The research objectives require the accurate specification of model input data and a measured data set which may be used to compare to the model output for validation purposes. A degree of flexibility in modifying canyon dimensions is desired in order to examine a range of H/W and their effect upon the cooling of the canyon. The approach adopted here combines elements of studies performed in both reduced scale and full-scale urban canyons. A simplified model of an urban canyon was designed and constructed at a reduced scale using the single geometric scaling criteria height to width ratio (H/W) to preserve length scales. The model was constructed outdoors utilizing natural daylength and meteorological conditions. The reduced scale of 11 the structure allowed different H/W ratios to be tested and overcame some of the logistical problems commonly encountered by observational studies. The overall scaling of the model is such that extensive within-canyon measurements can be made, a procedure attempted previously only in single, full-size canyons. Thus, in a spectrum of model sizes this canyon occupies an intermediate position between real canyons and those described in Section 1.3.2. The model canyon is not a true scale model in the manner which most dimensional analysts define the term (Schuring, 1977; Skoglund, 1967; Venikov, 1969) because full dynamic similarity is not achieved. Canyons of similar H/W exist in the real world with very different absolute dimensions, thus no single prototype exists upon which the model is based. Strict adherance to scaling criteria is not viewed as a limitation to the successful validation of the Arnfield model, the accurate prescription of input variables and the availability of a matching measured data set define a complete validation set. To investigate the role of surface geometry upon the cooling of urban surfaces, scaling limitations become more important and are outlined in Chapter 2. Extensive instrumentation of the canyon was made using a combination of stationary and traversing sensors. The latter were used to obtain two of the three components of the long-wave radiative balance. A fully automated traversing system referred to as the canyon traversing system (CTS) was especially constructed for this purpose. A second, open, site was 12 instrumented near the canyon to allow comparison of canyon cooling with surfaces having a plane surface geometry. 13 CHAPTER 2. THE CANYON MODEL, INSTRUMENTATION, AND TESTS 2.1 INTRODUCTION This chapter describes the canyon model, it's instrumentation, various tests to ascertain it's performance and any limitations to the data collected. Following a general description of the canyon model, the field site, canyon dimensions, materials used, and construction methodology are described in greater detail. The canyon instrumentation is outlined in Section 2.4 and tests conducted in relation to the surface temperature, surface emissivity and traversing speeds are described in Section 2.6. A detailed error analysis of measured input is presented in Appendix D. 2.2 SIMULATION METHODOLOGY The conditions to be simulated are set according to the research objectives outlined in Chapter 1 and form guidelines for the design of a suitable canyon model as well as important limitations when the performance of the model is assessed. The conditions to be simulated in order to achieve each of the main objectives are described below. To validate the night-time long-wave radiative fluxes predicted by the Arnfield model requires only the simulation of 14 urban surface geometry and nocturnal conditions. The simulated urban surface geometry conforms to the requirements of the Arnfield model (see Chapter 3) by using the scaling H/W (height to width ratio) of urban canyons to give a number representing the 'openness' of the canyon. Large values of H/W indicate a narrow, deep geometry. To match nocturnal meteorological conditions, the model is operated out-of-doors at night. With the satisfaction of these two criteria, no further restrictions exist for model validation. Investigation of surface geometry effects on the long-wave radiative balance and surface cooling of canyon facets requires the same simulation conditions necessary for model validation. In addition, the assumption that anthropogenic heat is of negligble importance is made. The control by surface geometry on surface cooling and radiation is best expressed under calm, clear and dry conditions which maximize radiative exchange and minimize the turbulent fluxes of sensible and latent heat, (QH and 0_E respectively). These ideal conditions, along with the absence of advection have been adopted by Oke (1981) in his study of the effects of surface geometry upon the formation of the urban heat island. Use of an outside location precludes the complete elimination of these influences in this study. The data collected may, however, be analyzed to investigate the degree to which it meets these assumptions, based upon recorded local meterological conditions. On this basis, data may be grouped for comparison. 15 Similarity with real-world canyons is limited to the geo metric similarity obtained through the use of the H/W ratio. Canyon materials and construction techniques have not been ex-plicilty scaled, although they bear some resemblance to those found in real, full-scale canyons. Processes governing radiative transfer have not been scaled. Oke (1981) considered the char acteristic length scale of radiative transmission to be neg ligible compared to that of his smaller model. The path length available for gaseous absorbtion and re-emission of radiation within the canyon is less than that available in the real world and is not scaled. The time available for canyon heating and cooling is governed by astronomical and meteorological factors. 2.3 THE CANYON MODEL 2.3.1 General Description The model canyon is composed of two identical walls approximately 10 m long and 1 m high oriented North-South on a base of poured concrete. Canyon width is varied from 0.5 m to 1.5 according to the H/W ratio desired. Each wall is constructed using a stack of five overlapping layers of 200x200x400 mm two-cell, hollow concrete blocks, capped by a single layer of 200x200x50 mm solid concrete slabs with the exception of the smallest H/W, (0.41) which used only 3 layers of blocks. No supporting framework is used and the blocks are not joined by 16 any bonding material. A 25 mm layer of extruded polystyrene insulation is taped to the exterior of the walls to aid in isolating the inner, active canyon surfaces of interest. The canyon traversing system (CTS), described in Section 2.4.3, is located just North of the canyon mid-length point, so that the traversed instruments and thermocouples were centred on the canyon mid-length. The following sections provide greater detail regarding specific aspects of the canyon model, the CTS and the canyon instrumentation. 2.3.2 Site The model site is a parking compound administered by the Department of Transport at Vancouver International Airport. The airport is located on Sea Island in the Lower Mainland region of British Columbia, Canada (Figure 2.1). The site provided the necessary security, open exposure and a flat, concrete base for the canyon model. The concrete base was formerly the foundation of a large building. A large hangar to the Northwest of the site casts shadows over the model canyon before the time of actual sunset. Sky view-factor ($s) estimates for the site, using the method described by Steyn (1980), were in excess of 0.99. 17 18 2.3.3 Materials To validate the Arnfield model the materials used for the canyon facets are irrelevant as long as they are of known emissivity and surface temperature and are homogeneous in the along-canyon direction. Two-cell hollow concrete blocks (Figure 2.2) were selected for use in the canyon model because: only a small number are necessary to construct the canyon, they can easily be handled by a single person and, when made into a wall, are stable enough to not require any supporting framework. They possessed the further advantages of ready availability, low cost, and durability. The solid concrete slabs used to cap the walls are .manufactured using materials similar to those used in the blocks. The insulation is an extruded polystyrene 'Styrofoam - SM Brand' available in .0.6" m x 2.4 m sheets. The insulation functions in two ways: it reduces heat loss through the backs of the canyon walls at night, and it's light colour is a good reflector of incident short-wave radiation on the outside of the canyon walls-during t^ve day. 2.3.4 Construction Technique Standard overlapping brick construction is used to build the walls. No adhesiv-es are used because tear down and rebuilding of the wall is-necessary to generate new H/W ratios. The styrofoam insulation is taped to the exterior of the canyon walls using 19 38 < » 49 SIDE VIEW 32 27 36 « ;> 193 END VIEW 32 193 TOP VIEW 395 Figure 2.2 The hollow, two-cell concrete block. Dimensions in millimetres. 20 two-sided carpet or duct tape. Two pieces of lumber 50x100 mm and approximately 2 m in length were laid across the canyon ends on the cement base and taped to the cement to prevent the accumulation of dirt inside the canyon. 2.3.5 Canyon Height and Width Canyon height and width are considered together because their ratio sets the scaling parameter H/W. Canyon H/W is varied in all but one case (0.41) by. varying the width rather than the height. This method is adopted because the CTS allows more variability in the length, rather than the height of traverse. Maximum canyon width is limited to 1.9 m, limited by the length of the horizontal drive screw of the CTS (Figure 2.7). The minimum width is 0.5 m and is set by the arc of rotation required by the traversing instruments (Section 2.4.3). Two canyon heights are used; 1 m and 0.62 m. The height is varied by the addition or removal of an equal number of layers of blocks from each wall. The 1 m height was used with H/W ratios of 2.0, 1.33, 1.0, and 0.67. The 0.62 m (3 rows of blocks) wall height was used in conjunction with a canyon width of 1.5 m to achieve the minimum H/W of 0.41. The combinations of H and W selected may be achieved, using only two spacings of measurement points for model input on the floor, 0.1 m and 0.15 m (Table 2.1). This reduces the number of times thermocouples must be reconstructed and reaffixed to the canyon floor. 21 Figure 2.3 Increase in wall view-factor (^w) for a point located mid-way up the opposite canyon wall at mid-canyon for increasing lengths of wall. 22 2.3.6 Canyon Length The theory of the Arnfield model (Chapter 3) assumes an infinitely long canyon; an assumption which must be relaxed in both the numerical implementation of the model and in the model canyon. Arnfield (1976) suggests an appropriate approximation to inifinity is achieved for canyon lengths of 8xH or W, which ever is the larger. This value is derived from an analysis designed to find the length of a perfectly reflecting canyon that is necessary to produce convergence to a canyon reflectivity value of 1.0. A similar measure of inifinity may be derived from view-factor geometry. For a given canyon width and wall height the view-factor of one wall may be calculated for a point located at canyon mid-length half way up the other wall. If this calculation is repeated for a number of increased wall lengths the differences in the view-factors obtained can be plotted, as in Figure 2.3, to show the increase in view-factor achieved with longer walls. The results for the H/W=1.0, 2.0 and 0.41 canyons show that when the 1.0 canyon reaches a length of 5 m the increase in view-factor is less than 0.1, and after 8 m the increase is less than 0.001. These results therefore confirm the findings of Arnfield (1976). The model canyon length was set at 10.2m and was not varied with the H/W ratio used. This results in a varying approximation to infinity for the canyon length, with a 23 view-factor change of less than 0.0005 for the 2.0 canyon and 0.001 for the 0.41 canyon. 2.4 CANYON INSTRUMENTATION 2.4.1 Surface Temperature The method of surface temperature measurement is adopted from Fairey and Kalaghchy (1982). They construct thermocouples incorporating a loop, or arc, of wire between the junction and the insulated leads to measure the surface temperature of hollow concrete blocks and frame walls. The use of the arc method gives a good approximation to the true surface temperature without requiring the thermocouple junctions and lead wires to be imbedded in the surface material (Fairey and Kalaghchy, 1982). The arc of wire reduces conduction errors which occur due to the high conductivity of the thermocouple leads when only the junction is attached to the surface. The choice of arc size is related to the wire gauge, the temperature difference across the surface boundary and the conductivity of the surface material (Fairey and Kalaghchy, 1982). Surface temperature measurements on the canyon facets are made using thermocouple arcs constructed from 30 awg copper-constantan thermocouple wire with double insulated fibreglass coating. All thermocouple arcs are constructed using the same cylindrical form so that the diameter remains constant 24 (approximately 10 mm). Larger sizes are difficult to attach to the rough surface of the block..Junctions are tightly twisted and trimmed to a length of 2 mm prior to soldering. The entire arc is attached to the surface using a fast bonding two-part adhesive. Additional bonding is achieved by applying a thin coating of the adhesive over the entire arc. While the second coat of adhesive is still tacky a dusting of powdered cement is applied to keep the surface radiative properties similar. Thermocouples are affixed in the same relative position on each block to minimize biases due to temperature variations across the surface of the block arising from it's internal architecture (Section 2.6.2). On the walls, the insulated leads are led away from the measurement point horizontally along the block face to the nearest space between blocks and then to the back of the wall. Table 2.1 Canyon H/W, Dimensions, and Number of Grid-Points. H/W H (m) W (m) Grid-points on Grid-points on Each Wall Floor 2.0 1.0 0.5 10 5 1 .33 1.0 0.75 10 5 1 .0 1.0 1.0 10 10 1 .67 1.0 1.5 10 10 0.41 0.62 1.5 6 10 25 The number of measurement grid-points varies with the absolute dimensions and H/W of the canyon. Table 2.1 summarizes the canyon H/W, absolute dimensions and number of thermocouples on each facet. 2.4.2 Radiation Estimates of long-wave radiation are needed for two purposes; model input and model validation. Model input requires the long wave irradiance incident on a horizontal plane situated coincident with the canyon top CLictr) • Model validation requires the three long-wave flux densities at each canyon surface; incident (L^), outgoing CL0)., and net long-wave radiation (L*). Measurement of two of the three fluxes allows the calculation of the third by residual. L^ct is measured using an Eppley PIR pyrgeometer located on the top of the west canyon wall. Two miniature net radiometers (Swissteco Model S1 Minor Mk 2) are mounted on the traversing system (see 2.4.3) to measure radiative fluxes within the canyon. One of the instruments is eguipped with a blackbody cavity to measure LD from the canyon walls and floor. The second is operated in a net radiation x-oniiguration. LQ is measured in preference to because the height of the instrument dome is less than that of the blackbody cavity, and therefore allows the instrument to be located closer to the surface. 26 The instrument specifications of the more commonly used full-size Swissteco S1 net radiometers are compared with the miniature version in Table 2.2 Table 2.2 Comparison of Miniature and Full-Size Net Radiometer Specifications. Source: Fritschen and Gay (1979). Parameter Miniature Full Size Diameter of sensing surface Instrument diameter Height of dome above sensing surface Sensitivity (typical) Accuracy of Calibration Response Time 1 6 mm 22 mm 1 0 mm 0.006 mV W"1m2 +/- 2.5% 98% in 25 sec 50 mm 95 mm 30 mm 0.04 mV W_1m2 +/- 2.5% 98% in 25 sec The use of miniature net radiometers for within-canyon measurements offers several advantages over the standard model. The lighter weight of the miniaturized instrument reduces the power and strength requirements of the CTS. The smaller instrument domes allow the radiometers to be located much closer to the surface. Figure 2.4 presents the radius of the area seen by a radiometer at a given height that is necessary to achieve a given view-factor. It emphasizes that a .smaller area is needed to achieve a given view-factor (Figure 2.4). This is an important consideration because the Arnfield model predicts the flux density for a specific point on the surface while the 27 0.5 r o.o h 1 — 1 1_ 10 20 30 40 Radiometer Height Above Surface (mm) Figure 2.4 Radius of the area seen achieve a given view-factor (\p) for above the surface. by a radiometer necessary to different instrument heights 28 radiometer measures the average flux density for the area viewed. The view-factor of the surface becomes critical near the ends of the facets, particularly the tops of the canyon walls. With increasing instrument distance above the canyon facet (measured perpendicular to the facet) in these regions an increasing proportion of the instrument's view-factor will be occupied by a facet other than that being traversed, or, in the case of the tops of the walls, the night sky. Figure 2.5 illustrates this 'end effect' for a given radiometer distance above a facet. The lower limit to the distance above the surface at which the radiometer may be placed is determined by the roughness of the surface and the height to which the instrument domes project above the sensing surface. Another factor is the obstruction of (//s (and wall and floor view-factors) for the facet being measured. The placement of a radiometer close to the surface obscures a portion of the view-factor for that point (Figures 2.6a,b) and replaces the sources of sky, walls and floor with Lj emitted from the radiometer. This possibility is explored by Idso and Cooley (1972). They find no gradients in surface temperature beneath a full-size radiometer located 0.2 m above a grass surface. The tests are repeated here (see 2.6.3 below) for miniature and full-size radiometers mounted 50 mm above an open surface. No discernible surface temperature changes were detected using a narrow-view infrared thermometer (Barnes Model PRT 4A). 29 1.0 _ 0.9 o u o •D e m o 0.8 > o o 0.7 *o o u. I > Height ot Trov»r»« (mm) 50 40 30 20 10 < 0.6 0.5 0.5 0.6 0.7 0.8 0.9 Distance From Start ot Traverse (m) 1.0 Figure 2.5 The 'end effect' for view-factors of a traversed canyon facet as a traversed radiometer approaches the end of the facet. The effect is diminished at lower traverse heights. 30 10 20 30 40 Radiometer Height Above Surface (mm) Figure 2.6a Obstruction of ^5 by a miniature radiometer located above a canyon surface. View-factors are calculated for a point directly beneath the radiometer (limiting case) and for the circular areas which make up the surface view-factor of the instrument. 31 Radiometer Height Above Surface (mm) Figure 2.6b Same as for Fig. 2.6a but using a full-size net radiometer. 32 A final advantage to locating the radiometer close to the surface is the reduction of errors due to emission by the intervening air layer (Idso and Cooley, 1971). This might be important in the early evening when the surface temperature is significantly different from air temperature. 2.4.3 The Canyon Traversing System The Canyon Traversing System (CTS) is a custom-designed and built apparatus used to traverse radiometers around a canyon cross-section. In the configuration employed, the traversed sensors included two miniature net radiometers, one of which was equipped with a uni-directional cap, and a 30 awg type-T unshielded thermocouple for monitoring air temperature. Figure 2.7 shows a generalized side-view of the CTS (top) and an end-view of the vertical traversing assembly (bottom). (The numbered labels correspond to those used in the following description). The CTS uses two electric motors (1,2) to provide power for horizontal (3) and vertical (4) bolt screws which drive the instrument carriage (5) around the canyon cross-section. A third motor (6), mounted on the carriage, is used to rotate the radiometers (7). Control and power are provided via a panel mounted behind the East wall of the canyon. The drive screws are mounted in a framework (8) bolted to the ground outside of the canyon and stiffened by a guide wire (9) running through the walls across the bottom of the canyon. Electro-mechanical limit switches (10).govern the length of travel of the instrument 33 Figure 2.7 Generalized drawing of the Canyon Traversing System (CTS). Top: side view, bottom: end-view of the vertical traversing assembly. Labels: 1 - horizontal drive motor, 2 -vertical drive motor, 3 - horizontal bolt screw, 4 - vertical bolt screw, 5 - instrument carriage, 6 - instrument rotation motor, 7 - miniature radiometers, 8 - support frame, 9 - guide-wire, 10 - limit switches, 11 - instrument carriage arm. 34 carriage and are used to trip the rotation and delay sequence of the instruments. The radiometers are mounted on an arm (11) extending outwards from the traversing carriage to reduce obstruction of the instrument's view-factor by the CTS. Manual and automatic modes of operation are available. Manual operation provides individual control over each motor so that the instrument carriage may be placed anywhere in the canyon cross-section boundaries defined by the limit switches. In the automatic mode the instruments traverse around the canyon cross-section and automatic instrument rotation and delays are engaged. This is the primary mode for data collection. Figure 2.8 depicts the CTS in operation in the field during 1988. The distance between the radiometer sensing surface and the canyon facet being measured averages 30 - 40 mm for the walls, and 20 mm for the canyon floor. At the canyon top the instruments were set coincident with the plane across the canyon top. Irregularities in the level of the cement base upon which the canyon walls were constructed resulted in the traversing system not providing a perfectly parallel traverse to all the canyon facets. The appropriate speed of traverse was calculated from information on the response characteristics of the radiometers and modelled predictions of the radiation distribution across the canyon facets. Using Fritschen and Gay (1979), the response of an instrument with a known time constant to either a ramp or sinusoidal change may be approximated by a differential equation if the instrument begins in equilibrium with the true value. The Figure 2.8 The CTS as mounted in the model canyon. 36 difference between the true and measured radiation can then be determined for different traversing speeds (see Appendix A for details). From this analysis it is estimated that a traverse time of approximately 5.5 mm s~1 is adequate. Inclusion of a delay of 27 seconds before beginning the traverse of each facet fulfills the requirement that the instrument begin the traverse in equilibrium with the environment. Appendix A provides further details. The sensor position may be determined at any point though knowledge of three parameters: traverse speed, state of the traverse (delay or traversing), and start location. The state of the traverse is indicated by a voltage at the control panel (high when the traversing system is in a delay and low otherwise); a number representing the state of the traverse is then recorded along with the sesnor outputs (See Appendix B for more on the assignment of recorded values to particular grid-points). 2.5 OTHER VARIABLES MEASURED In addition to the instrumentation already documented, a number of other variables were recorded in or near the model canyon. These included: the surface temperature of the open cement surface measured using a single arc thermocouple, the net radiation (L*0) of the open cement at 1m (Swissteco Model S1 net pyrradiometer), and wind speed at 1 m (MET-ONE Model 014A 3-cup 37 anemometer). Information on cloud cover and general surface meteorological conditions was obtained from the Atmospheric Environment Service (AES) records for the Vancouver International Airport Site. 2.6 TESTS 2.6.1 Surface Emissivity The Arnfield model requires values of surface radiative properties for each grid-point. Under the restriction of nocturnal conditions, the only parameter to be determined is the surface emissivity of the canyons walls and floor. Measurements were made using the procedure outlined by Davies et al . (1971) in which emissivity (e) is determined from e = (Tr4 - Tk4) / (Ts4 - Tk4) (2.1) where Tr is the apparent surface temperature measured directly by an infrared thermometer, cTr4 = eaTs4 + (1-e) Li (2.2) Tj,. is the radiative temperature of the sky, and Ts is the true surface temperature. This equation assumes that the emissivity is constant with wavelength and that the range of temperatures 38 is small so that the filter coefficients defining the fraction of radiation transmitted by the filter are equal (Davies et al., 1971). Temperature measurements were made using a Barnes Infrared Thermometer (Model PRT-4A) which has a bandpass filter of 8.0 to 14.0 Mm. The output from the thermometer was sampled every second and recorded as a voltage on a Campbell Scientific CR 21X digital recorder. Using a calibration curve determined previously (see Appendix C) the voltages were converted to equivalent blackbody temperatures. Estimates of T^ were made following the approach of Lorenz (1966) in which samples of T^ are taken from various zenith angles and azimuths to determine an overall value of T^. Measurements were made under 10/10 low to medium level cloud so that variation in T^ with zenith angle was minimized. Ts was measured by placing an aluminum cone with a polished inner surface over the concrete and taking a reading with the IR thermometer through an aperture at the apex of the cone. When the temperature of the cone is equal to the surface temperature, the cone changes the effective surface emissivity to unity so that it behaves as a blackbody; the second term of (4.2) disappears and Tr = Ts. Fuchs and Tanner (1966) have shown that the method is not sensitive to differences between the surface temperature and that of the inner surface of the cone . Measurements taken under cloudy conditions or at night minimize alterations in the surface radiative balance and Ts which occur when the cone is placed over the surface. Recording Ts 39 immediately after placement of the cone upon the surface, also minimizes errors. Davies et.al (1971) observed a period of 20 seconds when the surface temperature remained constant; for Fuchs and Tanner (1966) the period was 5 to 15 seconds at night. The experimentally determined values of surface emissivity are listed in Table 2.3. Table 2.3 Emissivity of Canyon Surfaces. Concrete Blocks Concrete Base n e s0 n e s0 13 0.964 0.015 47 0.954 0.017 The range of values for the emissivity of concrete published in the literature range from 0.71 - 0.90 (Oke, 1978), 0.85 - 0.95 (ASHRAE, 1981), and 0.98 Verseghy (1987). To determine if the emissivities of the blocks and base are significantly different a T-test between the two sample means was conducted at the 0.01 confidence level. The null hypothesis was taken to be no difference between the means. The T-statistic calculated was 1.96, which, at the 0.01 level of significance, results in the acceptance of the null hypothesis. 40 2.6.2 Surface Temperature Several tests to ascertain the precision and accuracy of the temperature measurements were made. Prior to the attachment of any thermocouples to canyon surfaces twenty arc thermocouples were tested in the laboratory. The thermocouples were carefully constructed using the method outlined in 4.2.1 to be as similar as possible. They were placed in a sealed cardboard box in the darkened laboratory temperatures sampled every 30 seconds and averaged over 10 minute intervals. The standard deviation after the first 20 minutes was less than 0.03°C. Next, a test of the precision of the surface temperature measurements was conducted on the open concrete surface of the site. Five arc thermocouples were attached to the concrete in the method described in 4.2.1. The surface temperature measured by the thermocouples is presented for selected times in Table 2.4. Table 2.4 Surface Temperature Precision Time T1 T2 T3 T4 T5 Tavg s range 1500 45.01 44.48 44.44 44.57 44.92 44.68 0.26 0.57 2245 23.95 23.90 24.03 23.90 23.77 23.91 0.09 0.26 0035 21.53 21.53 21.64 21.56 21.47 21.55 0.06 0.17 0425 19.33 19.33 19.38 19.31 19.24 19.32 0.05 0.14 41 The results indicate greater precision in the evening, primarily due to reduced radiation errors. Overall, adherance to careful mounting procedures appears to allow precise surface temperature measurements to be made using this method. A measure of the accuracy of surface temperature measurements was desirable both to confirm the accuracy of the mounting method and to overcome the limitation of the original study by Fairey and Kalaghchy (1982). Two separate validations of the surface temperature accuracy have been made (Figure 2.9). In the first, an aluminum cone was used to cover a group.of thermocouples attached to the open concrete surface and increase the effective surface emissivity to unity. The readings from an • IR thermometer taken from the apex of the cone were compared with the average surface temperature recorded from the thermocouples. The second method entailed rearranging equation (2.2) and solving it to find Ts: Ts = [(oTr4 - (1-e) / eo ]1 /4 (2.3) The experimentally determined emissivity of the concrete surface was used and L^ was measured by a miniature net radiometer equipped with a uni-directional cap over the lower surface. Tr was obtained from an IR thermometer mounted above the surface. The results in Figure 2.9 indicate that the first method slightly (0.5 °C) underestimates the arc temperature over the 42 20 -L 21 22 23 Surface Temperature (°C) 24 25 _i_ 26 Figure 2.9 validation, Surface temperature validation. Squares - cone triangles - radiative energy balance validation, 43 range of temperatures tested. The second method produced very good agreement. Earlier, it was stated that thermocouples were placed in the same relative position on each block in an attempt to prevent anomalies from surface temperature distributions due to the construction of the concrete blocks. Measurement of surface temperature distributions across the face of concrete blocks with no backing insulation on the walls (but painted white) revealed radiative temperature differences of up to 0.6 degrees in the early evening between portions of the brick which have a solid concrete core and over the hollow cell. The chosen placement of the thermocouples over the middle of the cell may therefore induce a biased underestimate of surface temperature relative to that sensed radiatively by a radiometer located above the surface. However, given the greater proportion of surface area underlain by a hollow cell, the choice is logical. The placement of insulation behind the walls may reduce the surface temperature changes over the block face, particularly for the west wall, since heating from behind the wall near sunset will be reduced. 2.6.3 Radiometer Distance Above Facet Given the differences in distances and of radiometer sizes used in the model canyon from those used in the analysis of Idso and Cooley (1972), tests were conducted to determine if any surface temperature gradient induced by the presence of a 44 radiometer placed close above the surface could be detected. A worst-case scenario was constructed: the miniature and full-size net radiometers were placed close to the surface over an open site for an extended period under cloudless sky conditions, and surface temperature transects were taken using a narrow-view IR thermometer. Even using the full-size radiometer no changes were detected. Within a canyon the effect is small because the \ps for points is already very much reduced and the differences in radiative temperature between the radiometer and canyon surfaces are minor. High surface emissivities mean that even minor changes in the incident flux result in surface temperature changes which are sensed by the radiometer, because the long-wave reflectivity of the surface is low. The greater area viewed by the radiometer when compared to the narrow view IR thermometer used to search for surface temperature changes will decrease the effect of any change occurring in a small area. Therefore, the use of miniature net radiometers offsets to some degree the reduced incurred by using lower traversing heights. Continual traversing of the radiometers probably renders any effect negligible. 2.6.4 Traverse System Tests of the CTS were performed to determine if the delay interval or traverse speed (Appendix A) are appropriate under field conditions. 45 Confirmation of the delay interval can be easily accomplished by plotting the instrument output from the radiometer after a rotation has occurred and while the CTS is in a delay mode. If the trace indicates little or no change by the end of the delay interval, then the length of the delay is adequate. The step change in radiation between facets will be most clearly evident as the instrument traverse changes to and from the canyon top because of the contrast between the sky and canyon temperatures. Figure 2.10 illustrates the nature of the change in radiation measured after these rotations. To test if the radiometers accurately measure the changing radiation while traversing, a single net radiometer was set in a fixed postion over a canyon facet and the readings compared to those of the traversed instruments as they passed the point. The fixed radiometer may be considered to give the 'best' estimate. By necessity, the fixed radiometer was offset from the track of the traversed radiometers so that the areas viewed by the two instruments differ slightly. Table 2.5 summarizes the results of these tests completed using this method and Figures 2.11 - 2.14 show plots of the fixed radiometer output (open circles) and the traverse data (crosses). The error bars on the traverse data are the standard deviations from the average value for all samples taken within the grid-point boundaries of the point being tested. The error bars for the fixed radiometer data represent the standard deviation from the average value over the time taken for the traverse. The fixed radiometer output is a one minute average, thus the standard deviations are generally 46 420) E 5 O 400 f O QL a > § 380 f I •> c o D 360 f 340 Sky-to-wall transition Woll-to-sky transition —B —a 10 15 Time From Start of Delay (s) 20 25 Figure 2.10 Change in long-wa instrument rotates to and from at the canyon top, LQ from the ve radiation measured as the the canyon top. (L{ is measur walls). 47 39S 398 400 402 404 406 408 L. (W m-») 410 400 405 410 L» (W rn"*) 415 Figure 2.11 Tests between a fixed (crosses) and traversed (squares) radiometer for Lo at point 8 on the West wall. Error bars are standard deviations of all samples taken over each grid-point during the traverse. 48 to • l—6—' 9 -a— * B i B—i • * 7 c e 6 <—B—i Point S i B-—I Foei 4 • • • < 3 2 i i 1 1 i • i 400 404 408 412 L. (W m-*) 10 • -B-• • i 8 i-e-i 6 4 i-e-i 2 ©1 390 395 400 405 410 L. (W m-») 415 10 - -B-i i—e-8 I-B-I 6 4 t-B-2 I • i •&< 390 395 400 405 410 415 «, (W m-») Figure 2.12 Tests between a fixed (crosses) and traversed (squares) radiometer for LQ at point 3 on the West wall. 49 small. The large error bars for the traversed instrument, result from noise in the data, the origin of which is discussed in Appendix B. No filtering of the data was performed in this analysi s. Table 2.5 Summary of Fixed Versus Traversed Radiometer Tests. Date Time Facet Point Flux Figure July 20/21 0100-0230 3 7 L* 2.13 3 4 L* 2.14 July 21/22 0100-0300 1 8 L0 2.11 1 3 LQ 2.12 The comparision between the fixed and traverse estimates of L0 for Wall A (Figures 2.11, 2.12) indicate a slight overestimate by the traversed radiometer. The test for grid-point 3, which involves a greater length of traverse also indicates an overestimate of between 2-3 W m~2. Given the direction of traverse (towards the base of the wall), and the expected distribution of radiation during this period of the evening (see Figure A.1), the tests do not produce evidence of a lag in the sensor response. A lag in response to a ramp change (Figure A.2) would produce a lower value for the traversed sensor compared to the fixed radiometer whereas the tests indicate the opposite. It is possible with point 3 that an S-shaped distribution of radiation (as illustrated in A.1) could produce an overestimate of the flux density as the traversed instruments lag in their response to the decreased change in LQ. 50 4 5 6 7 Facet Point on Floor 8 9 4 5 6 7 Facet Point on Floor 4 5 6 7 Facet Point on Floor Figure 2.13 Tests between a fixed (crosses) and traversed (squares) radiometer for L* at point 7 on the canyon floor. 51 2.0 2.5 3.0 3.5 4.0 • Facet Point on Floor 4.5 5.0 2.0 2.5 3.0 3.5 4.0 Facet Point on Floor 4.5 5.0 2.0 2.5 3.0 3.5 4.0 Facet Point on Floor 4.5 5.0 Figure 2 14 ^Tests between a fixed (crosses) and traversed (squares) radiometer for L* at point 4 on the canyon floor. 52 The chances of this occurring at point 7 are much less. It is more likely that the results are due to: (a) minor differences in the angle of the two radiometers relative to the surface they view and/or (b) the offset of the fixed radiometer from the line of traverse. Comparison of L* between the fixed and traversed radiometers (Figures 2.13 and 2.14) shows negligible differences between the two instruments. Unfortunately the large standard deviation of the net radiation from the traversed radiometers detract from the test. A final test conducted prior to data collection was the use of the CTS in manual mode rather than automatic mode. The results from this test are described in Chapter 4. 53 CHAPTER 3. THE ARNFIELD MODEL 3.1 INTRODUCTION The numerical model selected for validation is that described by Arnfield (1976, 1982), referred to hereafter as the Arnfield model. The model can be used to calculate estimates of the radiation budget components at all surfaces within the unit of an urban canyon, including the canyon top, for a given geometric configuration and distribution of surface materials. Using view-factor geometry and the assumption that canyon facets are Lambertian reflectors, multiple reflection events are included in the modelling methodology. Table 3.1 lists the radiation budget components which may be calculated using the model, various options available, and the necessary input fluxes. Only a brief account of the model is presented here. For a more complete explanation of the computational methods, refer to Arnfield (1976). This chapter describes the framework of the model, it's implementation and the required input data. Modifications made to the original model are described. Sensitivity tests to the major input parameters are presented in Section 3.5. 54 Table 3.1. Components of the Radiation Budget Calculated in the Arnfield Model with Options and Required Input Fluxes. Calculated Options Required Input Absorbed Global isotropic dist. of Solar Radiation diffuse solar overcast sky radiance distribution of Steven and Unsworth (1980) clear sky radiance distribution of Steven and Unsworth (1979) isotropic radiance distribution radiance distribution of Unsworth and Monteith (1975) Long-Wave Rad. from the sky Long-Wave Rad. at a canyon facet Long-wave rad. emitted by canyon facets Net All-Wave Radiation standard irrad. of direct solar standard irrad. of diffuse solar std. irrad. of long-wave rad. std. irrad. of long-wave rad. std. irrad. of long-wave rad. 3.2 MODEL FRAMEWORK In the model, an urban canyon is represented as an infinitely long, rectangular space bounded by walls of height 'H' and a floor with width 'W' (Figure 3.1). This permits a simplified representation of the urban surface as a series of urban canyons separated by roofs of width 'R' apart (Arnfield, 1982; Sievers and Zdunkowski, 1986). For the purposes of the present 55 Figure 3.1 Canyon coordinate system. The facet and point numbering conventions are taken from Arnfield (1976, 1982) and are: West wall - Wall A or IF 1, East wall - Wall B or IF 2, Floor - IF 3, Top - IF 4. Points are numbered upwards on the walls from IP 1 (base) to IP 10 (top). Points on floor and top are number in increasing order from wall A (IF 1) to wall B (IF 2). 56 validation, only a single canyon is modelled and the roof area is not incorporated. The canyon is aligned at an azimuth 0 (0 = 0 or 360° for the model canyon) from North and the walls identified as A and B. Wall A is defined as that which would be irradiated by a point source located at an azimuth a, such that 0 < a < (0+7r). In the model canyon constructed, Wall A is synonmous with the West wall or IF 1 (Facet number 1) (the wall with the inner surface oriented East). Wall B is the East (or West-facing wall), and has a facet number of 2. Where possible, the walls will be referred to as East and West, even though directionality may be of no consequence, as in most of the sensitivity tests. Points within the canyon may be uniquely identified by means of a coordinate system in which x denotes distance along the canyon axis from the origin at canyon mid-length; y and y' represent distances across the canyon floor (IF 3) and top (IF 4) measured from wall A; and z and z'are the vertical coordinates measured upwards on walls A and B respectively. Figure 3.1 also illustrates the facet and point numbering convention utilized by the model. Geometrical and radiative properties are assumed invariant in the along-canyon dimension. Values for the emissivity and albedo of canyon materials are assigned to individual grid-points and therefore represent infinitely long horizontal strips running the length of the canyon floor and walls. 57 3.3 MODEL IMPLEMENTATION The Arnfield model consists of a set of four FORTRAN subroutines, called by a user-written main program which defines constants, initializes variables and arrays and performs the necessary input/output operations. Table 3.2 lists the subroutines and briefly describes the purpose of each. One of the input data files contains measured values of L0 and L* for specified canyon points. Using information for a point which has been validated for a particular averaging period, the main program outputs the date, time, facet and point numbers, and measured and modelled data for the point. Table 3.2 Arnfield Model Fortran Subroutines Subroutine Name Function CARABU CAnyon RAdiat ion Budget RADIOS RADiat ion on Inclined Obstructed Surfaces CNRDF2 CaNyon RaDiation version 2 SIMPS SIMPSon's rule integrat ion Main subroutine: other subroutines are called from CARABU. Uses input data to determine the canyon rad iation budget. Calculates view factors if required. A general routine to calculate the irradiance on a plane of given orientation (from both the upper and lower hemispheres), including obstructed and unobstructed port ions. Calculates multiple exchanges of radiation within the canyon. Performs Simpson's rule integra tion of a function defined by a table of equi-spaced values. 58 Model input is described in Appendix E, Table E.1. Two cases require approximations to be made to the model theory. The first is the assumption of an infinitely long canyon. The theoretical limit of infinity is replaced by the canyon half-length, measured from the canyon midpoint to one end; (i.e. one half the total canyon length). The second approximation concerns the upper limit of integration for multiple reflections within the canyon. In this instance, a critical value for the difference between successive calculations of the flux leaving the canyon top is specified by the user; when the difference falls below the set value, iterations cease. The model has been implemented on a personal computer (IBM-Compatible PC-AT 286) using WATFOR-77 (Coschi and Schueler, 1985). Compile and execution times for the model using a nocturnal data set with an isotropic radiance distribution are presented in Table 3.3. Table 3.3 Approximate Compile and Execution Times for the Arnfield Model Using an Isotropic Radiance Distribution. Computer Compile Time Execut ion Times (sec) (sec) First Subsequent Point Points IBM PC AT-286 12.2 68.6 4.4 8087 equipped 59 When the Unsworth and Monteith (1975) radiance distribution is used, compile times are similar and execution times are equivalent to the first point of the isotropic runs when the optical water depth, u, changes. 3.4 MODIFICATIONS TO THE ARNFIELD MODEL A number of modifications have been made to the Arnfield model to ensure it matches the set up of the scale canyon as closely as possible, especially when the surface temperature measurement locations do not represent a regular grid. The Arnfield model implicitly requires that the locations of the surface temperature measurements be at regular intervals across each facet. The number of grid-points was set equal to the dimension of the facet and the points distributed at equal intervals across it. The height and width are only related to the actual dimensions of a canyon through the H/W ratio and have no meaning on their own. Figure 3.2 illustrates the regular grid pattern assumed by the Arnfield model (crosses) and how the scale canyon deviates from it (dots). The addition of the capping blocks on the tops of the walls upsets the regular grid established over the remainder of the bricks. The additional height from the capping block also causes the grid spacing on the canyon floor to be slightly different from that on the walls. To overcome the irregularities imposed by the sampling grid of thermocouples, a number of changes were made to the model, primarily affecting 60 -* *r- -* —*- "* X * *-^n^L Z^llt^ll^^^ Tid pattern 61 the specification of the height, width and canyon view-factor arrays. 3.4.1 Canyon Height and Width Canyon height and width can no longer be directly tied to the spacing of grid-points as in the-original model formulation. In the modified model, an integer parameter for the height and width is specified to control the number of grid-points to be used for the canyon facets. A second constant is set within the CARABU subroutine to represent the actual canyon height and width for use in subsequent view-factor and geometry calculations. Finally, to address the change in grid spacing between the floor and walls, the grid-point 'coordinates' are read in from an external file. These are distances measured upwards from the floor for the walls, and across the canyon from wall A for the floor and canyon top. The units of the coordinates are arbitrary, but must be consistent with the values specified for the canyon height and width. 3.4.2 View-Factors Additional view-factor arrays are dimensioned for the specification of within-canyon view-factors. Due to the difference in spacing of points on the walls and floor, view-factor relationships between pairs of perpendicular facets are no longer reciprocal as assumed in the original model; (the 62 reciprocity between parallel facets is maintained). All canyon view-factors have been calculated using equations for an infinitesimal surface element parallel and perpendicular to a plane of given length and width (height) derived using Nusselt's "Unit Sphere Method" (Siegel and Howell, 1972; Steyn and Lyons, 1 985). The view-factor \p, for an element perpendicular to a plane surface from a point located at x=0 (canyon mid-length) is ^p 0,y = (1/2TT) [2tan"1A - Btan"1C] (3.1) with A = b/2y B = 2y/(h2+y2) C = b/2(h2+y2) where y is the distance perpendicular to the element, b = total length of the plane element, and h = height of the plane element. The subscript p denotes the view-factor of the plane element. Perpendicular view-factors for each grid-point are determined by calculating the view-factor of the partial height of wall determined from the sum of grid-point heights up to and including the point of interest and then subtracting the view-factor for the partial height of wall determined by all grid-63 64 points located below the point of interest. For example, the view-factor of grid-point 8 on wall A for a point on the floor is calculated using (1) with h equal to the sum of grid-point heights from point 1 to 8 and subtracting the view-factor calculated using h set to the sum of heights of points 1 to 7. In mathematical notation, this procedure may be expressed as j J-1 <//(j) = ^ I gpht - </> I gpht (3.2) gp=1 gp=1 where the view-factor of grid-point j (\Mj)) is calculated from information on the grid-point height (gpht) for each grid-point (gp). For an element parallel to a plane surface element, 0,y = (1 /2ir) [D(2tan~1E) + F(2tan~1G)] (3.3) with D = l/(l+y2/h2) E = (b/2)/(y2+h2) F = {1/ti+y2/(b/2)2]} G = h/[y2+(b/2)2] 65 and y is again measured perpendicular from the plane element. For a grid-point directly opposite, h is set at one-half the grid-point height and the view-factor is multiplied by two. For points above or below the point of interest, a method similar to that employed in the perpendicular view-factor calculation is used. (See Figure 3.3). 3.4.3 Additional Grid-Points The additional area which the capping blocks add to the regular grid of thermocouples on the walls may be accounted for in one of two ways. The area may be added to that represented by the tenth grid-point of each wall. In this case, the temperature measured at this point would represent the area from the top of the wall to a point midway down the topmost hollow concrete block. The second method is to maintain a regular grid for the ten thermocouples and create an eleventh 'fake' thermocouple located at the mid-point of the extra area added by the capping block. Since no measured temperature is available for this point, it must be estimated by some means. Each method has advantages and disadvantages. The first scheme does not require the estimation of a surface temperature, but increases the area which the tenth thermocouple represents, in an area where relatively high temperature gradients are expected. Given the facet temperature distributions of 6.2.2 the addition of the capping block area to grid-point 10 would result 66 in a bias towards over-estimation of the temperature for the grid-point area. Sensitivity tests of surface temperature (Section 3.5.2) indicate errors in the specification of surface temperature for corner grid-points would result in model errors at the point in error and at the first point on the plane of the canyon top where the view-factor for the tenth point on the walls is significant. Effects on other points would be minor. Representing the extra area by the addition of an eleventh point allows the measured temperature at the tenth grid-point to represent the same area as all the other points on the walls. Since the added point is never validated on its own, errors in the estimation of the temperature for the point would only be reflected in the validation of points on the canyon top nearest the walls. The disadvantage of having to estimate a temperature for the additional point is offset by the advantage that no further errors will be incurred in the temperature representation of the tenth point. The net effect should be that the addition of an eleventh point will reduce the number of points in error from two to one. An added advantage of the second method is that the traverse path includes the tenth grid-point on the walls but not the first or last point on the canyon top. This is a result of the arc necessary for the radiometers to turn between facets and the added height of the capping block on the walls. Thus, those points which will incur the maximum error due to the addition of an eleventh point on the walls are not included in the traversed 67 data. Given these advantages, the method of creating an extra grid-point on the walls was selected. Procedures for estimating the temperature of the eleventh point are described in Appendix B. 3.5 SENSITIVITY TESTS 3.5.1 View-Factors/Grid-Points Radiation estimates within complex geometric settings are strongly dependent upon the accuracy of view-factor calculations. Within the Arnfield model, view-factors are defined for pairs of canyon facets and stored as arrays. Each grid-point on a canyon facet has a view-factor associated with every grid-point on the associated paired facet. Each point represents an area, which increases or decreases as the density of grid-points decreases or increases. For a canyon of given dimensions, a higher density of grid-points will result in a greater ability to resolve the radiation balance of the surface. During daytime this becomes important as shadows extend across the canyon facets. The Arnfield model provides for the calculation of canyon view-factors internally, or as an option, to be read in from an external file. A number of tests have been conducted on the sensitivity of the model to the number of grid-points (Arnfield, pers. comm., 1987). Having substantially altered the view-factor calculation 68 procedure and the grid-point structure of the canyon, several tests were repeated for the model as initialized for the experimental canyon. The tests are designed to illustrate the model response to a set of input conditions for which the theoretically true value is known. Table 3.5 Test 1 of Model Sensitivity to the Number of Model Grid-Points. This test calculates Lc (W m~2) at the canyon top for the following model input parameters: Lict: 100 W m 2 Surface Temp.: 283 K Distribution: isotropic Surface Emissivity: 0.0 Expected Result: L0 = 100 W m~2 Original Scale Canyon Min. Canyon Dimension Lo Lo 10 104.2 99. 1 20 102.3 n/a 50 100.1 n/a 100 99.7 n/a Table 3.6 Test 2 of Model Sensitivity to the Number of Model Grid-Points. Model Input Parameters: L^: 363.7 W m~2 (equiv. black body emittance at 283 K) Surface Temperature: 283 K Distribution: isotropic Surface Emissivity: 0.5 Expected Result: L* = 0 W m~2 Min. Canyon Dimension Original L* Scale Canyon L* 10 -8.7 1 .3 20 -4.6 n/a 50 -1.6 n/a 100 -0.8 n/a 69 The results in Tables 3.5 and 3.6 indicate a significant difference between the two canyon models. The only major changes made in the model were the view-factor specification and the addition of the eleventh grid-point on the walls. Each of these may affect estimates of the fluxes at the canyon top. For a strict comparison of model output as it varies with the method of calculating view-factors, Test 1 was repeated first using the default view-factors calculated by the program for a 10 by 10 canyon, and secondly using the view-factors calculated from the equations provided by Steyn (1987 pers. comm.). Table 3.7 Test 1: View-factor Comparison. Grid-points Default Nusselt View-factors Sphere LD (W m~2) 10 104.2 98.6 (Average over 20 102.3 99.4 top; W m 2) The results in Table 3.7 and Figure 3.4 support the hypothesis that the method of calculating the view-factors is the major difference in the tests. The plots of Figure 3.4 are designed so that the axes represent the canyon facets, with the scaling of the data performed automatically, given the range of data input. Therefore, scaling varies between facets and between plots and reference to the scales is necessary to avoid visual mis-interpretation. Note the difference in LQ between the Focet Point: Top Lo Focet Point: Floor Lo S c o ^ u rn " 0.0 ~i—i—r 2.0 I 4.0 Focet Point: Top 123456789 AAAAAAAAA -ftl—y y—^—y y—^—^—^ 3 4 5 6 7 8 Focet Point: Floor 9 10 5.0 ^ 1 3.0 L. in. 1.0 Figure 3.4 Test 1 of model sensitivity, circles - original model view-factors, triangles - Nusselt Sphere view-factors. Fluxes in W m~. 71 original and the modified models is greater in each case than the difference between the two modified models. As further comfirmation, the test was repeated for a 20 x 20 unit canyon. The increase in accuracy due to the added grid-points using the externally read view-factors is less than that achieved when using the default view-factors provided within the program. The apparent discrepancy in the results due to the view-factor calculation method has been explained by Arnfield (1988 pers. comm.) as resulting from the finite difference approximation of the flux (Q) travelling from one grid-point to another Q = (NT COS^ cos/32 AT A2) / r2 (3.4) where 0^ and 02 are the angles between the perpendicular to each grid-point, the A's are the areas associated with the grid-point, r is the length between the points and N the radiative flux. In cases where r is not a good representation of the paths which radiation may take between the elements errors increase. This occurs when r is small. In the view-factor arrays, r reaches a minimum in any pair of perpendicular canyon facets, where two grid-point areas adjoin; ie. the corner elements. The errors in the corner elements are shown clearly in Figure 3.4 which displays the entire Test 1 results for the original and modified models. The results indicate the modified model tends to underestimate L0 and in corner elements. Table 3.8 illustrates the differences in the view-factors calculated using 72 the two calculation methods for grid-points on wall A for the grid-point on the floor nearest wall A. Table 3.8 Comparison of View-factor Calculations: Wall A/Floor. Point on Wall Arnfield Model Nusselt Sphere Difference (Percent) 1 • 0.35355246 0.27639282 21 .8 2 0.09486705 0.10233772 -7.3 3 0.03771256 0.03906620 -3.5 4 0.01979602 0.02017921 -1.9 5 0.01211674 0.01226169 -1.2 6 0.00815845 0.00822449 -0.8 7 0.00585961 0.00589380 -0.6 8 0.00440878 0.00442821 -0.4 9 0.00343535 0.00344712 -0.3 10 0.00275088 0.00275850 -0.3 The adverse effect of using the model calculated view-factors was offset by using a greater number of grid-points per facet (note the increased accuracy in the tests of Tables 3.5 and 3.6 as the number of points is increased). The over-estimation that results from using this method of calculation also compensates for the under-estimation arising from the truncated number of multiple reflections allowed (Arnfield, 1988 pers. comm.). The advantage of using the view-factor equations derived from the Nusselt Sphere method is higher accuracy at lower grid-point resolutions. Repeating Test 1 with a higher grid-point density with this method provides only a slight increase in accuracy (Table 3.7). It is concluded that both methods of calculating the view-factors suffer from inaccuracies when the elements are close together, but the equations derived from the Nusselt 73 Sphere Method are better than those available in the original program code. 3.5.2 Surface Temperature Surface temperature measurements are the most numerous of the input parameters to the Arnfield model and thereby constitute the greatest possible source (numerically) of measurement error. At night, under clear and calm conditions, surface temperature is the dominant control of the surface radiative balance. Successful modelling of the radiative balance within the canyon under these conditions will require accurate measurement of the surface temperatures. The objective of the temperature sensitivity tests is to examine the effect of differences in measured surface temperature from the 'true' value upon model output for the long-wave radiative fluxes. Variations in measured surface temperature may arise due to differences in the attachment of individual thermocouples to the canyon facets. These errors may be local, affecting only a few isolated thermocouples, or more general, resulting in an overall under- or overestimation of the surface temperature. The sensitivity tests of surface temperature have been designed to cover both scenarios. Model parameters for the temperature sensitivity tests were set as follows: Incident long-wave radiation at the canyon top 74 was set at 363.7 W m~2, the equivalent blackbody radiation for a surface temperature of 283K. The experimentally determined emissivities for the floor and walls were used. RSTOP, the convergence criterion for the canyon multiple reflection routine, was set at 0.0333. Since it is called up to three times the total error resulting from the multiple reflection process should be less than 0.1 W m~2. This is low enough not to be a limiting factor. The surface temperature input, was varied in the following ways: (1) the surface temperature was fixed at 283K for all facets (the control run) (2) the surface temperature of a single point on a wall was varied (IF 1,IP 5) to determine the effects on the modelled values at all other points (3) the surface temperature of the extrapolated point on the walls (IP 11) is increased to determine the sensitivity to the estimation of this temperature (4) the surface temperature of a point on the floor was varied in a manner similar to (2) (5) all surface temperatures were increased equally to investigate the effects of a general over-estimation. Figure 3.5 presents the output of the model control run. The values of LD vary between 363.8 and 363.6 W m~2 for points on the canyon walls (data for the eleventh point are omitted). For points across the top L0 is constant at 362.8 Wm~2. The values of vary slightly from point to point; this is attributed to Focet Point: Top Facet Point: Top Figure 3.5 Model control run. Fluxes in W m 76 the manner in which the view-factors have been calculated. The behaviour of L* is affected by the instability in the values of L^. In the other comparisons of model output, only the differences from the control run are tabled. Figure 3.6 illustrates the results of increasing the surface temperature at the mid-point of the West wall. The calculated differences indicate major increases in the model output of LQ at the point at which the surface temperature was increased, a result which is to be expected. A secondary area of influence is found across the canyon top where LQ values are increased slightly. Minor variations in the modelled fluxes occur at points on the wall opposite the affected point and on the floor, resulting from multiple reflections. increases slightly for points on the floor and near the top of the East wall. L* becomes negative across the top in accordance with the increase in the LQ and positive in response to increases in L^ for the floor and wall B. Figure 3.7 presents the results when the temperature of point 1 (IP 1) on the floor is increased. Again, the major increase in LQ is at the point of the anomaly, with minor increases across the canyon top, especially towards the East wall, and at the . point on the floor nearest the affected wall. L^ is increased strongly for the points on the floor adjacent to the West wall. Increases are also noted for the lower portions of the opposite wall. L* increases positively for the opposite wall and the floor and decreases across the canyon top. 77 Facet Point: Top Surface Temperature Increased By. O 0.2 K A 0.5 K + 1.0 K X 2.0 K O 3.0 K • 5.0 K Figure 3.6 Sensitivity of modelled fluxes to surface temperature changes at point 5 on the West wall (IF 1, IP 5) Differences (W m~2) from a control run with TS=283K. 78 Facet Point; Top 0.0 10.1 20.2 1 2 3 4 5 6 7 8 9 10 0.1 0.0 0.0 Lo Focel Point: Floor Lo Focet Point. Top Surfoce Temperoture Increased By: O 0.2 K A 0.5 K + 1.0 K X 2.0 K «• 3.0 K • 5.0 K Figure 3.7 Sensitivity of modelled fluxes to surface temperature changes at point 1 on the West wall (IF 1, IP 1). Differences (W rn"2) from a control run with TS=283K. 79 Maximum errors resulting from an overestimate of the extrapolated surface temperature of IP 11 on the West wall are shown to occur for and L* at the top of the opposite wall and for LQ and L* at the canyon top adjacent to the affected point. The errors are localized and are less than 3.0 W m""2 for a 5 K increase of the extrapolated point. It would therefore appear that the model is not unduly sensitive to the method by which the temperature of the extra points is obtained. The temperature of a single point on the floor (IP 5) has also been varied in an analogous manner (Figure 3.9). The largest differences in L0 again are observed directly over the increased surface temperature with a slight indication that small increases are present for some other points on the walls and floor due to multiple reflections. The major difference observed between this test and that for a point on a wall is the difference in L0 observed across the canyon top. The increases in LQ at the canyon top over the control run are approximately 50 to 60 percent greater for the floor case. A significant increase is observed at the canyon top even for a 1 degree increase at a single point on the canyon floor. Increases in are noted for both walls. As a result, L* exhibits a greater decrease across the top. Model results obtained from an anomolous temperature located on the floor next to the West wall (IP 1) are presented in Figure 3.10. The location of maximum differences for LQ and L* on the canyon top shifts westard. Points low on the West wall Focet Point: Top 3. 4 5 6 7 8 9 10 + * * ^ ' O 0.2 K 1 23456 789 10 Focel Point: Floor Surfoce Temp«roture Increosed By: A 0.5 K + 1.0 K X 2.0 K «. 2.0 K Figure 3.8 Sensitivity of modelled fluxes to «„rfa« D^rencel (5'S9!? f P°lnt 11 °" theWeVSalT mrxerences (W m from a control run with TS=283K. 81 l i Focet Point: Floor I; Focet Point: Top Focet Point: Top ) 23456789 10 -Surfoce Temperature Increased By: O 0.2 K A 0.5 K 4- 1.0 K X 2.0 K « 3.0 K *• 5.0 K Figure 3.9 Sensitivity of modelled fluxes to surface temperature changes at point 5 on the canyon floor (IF 3, IP 5). Differences (W m 2) from a control run with TS=283K. 82 Focet Point: Top Surfoce Temperature Increased By: O 0.2 K A 0.5 K + 1.0 K X 2.0 K © 3.0 K • 5.0 K Figure 3.10 Sensitivity of modelled fluxes to surface temperature changes at point 1 on the canyon floor (IF 3, IP 1 Differences (W m~2) from a control run with TS=283K. 83 and towards the top of the East wall exhibit the greatest increase in and L*. The sensitivity tests of increasing a single grid-point temperature produce results easily explainable in terms of the view-factors of the grid-point. The most noticeable change is the increase in emittance, and hence decrease of net radiation, for the point modified. Differences in the radiative fluxes at other points are directly related to the view-factor of that point for the affected point. Increases in long-wave radiation at a point result in an increase of reflected long-wave for the point, although this effect is damped somewhat by the high values of emissivity of the canyon materials. Any increase in the temperature of a grid-point for the tests results in an increase in the flux leaving the canyon top and therefore decreases the net radiation. Except at the point of change, differences in L* on the floor and walls are controlled by and by L0 across the canyon top. Consider now the effect upon the model output if a general increase or decrease were to affect all temperature measurements. Figure 3.11 illustrates the differences from the model run when the surface temperature of all points within the canyon is increased by an equal amount. The temperature was increased by 0.2,0.5,1,2,3, and 5 K above that of the control run. The results show that the modelled values of Lc will increase more or less equally for all points within the canyon. For a temperature increase of 0.5 K the increase in LQ is 2.5-2.6 W m~2; with a temperature increase of 1 K for all points the 84 3 4 5 6 7 8 Focet Point: Floor 21 .9 .„-<><, 1 .0 -*i—«r M .0 Lo 21 .1 Focet Point: Top 3 4 5 6 7 8 10 o> 4—t—t_ -* 4--4--4—•—*— r\j _ rn -I 1 1 1 1 1 1 1 1 -ts—©—©— "p 8- s e e i 3 4 5 6 7 8 9 Focet Point: Floor 10 26 2 '""oo | UJ <>tht£> ~ C o •*(>-_ 16.1 Lo 6.0 Focet Point: Top 1 2 3- 456 789 !0o 8-888888886 o 0.2 K 1 1 1 1 T—=1 1 1 1 I 23456789 10 Focet Point: Floor Surfoce Temperoture Increosed By: 0.5 K + 1.0 K X 2.0 K o 3.0 K • 5.0 K Figure 3.11 temperature control run Sensitivity of modelled fluxes to equal surface changes at all points. Differences (W m 2) from a with TS=283K. 85 increase is 5.0-5.2 W m~2; an increase of 2 K boosts L0 values by 10.2-10.3 W m~2. values are increased, particularly for the lower portions of the walls, due to the effect of multiple reflections. L* decreases across the canyon top, near the tops of the walls and in the centre of the floor. 3.5.3 Radiation To determine the effect of variations in measured at the canyon top upon modelled values of LQ at all other points, a sensitivity test was conducted holding the surface temperature fixed at 283K for all facets, setting the emissivity at the experimentally determined values and increasing from 363.7 W m-2 (the control) to 383.7 W m~2. As before, RSTOP was set at 0.0333. Figure 3.12 presents model output for LQ, L^, and L* when increasing at the canyon top by 1, 2, 5, 10, 15 and 20 W m~2. Incoming radiation changes in accordance with i/>s; the largest increases are seen for the tops of the walls and in the middle of the canyon floor. The differences in L0 are minor, even for increases of 15 and 20 W m~2. A trend towards slightly higher values towards the tops of the canyon walls is noted, mirroring the increase in . The increase over the canyon floor is smoothed out, likely due to the multiple reflection process. With lower values of emissivity greater differences may occur due to increased 86 1 2 3 4 5 6 7 8 Focet Point: Floor 10 Focet Point: Top I 1 1—T 123456789 10 0.4 0.2 0.0 Focet Point: Floor lo Focet Point: Top 1 23456789 10 f -4--4--4—+- —•— -4—-«= =*= =*=#= ft ft ft 1 23456789 10 Focet Point: Floor 8.9 O to Lw Increased By: A 2.0 ' + 5.0 X 10.0 « 15.0 • 20.0 (W m*) Figure 3.12 Sensitivity of modelled fluxes to LiCf Differences (W m~2) from a control run with TS=283K. 87 reflection of L^; the effect of emissivity is considered in the next section. The changes in L* are dominated by the changes in Lj and follow the patterns outlined above. 3.5.4 Emissivity Variations exist in the measured values of emissivity for both the concrete blocks used in the walls and the concrete surface of the site (see Table 2.3 for the data on measured emissivity). An average of these values is used in the model. While the standard deviations of both the concrete surface and canyon block is near 0.02, the range of values measured is much higher. The outgoing flux density of long-wave radiation from a surface may be expressed as LQ = eaTs4 + (1 - e)Li. (3.5) Note that the emissivity appears twice in the equation in an opposing fashion. If were to exactly balance LQ at a point the emissivity would have no net effect (as in the conditions for Test 2). Under radiative cooling conditions, the first term of (3.5) will exceed the second so that as the surface emissivity decreases the long-wave emittance will decrease. The sensitivity of modelled radiation to values of surface emissivity was tested by using a two sets of measured input data from a clear, mostly calm evening (Aug. 3/4; H/W=1.0). The first is from the early evening (approximately 0.5 h from sunset), when surface temperatures are relatively high and the second is late at night (6 hours after sunset). Three emissivities were tested (all canyon facets are assumed to have equal values of e), 0.96, the control run, 1.00, and 0.90. These correspond to the measured e ± 0.06 which is the probable error calculated for e (Appendix D). The differences from the control run are plotted in Figures 3.13 (early evening run) and 3.14 (late evening). As expected, LQ increases with e due to the increased emittance of the surface. The incident radiation for points within the canyon also increases due to the increase of the portion of the long-wave irradiance derived from other canyon facets. This increase is largest for points with a low sky view-factor; near the tops of the walls and at the mid-point of the floor it is a minimum and causes larger L0 values despite lower surface temperatures. L* is decreased for all points excepting the bottom portions of the walls where a slight increase is noted (Figure 3.14). Errors in correctly determining facet .emissivities will be largest in the early evening when surface temperatures are high and the first term of (3.5) dominates. As the canyon cools, assuming constant meteorological conditions, the difference will lessen and errors due to emissivity. will decrease. Maximum differences of ±3.0 W m~2 are observed in the early evening for LQ and L* across the canyon top and LD for points near the tops of the walls.. 89 Focet Point: Top 123456769 10 Figure 3.13 Sensitivity of modelled fluxes to e, differences (W m-2) from a control run of e=0.96. Circles - e=0.90, triangles - e=1.00. Surface temperature distribution used is typical for the early evening. Focet Point: Top Figure 3.14 Sensitivity of modelled fluxes to e, differences (W m~2) from a control run of e=0.96. Circles - e=0.90, triangles - €=1.00.. Surface temperature distribution used is typical for the late evening. 91 3.5.5 Radiance Distribution The Arnfield model provides two sky-derived long-wave radiance distribution options (Table 3.1), that of Unsworth and Monteith (1975), Lp = [c + b ln(u sec/3)] TT"1 (3.6) and an isotropic distribution = (3.7) Previous modelling of the canyon long-wave reflection coefficent (Arnfield, 1982) has compared the two distributions and found the results to be insensitive to the distribution used. Verseghy (1987) also found isotropic radiance distributions to incurr only minor errors. As a guide to the magnitude of changes in the radiative fluxes which may result using the Unsworth and Monteith (1975) radiance distribution, Test 2 was repeated for optical water vapour depths of 0.83 and 4.21 (corresponding to the saturation vapour pressure values at 0 and 25°C respectively). The differences from the isotropic results are plotted around the canyon cross-section in Figure 3.15. The variance of the radiance distribution with zenith angle is evident in the results. Points at the top of the walls show a large increase in over the isotropic distribution since they view low zenith angles of the sky. At the canyon base, only large zenith angles are viewed and a decrease in Lj from the control results. Across the floor a decrease in L^ is observed which is strongest at mid-canyon, again in accordance with the ^s of the point. The Facet Point: Top Focet Point. Top Figure 3.15 Sensitivity of modelled fluxes to radiance distribution used. Differences (W m~2) from an isotropic distribution using the Unsworth and Monteith (1975) radiance distribution with u=0.83 cm (triangles) and u=4.21 cm (circles) 93 pattern of LQ follows that of and is made evident by the relatively low value of emissivity used in this test. The average value of L* across the canyon top is very close to 0 with the decrease near mid-canyon offset by the increase near ythe edges. A difference of approximately 1.2 W m-2 from the average L* of Test 1 (Table 3.6) is noted. The variation between the values of u employed indicate greater differences from the isotropic control run as u (and therefore surface vapour pressure) decreases. Use of the isotropic distribution will result in maximum errors for points near the tops of the walls under lower surface vapour pressure. 94 CHAPTER 4. MODEL VALIDATION 4.1 INTRODUCTION This chapter presents model validation using selected data sets. -Examples are drawn from automatically collected data chosen to represent the results obtained under a number of different conditions. Parameters which vary include: canyon H/W, meteorological conditions, number of model grid-points, number of samples per grid-point, and the averaging period for the model input data. Each set is composed of scatterplots of measured versus modelled data for each of the long-wave fluxes (LD, Lj, L*), for the Unsworth and Monteith (UM) (1975) radiance distribution using hourly averages by grid-point to reduce the number of data points plotted and enhance the clarity of the plots. Model performance statistics are presented for the average hourly data using the UM radiance distribution. The data set collected on Aug. 1/2 is used to compare scatterplots of both complete and hourly averaged data of each radiance distribution. Discussion of the sample sets is organized according to the day of test. A summary of the results is presented in Section 4.5. Validation sets collected but not presented here are available in Appendix F. 95 4.2 MODEL VALIDATION STATISTICS The statistics utilized are adopted from the work of Willmott (1981,1984) regarding the validation of models and evaluation of model performance. The reader is referred to these references for a full discussion of the mathematical implementation of the statistics. A brief summary of the equations used are available in Appendix G. Summary univariate measures of observed (measured) and predicted (modelled) means (0, P respectively in the tables) and standard deviations (sD, Sp) are provided as suggested by Willmott (1981). Measures of error are provided by the total root mean square error (RMSE), the mean absolute error (MAE), and the mean bias error (MBE) (actually P - 0). Further decomposition regarding the type of error is available from the systematic root mean square error (RMSEs) and unsystematic error (RMSEu) and their respective fractions of the total error as expressed by MSEs/MSE and MSEu/MSE. Indicators of agreement or correlation between the measured and modelled data are provided by the coefficient of determination, r2, and the index of agreement, d. The use of the latter is advocated by Willmott (1981) because of the insensitivity of r2 to additive and proportional differences which may exist between the modelled and measured data. The coefficients of the least squares linear regression a (intercept) and b (slope) are also presented to aid the analysis, although it will be shown later the assumption that 96 the measured data are free of errors is clearly not valid for some cases. The use of a may be of limited utility because comparison of measured and modelled LD and L^ involves only a small range of data with magnitudes much greater than zero. 4.3 MODEL VALIDATION USING DATA COLLECTED IN "POINT' MODE A small validation set was obtained using the CTS in manual mode to position the instruments above a canyon grid-point after which they remained stationary while a one- minute average of both model input and validation data was collected. This method of data collection is referred to as 'point' mode. The data obtained in this manner are not influenced by errors of instrument response arising from traversing but are more susceptible to possible errors due to obstruction of the sky-view factor for the underlying surface because the instruments remain fixed over a point on the surface. The point mode also provides identical averaging periods for both the model input and validation data. The net effect should be increased accuracy of the data. Two point mode tests were performed prior to the use of the CTS in automatic mode to give an initial indication of model performance and to identify any problems in the input data. The tests took place on the nights of July 19/20 and July 21/22, 1988 using a canyon H/W of 1.0. Validation points were obtained from each of the canyon facets. 97 The combined test results are presented in Figures 4.1 and 4.2; the former uses the isotropic radiance distribution and the latter the UM radiance distribution for sky-derived incident long-wave radiation. Each symbol represents a validation pair consisting of a measured (abcissa), and modelled value (ordinate), for a single occurrence (ie. from one traverse) of one grid-point on a canyon facet. Symbols are assigned to the points by canyon facet (see caption of Figure 4.1) and are consistent throughout this chapter. There is no differentiation between points on a given facet on the plots but this is discussed in the text where appropriate. The scatterplot of measured versus modelled L0 produces excellent agreement between for points on the West wall and floor. Some scatter is observed for points on the East wall and top. Use of the UM radiance distribution (Figure 4.2) has no discernable affect on the scatterplot. It does however, result in substantial improvement of modelled L* and , particularly for the canyon walls. The points showing the greatest difference when using the UM distribution are those with higher \ps, as expected. The plot of shows some points which lie above the 1:1 line and which do not appear to be affected by the choice of radiance distribution. These points are located on the West wall and canyon top. Those points on the West wall are likely lower on the wall where the sky radiance distribution has less influence; the lack of change on the canyon top occurs because the 'modelled' value of is Lict which is directly measured. Thus, differences between measured and modelled on the canyon 98 July 19/20, 20/21 1988 H:W 1:1 —" 1 1 1 i i_ 390 400 410 420 430 440 Mtosuntd L„ (W m~2) -80 -60 -40 -20 0 Measured L* (W m"2) —I 1 1 I L_ 340 360 380 400 420 M«osur»d L, (W m'2) + West Won ^ East Wall X Floor • Top Figure 4.1 Scatterplots of modelled and measured long-wave fluxes from the 'point tests'. The isotropic radiance distribution is used for modelled L;. 99 July 19/20, 20/21 1988 H:W 1:1 —1 1 i 1 «00 410 420 430 Meosured L, (W m"*) ' 1 L_ 1_ -80 -60 -40 -20 Measured L« (W m"2) flfnZZ i'r-L ?"tterplots of modelled and measured long-wave fluxes from the 'point tests'. The Unsworth and Monteith (1975) radiance distribution is used for modelled L• nonzeitn uy/^ 100 Table 4.1 Model Performance Statistics: Point Mode Validation Set. July 19/20, July 21/22 1988. Isotropic Unsworth and Monteith Statistic L* LD Li L* L0 Li n , 0 (W m~* P (W m~2 35 35 35 35 35 35 ) -36. .4 418. ,6 382 .2 -36. ,5 418. ,6 382. ,2 • ) -38. ,0 419. ,7 381 .6 -37. .0 419. ,7 382. ,1 s0 (W m-2 sp (W m~ * ) 26. ,2 13. ,8 25 . 1 26. ,2 13. .8 25. , 1 ) 25. ,5 13. ,9 24 .5 25. ,3 13. .9 24. ,4 RMSE (w m ~2l 4. .0 4. .0 5. 0 2. .4 4, .0 3. ,5 RMSEs (W 1 . .9 1 . . 1 1 . 2 0. .6 1 . .2 1 . , 1 RMSEu (W m"2) 3. .5 3. .9 4. 9 2. .3 3. .8 3. ,4 MSEs/MSE 0. .22 0. ,08 0. 06 0. .06 0. .09 0. ,09 MSEu/MSE 0. .78 0. .92 0. 94 0, .94 0, .91 0, .91 MAE (W m" I) 2, .8 2. .9 4. 0 2, .0 2, .9 2, .7 MBE (W m~ 2) -1 , .6 1 , .0 -o. 6 -0, .6 1 , . 1 0, .5 r2 0, .98 0, .92 0. 96 0, .99 0, .92 0, .98 d 0. .99 0. .98 0. 99 0. .99 0, .98 0, .99 a (W m~2) -2, .9 15. .0 15. 3 -o. .5 17, . 1 14, .6 b 0, .97 0, .97 0. 96 1, .00 0, .96 0, .96 n - number of observations 0 - Observed mean P - Predicted mean s0 - observed standard deviation Sp - predicted standard deviation RMSE - Root Mean Square Error RMSEs - Root Mean Square Error (systematic) RMSEu - Root Mean Square Error (unsystematic) MAE - Mean Absolute Error MBE - Mean Bias Error r2 - coefficient of variation d - index of agreement a - intercept of simple linear regression b - slope of simple linear regression 101 top are due to differences between the two instruments, the traversing procedure and the methods of recording and averaging the model input data compared with the data collected by the traversed instruments. No model effects are involved. It is also important to recall that on the canyon top Lj is directly measured and LD determined as a residual, in contrast to the other canyon facets. Model performance statistics for both radiance distributions are presented in Table 4.1. The use of the UM radiance distribution for L* and results in a decrease of RMSE by 40% and 50% respectively. The systematic portion of the error decreases for L* but increases for when the UM distribution is used. The index of agreement is not significantly affected by the distribution used. J 4.4 MODEL VALIDATION USING AUTOMATICALLY COLLECTED DATA 4.4.1 August 1/2 The validation set from Aug. 1/2 involved a canyon with H/W of 2.0. The prevailing weather was cloudless with light winds after sunset. The model used 5 grid-points on the horizontal canyon facets, the minimum number used by any canyon geometry. Vertical facets used 11 grid-points. Model input data were averaged over 2-minute periods and the fluxes measured by the 102 traversed instruments were matched to the appropriate model input averaging period. The large number of validation points in Figures 4.3 and 4.4 obscure the details of the plots, however, with the aid of the hourly averages presented in Figures 4.5 and 4.6 a number of observations can be made. Most noticeable is the distribution of L*. Two distinct populations are present for fluxes greater than 50 W m-2. Of these, points from the East wall lie consistently below the 1:1 line with increasing differences as L* decreases. Points from the West wall are located above and parallel to the 1:1 line. Validation points for the floor are not clearly visible as a separate population and appear to be clustered around the 1:1 line at approximately 30 W m~2. Strong agreement between measured and modelled values is indicated for points at the canyon top. Second, validation points for LQ from the canyon top and the East wall lie significantly above the 1:1 line and in general the scatter of points is above the 1:1 line as indicated by the positive MBE in Table 4.2. This may be evidence for a slight over-estimate of the model input surface temperature (recall that model validation of slight temperature increases for canyon facets always resulted in large increases in the emitted long wave from the canyon top). Differences between L0 and L* are shown to almost balance in the plots of L^. Very good overall agreement is indicated. for points at the canyon top lie above the 1:1 line but this is not a function of model performance as outlined in Section 4.1. 103 August 1/2 1988 H:W 2:1 390 400 410 420 430 440 450 Meosured L„ (W m_J) -100 -«0 -tO -40 -20 0 Measured L* (W m"2) jooL i i i i . L 100 320 S40 360 MO 400 420 440 Measured L, (W m~2) + West Wall ^ Eost Woll X Floor a Top Figure 4.3 Scatterplots of modelled and measured long-wave fluxes from Aug. 1/2 1988, H/W=2.0 using the complete data set. The isotropic radiance distribution is used for modelled Lj. 104 August 1/2 1988 H/W 2.0 390 400 410 420 430 440 450 Measured L0 (W m"2) —t 1 1 » • -100 —80 -60 -40 -20 0 Measured L» (W m-2) 3 420 3 •O £ 340 o S 320 Soob i • • i L 300 320 340 3*0 3S0 400 420 440 Measured L, (W m"2) + West Woll A East Wall X Floor • Top Figure 4.4 Scatterplots of modelled and measured long-wave fluxes from Aug. 1/2 1988, H/W=2.0 using the complete data set. The Unsworth and Monteith (1975) radiance distribution is used for modelled . 105 August 1/2 1988 H:W 2:1 —< 1 • -80 -60 -40 Measured L* (W m"2) u" 1 ' I 300 320 340 360 380 400 420 440 Measurtd L, (W m"2) Wotl A East Wall X Floor • Top Figure 4.5 Scatterplots of hourly averaged validation data grid-point for Aug. 1/2 1988, H/W-2.0. The isotropic radianc distribution is used for modelled 1^ 106 August 1/2 1988 H:W 2:1 i i i • 1 • ' 390 400 410 420 430 440 450 Mtasurad L. (W m-2) —i i i • -100 -80 -60 -40 -20 0 M«asur«d L* (W m"2) 3001* 1 1 i i i i L 300 320 340 360 380 400 420 440 Measured L, (W m"2) + West Won A Eost Woll X Floor o Top Figure 4.6 Scatterplots of hourly averaged validation data by grid-point for Aug. 1/2 1988, H/W=2.0. The Unsworth and Monteith (1975) radiance distribution is used for modelled L^. 107 Use of the UM radiance distribution improves model performance for the L* and fluxes (RMSE reduced by 21 and 17% percent respectively), particularly for those points on the East wall. Thus at least a portion of the error in and L* for points on the wall is due to model underestimation of those fluxes when using the isotropic radiance distribution. Table 4.2 shows the reduction of total errors and improvements in the index of agreement achieved through use of the UM radiance distribution. Note that the systmatic portion of the RMSE increases for Lj when the UM distribution is used. Table 4.2 Model Performance Statistics: August 1/2, • Individual Validation Points, Isotropic and Unsworth and Monteith Radiance Distribution. Isotropic UM Statistic L* LQ Li L* LQ Li 0 (W m_^) P (W m 2) l U m 2 1 RMSE (W m i) RMSEs (W rn"2) RMSEu (W m"2) MSEs/MSE MSEu/MSE MAE (W m"2) MBE (W m~2) r2 d a (W m~2) b 75 1 175 30. 4 420. 1 29. 3 421 . 2 25. 9 10. 2 27. 0 10. 1 4. 1 3. 2 1 . 4 1 . 2 3. 9 3. 0 0. 1 1 0. 14 0. 89 0. 86 3. 5 2. 5 1 . 0 1 . 1 0. 98 0. 91 0. 99 0. 98 2. 1 22. 3 1 . 03 0. 95 175 1175 389.8 -30.4 391.9 -29.5 29.5 25.9 29.7 26.8 4.5 3.3 2.1 1.1 3.9 3.1 0.22 0.13 0.78 0.87 3.7 2.8 2.1 0.8 0.98 0.99 0.99 0.99 2.4 1.7 1.00 1.03 175 1175 420.1 389.8 421.2 391.7 10.2 29.5 10.1 29.3 3. 2 3.7 1 . 2 1 .9 3. 0 3.2 0. 1 4 0.27 0. 86 0.73 2. 5 3.0 1 . 1 1.9 0. 91 0.99 0. 98 0.99 23. 5 6.9 0. 95 0.99 108 Statistics of the hourly averages (Table 4.3) yields reduced RMSE and increased d for Lc, with displaying minor improvements and L* remaining largely unchanged. Table 4.3 Model Performance Statistics: August 1/2, Hourly Averaged Points, Isotropic and Unsworth and Monteith Radiance Distribution. Statistic L* Isotropic Lo Li L* UM Li n - 229 229 229 229 229 229 0 (W m"*) -31 . 3 420.6 389. 3 -31 . 3 420.6 389. 3 P (W m"2) -30. 5 421 .9 391 . 4 -30. 7 421 .9 391 . 2 s0 (W m-2) 27. 1 10.0 30. 2 27. 1 10.0 30. 2 sp (W m~^) 28. 3 10.4 30. 5 28. 1 10.4 30. 0 RMSE (W m~2) 4. 2 2.6 4. 0 3. 3 2.6 3. 1 RMSEs (W m 2) 1 . 3 1 .3 2. 1 1 . 0 1 .3 1 . 9 RMSEu (W m 2) 4. 0 2.3 3. 4 3. 2 2.2 2. 5 MSEs/MSE 0. 09 0.24 0. 28 0. 09 0.24 0. 37 MSEu/MSE 0. 91 0.76 0. 72 0. 91 0.76 0. 63 MAE (W m"2) 3. 5 2.0 3. 4 2. 8 2.0 2. 6 MBE (W m~2) 0. 8 1 .3 2. 1 0. 6 1.3 1 . 9 r2 0. 98 0.95 0. 99 0. 99 0.96 0. 99 d 0. 99 0.98 0. 99 0. 99 0.98 0. 99 a (W m~2) 1 . 9 -5.8 0. 4 1. 5 -7.9 4. 7 b 1 . 03 1 .02 1. 00 1. 03 1 .02 0. 99 4.4.2 August 3/4 The second validation set selected for presentation is from a 1.0 canyon H/W collected on August 3/4. Continuous traversing was maintained for a 24-hour period beginning in the early morning of August 3. A longer averaging period (5-minutes) was used for model input data. Only validation data following sunset 109 are presented here. Cloudless, light wind conditions dominated throughout. The model run uses 10 and 11 grid-points for horizontal and vertical canyon facets, respectively. Comparison of modelled and measured results (Figure 4.7) of LQ are similar to those of August 1/2. Error statistics (Table 4.4) are slightly greater for the UM radiance distribution compared with August 1/2. Table 4.4 Model Performance Statistics: August 3/4, Hourly Averaged Points, Unsworth and Monteith Radiance Distribution. Statistic (Units) L* LQ L± n _ 333 333 333 0 (W m *) -45. 4 435.3 389. 9 P (W m 2) -45. 5 436.5 390. 9 sD (W m-2) 26. 1 12.8 29. 1 sp (W m*^) 26. 2 14.2 28. 1 RMSE (W m"2) 2. 4 3.3 2. 4 RMSEs (W m~2) 0. 1 1 .6 1 . 5 RMSEu (W m~2) 2. 4 2.9 1 . 9 MSEs/MSE 0. 003 0.23 0. 37 MSEu/MSE 0. 997 0.77 0. 67 MAE (W m-2) 1 . 8 2.3 1 . 9 MBE (W m~2) -o. 1 1 . 1 1 . 0 r2 0. 99 0.96 0. 99 d 0. 99 0.98 0. 99 a (W m"2) -0. 1 -36.9 15. 4 b 1. 00 1 .09 0. 96 Distinct sub-populations of L* are again noted; in this case points from both walls lie below the 1:1 line with increasing errors for smaller values of L* (points higher on the wall). The validation points from the floor are located above the 1:1 line. 110 440 a* =, 420 • 400 E i J80 •D 350 o 340 320 r 320 340 360 380 400 420 Measured L, (W m"*) 440 + Wesl Wall A East Wall X Floor a Top Figure 4.7 Scatterplots of hourly averaged validation data by ?ii?c?°inJ.for V4 1988' H/W=1.0. The Unsworth and Monteith U375; radiance distribution is used for modelled L-. Ill The break in the L* plot for points at the canyon top is due to the absence of measurements for the period when the CTS was stopped for refuelling the generator. A slight tendency for the lowest L* values to be under-modelled and/or over-measured is noted. Significant improvement in agreement is achieived for and L* through use of the UM distribution (Table 4.5), particularly for East wall points (the RMSE for L* is reduced by 44% and by 29% for L^; mean absolute errors show similar improvement). The proportion of systematic error is reduced for L* but increases for Lt- . The RMSE of L* and L,- is lower than that of August 1/2. Table 4.5 Comparison of RMSE and d Statistics Calculated From Hourly Averaged Data Using Isotropic [IS] and the Unsworth and Monteith (1975) [UM] Radiance Distributions. Units of RMSE are W m~ Aug. 1/2 Aug. 3/4 Aug. 10/11 Aug. 12/13 L* RMSE [IS] 4.2 4.6 10.6 4.7 RMSE [UM] 3.3 2.4 8.2 4.1 d [IS] 0.994 0.992 0.952 0.984 d [UM] 0.996 0.998 0.973 0.989 Li RMSE [IS] 4.0 4.1 8.8 3.8 RMSE [UM] 3.1 2.4 6.7 4.2 d [IS] 0.996 0.995 0.967 0.989 d [UM] 0.997 0.998 0.982 0.987 Lo RMSE [IS] 2.6 3.2 2.8 3.1 RMSE [UM] 2.6 3.3 2.9 3.2 d [IS] 0.983 0.985 0.978 0.975 d [UM] 0.984 0.984 0.976 0.973 112 Compared with August 1/2, the increased averaging times of the input data do not seem to adversely affect the validation results. The increased number of grid-points on the horizontal facets do not appear to increase model accuracy as suggested by the sensitivity tests performed on the model using the externally calculated view-factors. 4.4.3 August 10/11 The validation set from the night of August 10/11 marks the first time that the thermocouples were reconstructed and re attached to the canyon floor to accomodate the second grid spacing used, in this case, with a canyon H/W ratio of 0.67. There is interest, therefore, in how L0 values for points on the floor compare with previous data. The plots of the hourly-averaged validation data (Figure 4.8) indicate a greater tendency of L0 for points on the floor to lie below the 1:1 line, indicating the possibility that the new thermocouples overestimate the surface temperature. Evidence supporting this analysis is available from the corresponding over-measurement of LQ for points at the canyon top, as expected from the results of the sensitivity tests. Points at the canyon top closest to the West wall consistently show the greatest error. This may indicate additional sources of error for those points. Validation points on the East canyon wall also show substantial differences in LQ. Analysis of individual points 320 340 360 380 400 Measured L, (W m-1) + West WoH A East Wall X Floor • Top Figure 4.8 Scatterplots of hourly averaged validation data grid-point for Aug. 10/11 1988, H/W=0.67. The Unsworth and Monteith (1975) radiance distribution is used for modelled L 114 reveals that the errors increase with height up the wall. The findings for the West wall are similar although the absolute magnitude of the differences between the modelled and measured points is less than those on the East wall. Overall the MBE of LQ is less than that calculated using the previous two example sets, and the RMSE also tend to be smaller (Table 4.6). The scatterplot of L* shows relatively good agreement between modelled and measured points at the canyon top and on the floor. However, serious divergence from the 1:1 line is shown for the canyon walls, which is not corrected for by the use of the UM radiance distribution. Differences increase inversely with the magnitude of L*. The greatest differences are indicated for grid-points at the tops of both walls, forming the two distinct lines of outliers in Figure 4.8. The deviations of L* directly affect the plots of L^. An explanation which accounts for the large differences between modelled and measured values of L*, LQ and for the canyon walls is based in part upon the observation made during data collection that these are errors in instrument orientation with respect to the plane of the walls. These errors have two origins: the first was a consistent over-rotation of the instruments which occurred prior to traversing the canyon walls. The second is an observed tendency of the East wall to be angled slightly outwards, so that the traverse path is farther from the wall near the canyon top than at the base of the wall. Consistent under-measurement of L0 and over-measurement of L* with respect to the modelled value for the grid-point is 115 possible for the East wall if the sensors are tilted towards the canyon top (ie. over rotation from the canyon base). LQ would be decreased, especially near the canyon top and L* would become more positive since the side of the instrument facing outwards from the wall would receive an increase in radiation from within the canyon. A tilt in the opposite direction would indicate more negative values of L* since a greater proportion of sky would be viewed by the instruments. The effect would be augmented by a wall angled outwards. Since the traverse does not completely cover the full extent of the tenth grid-point a portion of the difference could be attributed to a bias of samples in the average from the lower part of the grid-point where L* would be greater, creating further differences. A similar explanation for the differences of the West wall is used. Arguments that errors are due to over-estimated surface temperature, especially for upper points on the wall, may be discounted because no large errors exist for the canyon top. The additional sample points afforded by the increased grid-spacing on the canyon top and floor do not have a clear affect on the results, given the other influences noted earlier. It might be expected that a more accurate average would be obtained with more samples per grid-point. August 10/11 also marks the first occurrence of a major variation in L^ct. An incursion of cloud approximately 5 to 6 hours after sunset had no noticeable effect in the validation data. Of concern in this regard would be the time scale of variable L£ctwith regard to the model input averaging time (3 116 minutes for this night) and the averaging period of the traversed data (on the order of 24 seconds for walls and 42 seconds for canyon top and floor). Table 4.6 Model Performance Statistics: Aug. 10/11 Hourly Averaged Points, Unsworth and Monteith Radiance Distribution. Statistic L* Lo Lj L n 357 357 357 0 (W nT2) -39. ,5 410. ,02 370. ,58 P (W m~2) -44. ,7 410. ,29 365. ,62 s0 (w nT2 sp (W m 2 ) ) 27. 22. ,4 ,4 10. 9. ,0 .8 26. 22. ,4 .9 RMSE (W m ~2l 8. ,2 2. ,9 6. ,7 RMSEs (W 7. .4 0. .6 6. ,2 RMSEu (W m"2) 3. ,6 2. ,8 2. ,6 MSEs/MSE 0. ,81 0, .05 0. .9 MSEu/MSE 0. ,20 0, .95 0. .2 MAE (W m" 1) 6. .3 2. . 1 5. .3 MBE (W m~ 2) -5. .2 0. .3 -5. .0 r2 0. .97 0, .92 0. .99 d 0. .97 0, .98 0. .98 a (W m~2) -12. .8 23, .6 46. .5 b 0, .81 0, .94 0, .86 4.4.4 August 12/13 Scatterplots of the validation data for August 12/13 are presented in Figure 4.9. The canyon H/W is 1.33, which uses the same grid-point spacing as the 0.67 canyon but only 5 grid-points. The thermocouples which had been reconstructed and reattached to the canyon floor for August 10/11 were used again. 117 August 12/13 1988 H:W 1:0.75 1 1 1 1 1 ' • 390 400 410 420 430 440 450 Measured L. (W m"*) -100 Li i i i i i_ -100 -80 -60 -40 -20 0 Measured L* (W m"') + West Wan A East Wall X Floor a Top Figure 4.9 Scatterplots of hourly averaged validation data grid-point for Aug. 12/13 1988, H/W=1.33. The Unsworth and Monteith (1975) radiance distribution is used for modelled 118 Large differences between modelled and measured values of L0 for the top points of the East wall re-occur as a result. Large values of L0 for points on the canyon top are also evident. The RMSE of Lc is increased slightly from the previous day. The remainder of the points show relatively good agreement, with the error statistics for L* and L^ reduced improved compared to Aug. 10/11. Trends shown in the scatterplots of L* are similar to those of Aug. 10/11, with grid-points near the top of the canyon walls showing large differences. The effect is not as pronounced but the range of L* values obtained is only half of that displayed for Aug 10/11; RMSE values are almost half those for the 0.67 data set. Use of the UM radiance distribution improves the results, but to a lesser degree than is obtained with Aug. 10/11 (Table 4.5). Grid-points from the canyon top and floor are generally in good agreement. Plots of measured versus modelled L^ indicate that the modelled values of L^ for points on the canyon top are slightly high with respect to the traversed values. Grid-points on the canyon floor show very good agreement although the modelled values are again slightly high with respect to measured values. Points from the walls are visible as a second cluster of points with a greater slope than those from, the floor or walls. Agreement is improved by use of the UM radiance distribution for points on the walls, with the positive differences between L0 modelled-measured points cancelling the negative differences shown for L*. The occurrence of a few points, mainly on the West 119 wall, to positions above the 1:1 line is of interest. This results in an overall worsening of the statistical indices for error and agreement, the only case in which this was observed for the examples presented. Compared with the 11/12 of August case, the agreement of is improved. The data which are shifted to points visibly above the 1:1 line are the uppermost points on both walls and the differences are greatest during periods of increased and variable cloudiness. This is some evidence for a breakdown of validation during conditions of partial cloudiness due to differences in the averaging period for model input and validation data. The problem is compounded by the possibility of different view-factors for partially cloudy conditions between the instrument measuring L^ct and the instruments within the canyon when the instrument orientations are different, ie. when the traversing instruments are tilted to face the wall. This error should not be a problem when the orientations are the same, and the scatterplots tend to support this. Analysis of cloud data collected at Vancouver International Airport by the AES, and the trace of Ljct with time, indicate an increase in cloudiness to near overcast conditions after sunset, followed by a period of clearing 2 to 3 hours from sunset, then 9 to 10/I0ths cloud for the remainder of the night. 120 Table 4.7 Model Performance Statistics: Aug. 12/13, Hourly Averaged Points, Unsworth and Monteith Radiance Distribution. Statistic L* LQ Li n . 280 280 280 0 (W m~t.) -16.6 411 .7 395.1 P (W m"2) -18.0 413.8 395.8 s0 (W rn"2) 19.4 10.0 19.0 sp^(W m"2) 19.0 10.2 17.6 RMSE (W m~2) 4.1 3.2 4.2 RMSEs (W m 2) 1 .5 2.1 1.9 RMSEu (W m~2) 3.8 2.4 3.7 MSEs/MSE 0.14 0.4 0.22 MSEu/MSE 0.86 0.6 0.78 MAE (W m"2) 3.0 2.3 3.2 MBE (W m 2) -1 .3 2.1 0.8 r2 0.96 0.94 0.96 d 0.99 0.97 0.99 a (W m~2) -1 .9 5.4 37.9 b 0.97 0.99 0.91 4.5 SUMMARY OF VALIDATION RESULTS A number of conclusions can be drawn from the analysis of the validation sets presented here and the additional data presented in Appendix F, viz: 1. The use of the Unsworth and Monteith (1975) radiance distribution consistently reduces the error and improves the agreement between modelled and measured L^ and L* for points on the canyon walls. 121 2. Differences between modelled and measured fluxes of L0 and L* are shown to occur on the walls, particularly near their top. These are attributed to errors in the positioning of the sensor with respect to the wall. 3. Consistent differences between measured and modelled values may arise due to partial traverses of points near the corners of canyon facets, especially the canyon top. 4. Under variable cloud, the traversed radiometers may experience different view-factors for clouds than the instrument measuring L£ct and this can lead to differences between modelled and measured radiation values. 5. The use of longer averaging periods for the model input data than that used to collect the traversed data may result in errors under variable weather conditions, but was not found to be a large influence when the conditions were more constant. 6. Agreement between measured and modelled fluxes decreases somewhat with time due to a degradation in performance of the CTS and wear on the thermocouples used to measure surface temperature. 7. Surface temperatures may have been slightly over-estimated by the thermocouples, however the results are acceptable considering the filtering process necessitated by the noise. 122 8. The results from canyons which had a low number of grid-points on some facets did not appear to reduce model accuracy with the externally calculated view-factors used in the model. 9. Increasing the number of samples used to calculate the average measured fluxes for canyon grid-points on horizontal canyon surfaces in the H/W=0.67 and 1.33 canyons did not significantly enhance the quality of the results over those for the H/W=1.0 and 2.0 canyons. 10. The overall success of the validation is judged to be satisfactory. The index of agreement, d, is generally greater than 0.95 and most errors have been found to be a result of measurement problems. The majority of data lie within the calculated probable error estimates of Appendix D. 123 CHAPTER 5. MODEL RESULTS USING DIFFERENT ESTIMATES OF SURFACE TEMPERATURE 5.1 INTRODUCTION Chapter 4 concludes that the Arnfield model can satisfactorily predict fluxes of long-wave radiation under nocturnal conditions at points within simple canyon structures if the necessary model input is accurately specified. A very important consideration for many modellers, however, is the availability of accurate model input data. The model validation was performed using a full set of input data so that a 1:1 correspondence existed between modelled and measured grid-points for each canyon facet, except the top. The input data are directly measured at each grid-point location and therefore represent the most accurate and complete input data set available. The feasibility of obtaining input of the resolution and quality used for model validation for more applied uses of the Arnfield model is limited. This chapter investigates the model errors which may be expected when the primary model input of surface temperature is estimated by different methods. The necessary model input values of e and L£ct are reasonably easily estimated. The emissivity of a wide range of canyon materials can be obtained from tables, (eg. ASHRAE, 1981). A number of simple models are available for the estimation of incident long-wave radiation based upon screen-level air temperature and measures of humidity which may be derived from 124 commonly available meteorological measurements. Reviews of these models are given by Cole (1976) and Brutsaert (1982). Additional corrections may be necessary to account for the observed increase in within urban areas (Oke and Fuggle, 1972; Estournel et al . , 1983) due to the influences of increased air temperature and aerosols in the urban boundary layer (Oke, 1982) . Of the input required for the Arnfield model, the surface temperatures of canyon facets are the most difficult to specify and are also the dominant controlling factor of model sensitivity when modelling the long-wave radiation at night. Measurement of surface temperature at a large number of canyon grid-points is often not possible. This section presents modelled radiation flux differences obtained for Aug. 1/2 (H/W=2.0) and Aug. 3/4 (H/W=1.0) when the measured surface temperatures were replaced by an approximated value. These are two days with close to.ideal radiative cooling conditions in which geometry effects upon surface temperature are likely to be maximized. The schemes used to derive the surface temperatures are based on suggestions made by Arnfield (1976) and Wakefield (1987). In the following, comparison between the model output using the approximate surface temperatures at all grid-points against that using the measured surface temperatures is made at 5 times following sunset. These times are (except where noted): sunset (ss), ss+1 h, ss+2 h, ss+4 h, and ss+8 h. Differences between modelled fluxes obtained using the approximation scheme and 125 those modelled using the true surface temperatures are plotted around the perimeter of simplified canyon cross-sections. Each plot includes a separate cross-section for each component of the surface long-wave radiative balance. Incident long-wave at the canyon top is not included in the plots because the modelled flux is set equal to the measured value of LiCf 5.2 AIR TEMPERATURE When modelling daily mean and integrated values of long-wave fluxes, Arnfield (1976) used monthly mean air temperature for a rural airport station with an increment based upon urban location and the expected heat island intensity (calculated using relationships given by Oke (1973)). This temperature replaced all facet temperatures and was also used to estimate Lict. Direct comparison with this scheme is not possible here because only nocturnal long-wave fluxes are measured. However, the notion of using air temperatures to represent the canyon facet temperatures is investigated in two ways: a) Canyon air temperature is measured directly from a thermocouple mounted on the CTS. These temperatures are available by grid-point for each facet and can be used to generate an average canyon air temperature for a complete canyon traverse. The averaging period for the canyon air temperature is significantly longer than that of the surface temperatures so surface temperatures are averaged to match the period of the canyon air temperature. The first modelled time using this 126 approximation is sunset+0.5 h, because a complete traverse is not always completed prior to this time. b) The standard screen-level air temperature recorded at Vancouver International Airport by the Atmospheric Environment Service are used to represent the canyon facet temperatures. The readings are taken on the hour and are interpolated to the modelled times. Comparison with model output using measured surface temperatures is made using surface temperatures from the nearest recorded averaging period (these match to within 5 minutes). 5.2.1 Results: Average Canyon Air Temperature Differences of modelled fluxes for August 1/2 and August 3/4 are presented in Figures 5.1 and 5.2 respectively. Note - dashed lines are plotted to help identify between positive and negative differences. Both runs underestimate the incoming flux on all canyon facets. The differences are smaller near the tops of the walls and towards the middle of the canyon floor where L^ct makes up a larger portion of as a result of larger sky-view factors for those points. Differences decrease with time for both walls on Aug. 3/4 as air and surface temperatures converge; the lower portions of the walls show an increase with time on Aug. 1/2 due to the strongly reduced cooling rates in this canyon geometry. The differences in are strongly conditioned by LD which shows similar temporal trends. 127 Average Conyon Air Temperature Approximation August 1/2 1988 H/W 2.0 QSunsrf - 0.5 h A Sunset + 1 h + Sunset • 2 h X Sunset I4h O Sum* + 8 -23.4 -17.4 -H.4 Li Differences 2 3 4 5 Focet Point: Floor -8.9 -14.7 -20.6 Li Differences Facet Point: Top Figure 5.1 Modelled long-wave flux differences (W m~2) rtHf.»4„ A using the average canyon air temperature iS plL'i of measured surface temperature. Data is from Aug. 1/2 1988? H/W=2.0 Focet Point: Top Lo Differences Focet Point: Floor Lo Differences Focet Point: Top 123456769 10 ° L* Differences Focel Point: Floor I* Differences Figure 5.2 As per Fig. 5.1 for Aug. 3/4 1988, H/W=1.0. 129 Fluxes of L0 are strongly underestimated when using the average canyon air temperature, particularly for points near the top of the East wall following sunset and later in the evening at the base of the walls where surface temperature is observed to be high. The errors decrease with time from sunset for all facets on Aug. 3/4. Errors increase for, the lower portions of the walls with time on Aug. 1/2. Differences of L* for points on the West wall and floor are generally under 10 W m ~2. The largest differences are positive (ie. L* calculated using estimated surface temperatures is less negative than L* calculated from the measured surface temperatures) and occur due to the large gradient between surface and air temperature near the top of the East wall shortly after sunset. These differences are quickly reduced and become negative towards the end of the night as high surface temperatures in this area cool. L* is over-estimated on the West wall, except for points near the canyon top later at night.' The canyon floor is also overestimated, increasingly so with time, because differences of LQ decrease more slowly than those of . The largest differences of L* occur across the canyon top because of the large underestimation of L0. Differences are of the order 10 - 20 W m~2, with the maximum located near the canyon mid-point (differences of L* are equal in magnitude and opposite in sign to those of L0 across the canyon top since does not vary). 130 5.2.2 Results: Airport Air Temperature Use of the airport air temperature as the facet surface temperature for all canyon grid-points yields an additional underestimation of Lj and L0 for all canyon facets by approximately 5 - 10 W m"2 (Figures 5.3 and 5.4) indicating airport air temperatures are cooler than the average canyon air temperatures. Temporal trends are similar to those obtained using the average canyon air temperature. The greater changes which occur between the first two plots of each series are a result of the use of temperatures for sunset rather than the half hour after sunset (as used for canyon average temperatures). Circles on the plots represent the differences at sunset. Overestimation of L* increases over that shown by the use of average canyon air temperature for both days; however, the increase at points within the canyon is much smaller for the H/W=2.0 canyon than for the 1.0 case, differences of both and LQ are smaller for most times. 5.3 AVERAGE OR MID-POINT SURFACE TEMPERATURE The second approximation to the measurement of surface temperature at.all canyon grid-points is based upon the work conducted by Wakefield (1987) on sampling methodologies for input data needed in models of the Arnfield type. It assumes an 131 Airport Air Temperature Approximation August 1/2 1988 H/W 2.0 O Sunset A Sunset + 1 h + Sunset + 2 h X Sunset + 4 h « Sunset + 8 h Li Differences Focet Point: Floor li Differences Focel Point: Top I. Differences Focet Point: Floor Lo Differences Focet Point: Top L* Difference* Facet Point: Floor I. Differences-Figure 5.3 Modelled long-wave flux differences (W m~z) obtained using the airport air temperature in place of measured surface temperature. Data is from Aug. 1/2 1988, H/W=2.0. focet Point: lop L« Differences focet Point: Floor L*> Differences Focet Point: Top \ 2 3 4 5 6 7 6 9 10 « L» Diffetences focet Point: Floor L» Differences Figure 5.4 As per Fig. 5.3 for Aug. 3/4 1988, H/W=1.0. 133 infrared radiometer is available to take measurements of surface temperature. For homogeneous horizontal canyon surfaces, a single measurement of the centre of the configuration was considered adequate for the representation of the facet temperature. Homogeneous vertical canyon facets also use a single temperature measurement of the centre of the configuration using the largest 'spot' (area seen by the IR thermometer) possible (Wakefield, 1987). Direct comparison of this method is not possible with the available data but two approximations may be made. In the first, the temperature of the mid-point of the canyon facet, based upon the surface temperature of the closest grid-point (or linearly interpolated between the two nearest grid-points) is used for all points on that facet. The second uses the average facet temperature, i.e. the average of all points on the facet. Averages for the canyon walls include the extrapolated eleventh point and are weighted by grid area. 5.3.1 Results: Facet Mid-Point Temperature The plots shown in Figures 5.5 and 5.6 illustrate the differences due to the use of the facet mid-point temperature in place of the true surface temperature. Trends over time for both canyon geometries are very similar for L* and L0; shows more differences between the two geometries. 134 Mid-Point Facet Temperature Approximation August 1/2 1988 H/W 2.0 Q Sunset A Sunset + 1 h + Sunset + 2 h X Sunset t«h O Sunset • 8 h Li Differences Focet Point: floor Li Differences Focel Point: Top L« Differences Focel Point: Floor Lo differences Focet Point: Top L* Differences Facet Point: Floor L* Differences Figure 5.5 Modelled long-wave flux differences (W m~z) obtained using the mid-point facet temperature in place of measured surface temperature. Data is from Aug. 1/2 1988, H/W=2.0. 135 Mid—Point Facet Temperature Approximation August 3/4 1988 H/W 1.0 OSuns«. A Sunset + 1h + Sunset + 2 h X Sunset + 4 h • Sunset + 8 h ti Differences Focel Point: Floor Li Differences Focet Point; Top L* Differences Focet .Point: Floor Differences Figure 5.6 As per Fig. 5.5 for Aug. 3/4 1988, H/W=1.0. 136 On the West wall, Lj is increasingly overestimated for the upper portions of the wall, with larger changes occurring in the H/W=2.0 canyon. The lower half of the wall displays increasingly negative differences with time. These changes are directly controlled by the differences recorded for L0. The top portions of both canyon walls show increasingly positive differences with time; those of the H/W=2.0 canyon increase more with time, as greater changes in surface temperature were observed in this canyon near the tops of the walls (see Chapter 6). The lower parts of the wall display greater underestimations with time as the reduced cooling increases the temperature difference between temperature recorded at the mid-point of the wall and that near the base of the walls. The pattern across the floor for both runs tends to show greater underestimation of at points near the walls with time, again due to reduced cooling afforded by lower 4/s, as for the base of the canyon walls. The H/W=1.0 canyon exhibits overestimations near the East wall at times near sunset because L0 is underestimated for points lower on that wall. Lc differences are initially.slightly negative for the West wall and strongly so for the top of the East wall where high surface temperatures occur. The differences for both walls subsequently become positive near the tops and negative towards the base, following the difference between the surface temperature at the point and that at mid-facet. Points on the floor near the canyon walls also display increased underestimation with time. Across the canyon top initial large 137 negative differences near the East wall resulting from underestimated surface temperatures at the top of the East wall are reduced with time and positive differences near the West wall decrease so that positive differences exist near each wall, following the over-estimated LD for the tops of the walls. The pattern of differences of L* across the West wall established at sunset is enhanced with time so that points near the base of the wall are overestimated and points above the mid point are underestimated to a greater degree with distance from the facet mid-point. Near the top of the East wall substantial overestimation of L* occurs due to the poorly modelled values of LQ. Points on the lower portion of the wall are underestimated; strongly for the H/W=1.0 canyon and more weakly for the 2.0 case. As time after sunset increases, the pattern and magnitude of differences become similar to that of the West wall. Across the floor there is a tendency for overestimation of L* for points.near the canyon walls, particularly later at night, which is controlled by the differences in LQ. Positive differences of L* are initially displayed at the canyon top near the East wall. These decrease to establish a profile of negative differences for points close to walls later at night and are again controlled by LD. 138 5.3.2 Results: Average Facet Temperature Use of the average facet temperature in place of the mid point canyon temperature shifts the locations where differences switch from positive to negative and tends to decrease the calculated differences slightly (Figures 5.7 and 5.8). This occurs because the use of an average surface temperature will be altered more by the temperature extremes on the facets, particularly the East wall since all points are weighted. Otherwise, relatively little effect is exerted on the distribution of differences for each of the fluxes across the canyon facets at each time. This result is not unexpected because the mid-point facet temperatures for the walls are not very different from the average surface temperature and the differences of surface temperatures will therefore be similar (see Chapter 6 for plots of surface temperature distributions on canyon facets). The differences on the floors are better modelled using the average facet temperature later at night because the mid-point temperature is generally the minimum surface temperature under calm and. clear conditions. 139 Average Facet Temperature Approximation August 1/2 1988 H/W 2.0 O Sunset A Sunset + 1 h + Sunset + 2 h X Sunset + 4 h O Sunset + 8 h Lo Differences Focet Point: Floor L. Differences Focet Point: Top I 2 3 4 5 L" Diilerences Focet Point: Floor L« Differences Figure 5.7 Modelled long-wave flux differences (W m"^) obtained using the average facet temperature in place of measured surface temperature. Data is from Aug. 1/2 1988, H/W=2.0. 141 5.4 SUMMARY To summarize the findings of the plots, tables of the average differences by facet for each flux are presented (Tables 5.1-5.6). For applications with an interest in the fluxes leaving the canyon top (L*, L0), the tables allow comparison of the performance of each approximation scheme. Table 5.1 Summary of Average Differences (W m~z) by Facet Incurred as a Result of Using Temperature Approximations (Aug. 1/2, H/W=2.0). Approximation Time From West East Canyon Sunset Wall Wall Floor (h) Airport air 0 -20.0 -20.0 -18.5 temperature 1 -23.9 -24.7 -23.1 2 -22. 1 -23.5 -22.0 4 -20.9 -22.4 -21.2 8 -21.1 -21.9 -21 . 1 Average canyon 0.5 . -14.8 -15.2 -14.1 air temperature 1 -14.3 -15.2 -14.2 2 -14.8 -16.2 -15.2 4 -15.4 -16.9 -16. 1 8 -16.2 -16.9 -16.5 Mid-point facet 0 -2.9 -0.2 -0.8 temperature 1 -1 .5 0.1 -0.7 2 -0.8 0.3 -0.7 4 0.1 0.3 -1 .1 8 0.4 0.3 -1 .8 Average facet 0 0.3 0.0 1 . 1 temperature 1 0.0 -0.1 -0.1 2 -0.1 -0.2 -0.9 4 -0.2 -0.2 -2.0 8 -0.3 -0.3 -3.1 142 Table 5.2 Summary of Average L0 Differences (W m-^) by Facet Incurred as a Result of Using Temperature Approximations (Aug. 1/2, H/W=2.0). Approximation Time From West East Canyon Canyon Sunset Wall Wall Floor Top (h) Airport air 0 -25.6 -25.5 -21.2 -26.1 temperature 1 -31 .0 -29.6 -28.2 -29.4 2 -29. 1 -26.8 -28.0 -26.4 4 -26.9 -24.4 -29.7 -23.7 8 -24.8 -23.5 -33.5 -22.3 Average canyon 0.5 -19.6 -18.8 -16.0 -19.0 air temperature 1 -19.4 -17.9 -16.7 -17.8 2 -20.2 -18.0 -19.1 -17.6 4 -20.3 -17.7 -22.9 -17.1 8 -18.9 -17.5 -27.5 -16.3 Mid-point facet 0 -0.4 -4.6 -0.7 -3.7 . temperature 1 0.3 -2.3 -1 .2 -0.8 2 0.7 -1.0 -1 .6 0.9 4 0.7 0.5 -2.0 2.8 8 0.9 1 . 1 -2.5 4.1 Average facet 0 -0.2 0.4 0.0 -1 .6 temperature 1 -0.4 -0.1 0.0 0.1 2 -0.5 -0.3 -0.1 2.3 4 -0.6 -0.6 -0.1 2.3 8 -0.7 -0.7 -0.1 3.4 Of the procedures tested, the average facet temperature produces slightly smaller differences at most times than does the use of the mid-point facet temperature. Under the clear and light wind conditions tested, the use of air temperature in place of the measured surface temperatures results in large model errors because surface temperatures are considerably warmer, particularly in the early evening. When meteorological conditions are such that air and surface temperature differences are less, the ,flux differences will be reduced. The airport air 143 temperature estimate produces consistently greater differences than the average canyon air temperature, indicating some spatial modification of temperature at the site. This supports the practice of adding a heat-island increment when using rural airport temperatures (Arnfield, 1976).: Differences between methods of measurement of the temperatures at the two sites prevent rigorous comparison between the air temperatures. Table 5.3 Summary of Average L* Differences (W m~2) by Facet Incurred as a Result of Using Temperature Approximations (Aug. 1/2, H/W=2.0). Approximation Time From West East Canyon Canyon Sunset Wall Wall Floor Top (h) Airport air 0 5.7 5.4 2.7 26.1 temperature 1 7.1 4.9 5.1 29.4 2 7.0 3.3 6.1 26.4 4 6.0 1 .9 8.6 23.7 8 3.8 1 .6 12.5 22.3 Average canyon 0.5 4.9 3.6 1.9 19.0 air temperature 1 5.0 2.7 2.5 17.8 2 5.4 1.8 3.9 17.6 4 4.8 0.8 6.9 17.1 8 2.7 0.6 11.0 16.3 Mid-point facet 0 -2.6 4.3 -0.2 3.7 temperature 1 -1.8 2.4 0.6 0.8 2 -1.5 1.3 0.9 -1.0 4 -0.7 -0.2 0.9 -2.8 8 -0.5 -0.9 0.7 -4.1 Average facet 0 0.6 -0.4 1 . 1 1.6 temperature 1 0.4 0.0 -0.1 -0.1 2 0.4 0.2 -0.9 -1.1 4 0.4 0.4 -1 .9 -2.3 8 0.4 0.4 -3.0 -3.4 144 Table 5.4 Summary of Average Lj Differences (W m~^) by Facet Incurred as a Result of Using Temperature Approximations (Aug. 3/4, H/W=1.0). Approximation Time From West . East Canyon Sunset Wall Wall Floor (h) Airport air 0 -34. ,0 -29. ,8 -27. ,8 temperature 1 -28. ,2 -25. ,6 -23. ,4 2 -28. ,3 -26, ,5 -23. ,4 4 -21 . ,2 -20. ,3 -17. ,3 8 -14. ,8 -14. ,4 -11 . ,5 Average canyon 0.5 -23. ,6 -20. ,4 -19. ,5 air temperature 1 -23. ,5 -20. ,9 -19. ,5 2 -17. .7 -15. ,8 -14. .7 4 -13. ,3 -12. .3 -10. .8 8 -9. ,9 -9. ,6 -7. .5 Mid-point facet 0 -0. .5 0. , 1 0. .4 temperature 1 0. .3 0. . 1 0, .6 2 0, . 1 0, . 1 0. .3 4 0. .3 0, . 1 0. .3 8 -0. .4 -0, .4 -0, .5 Average facet 0 0, . 1 -0, . 1 0, .9 temperature 1 0. .0 -0, . 1 0, . 1 2 -0, . 1 -0, . 1 -0, .2 4 -0, .2 0, .0 -0, .6 8 -0, .2 0, .0 -0, .8 Some variation with the canyon H/W are noted, although differences observed may be due,in part to slightly different meteorological conditions on the two days. An extension of the investigation to other canyon H/W ratios has not been attempted. In general, the temporal variation of differences of all fluxes is greater in the H/W=1.0 canyon. Canyon air temperatures give lower average L* differences in the H/W=2.0 canyon when compared to the H/W=1.0 case, while differences using surface temperature approximations are larger in the H/W=2.0 canyon, particularly 145 for times just after sunset. The former effect is due to smaller differences between air and canyon surface temperatures in the H/W=2.0 canyon while the latter may be is a result of sharper variations of surface temperature across canyon facets for the 2.0 canyon at sunset, which are not well represented by the average or mid-point facet temperature. Table 5.5 Summary of Average L0 Differences (W m-^) by Facet Incurred as a Result of Using Temperature Approximations (Aug. 3/4, H/W=1.0). Approximation Time From West East Canyon Canyon Sunset Wall Wall Floor Top (h) Airport air 0 -43. ,9 -54. ,2 -38. ,6 -45. .6 temperature 1 -37. ,4 -43. .6 -34. . 1 -37. .7 2 -37. ,9 -42. ,4 -36. ,4 -38. .0 4 -28. , 1 -29. .9 -29. .6 -28. .2 8 -18, ,3 -18. ,8 -23. .6 -19. .4 Average canyon 0.5 -30. ,4 -38. .3 -26. . 1 -31 , . 1 air temperature 1 -30. ,8 -37. .2 -27. .4 -31 . . 1 2 -22. .9 -27. .5 -21 . .4 -23. . 1 4 -16. .9 -18. .8 -18. .4 -17, . 1 8 -11. ,5 -11. .9 -16. .8 -12. .6 Mid-point facet 0 -o. ,2 -1 , .6 0, .6 -1 , .3 temperature 1 0. .2 0, .5 -o. .2 0. .2 2 0. .4 0. .5 -0. .7 0. .5 4 0. .7 .. 1 , .5 -1 . .2 1. . 1 8 0. . 1 0, .3 -2. .0 0. .5 Average facet 0 -0. .2 0, .2 0, . 1 -1. .0 temperature 1 -0. .4 -0, .4 0, .0 -o, . 1 2 -o, .5 -0, .4 0, .0 0, .2 4 -o. .6 -0, .5 -0, . 1 0, .7 8 -0. .4 -0, .4 0. .0 0. .9 146 Table 5.6 Summary of Average L* Differences (W rn~2) by Facet Incurred as a Result of Using Temperature Approximations (Aug. 3/4, H/W=1.0). Approximation Time From West East Canyon Canyon Sunset Wall Wall Floor Top (h) Airport air 0 9.9 24.5 10.8 45.6 temperature 1 9.2 18.0 10.8 37.7 2 9.5 15.9 •13.0 38.0 4 6.9 9.7 12.3 28.2 8 3.5 4.3 12.2 19.4 Average canyon 0.5 6.8 17.9 6.6 31.1 air temperature 1. 7.3 16.3 7.9 31 . 1 2 5.2 11.8 6.7 23. 1 4 3.7 6.5 7.6 17.1 8 1 .5 2.3 9.4 12.6 Mid-point facet 0 -0.3 1 .6 -0.3 1 .3 temperature 1 0.2 -0.5 • 0.7 -0.2 2 -0.3 -0.4 1 .0 -0.5 4 -0.4 -1.4 1 .5 -1.1 8 -0.5 -0.7 1 .5 -0.5 Average facet 0 0.3 -0.3 0.9 1 .0 temperature 1 0.4 0.3 0.1 0.1 2 0.5 0.3 -0.2 -0.2 4 0.4 0.4 -0.6 -0.6 8 -0.6 0.5 -0.8 -0.9 Air temperature-based approximations perform best in the hours soon after sunset in the H/w=2.0 canyon, but worsen later compared to L0 and Lj in the 1.0 canyon. Smaller initial differences,between air and surface temperatures in the 2.0 canyon provide the better initial results. These differences increase due to the reduced rate of cooling due to canyon geometry. 147 Differences of L^ are controlled partially by LQ differences and the 4/s of the point. Where \JJS is large errors may be reduced because the true value of L^ct was used. Additional tables, (5.7 and 5.8) have been constructed to present the percentage difference from the 'true' modelled values of L* and LQ at the canyon top. Table 5.7 Percentage Difference of Fluxes Leaving the Canyon Top for Various Surface Temperature Approximation Schemes.(Aug. 1/2 1988 H/W=2.0). Approx imation Time From Canyon Top Sunset (h) Lo L* Airport air 0 -5.9 -24.8 temperatue 1 -6.8 -29.2 2 -6.2 -27.4 4 -5.7 -25.9 8 -5.5 -24.9 Average canyon 0.5 -4.4 -18.3 air temperature 1 -4.1 -17.7 2 -4.1 -18.2 4 -4.1 -18.9 8 -4.0 -18.2 Mid-point facet 0 -0.8 -3.5 temperature 1 -0.2 -0.8 2 0.2 1.0 4 0.7 3.1 8 1.0 4.6 Average facet 0 -0.4 -1.5 temperature 1 0.0 0.1 2 0.5 1 . 1 4 0.5 2.5 8 0.8 3.8 These show the percentage errors calculated by dividing the difference obtained by the 'true' value of the flux for averaged 148 values of LQ and L* on the canyon top. This comparison is for modellers interested in the errors to be expected in fluxes emitted from the canyons. Table 5.8 Percentage Difference of Fluxes Leaving the Canyon Top for Various Surface Temperature Approximation Schemes.(Aug. 3/4 1988 H/W=1.0). Approximation Time From Sunset (h) Canyon Lo Top L* Airport air 0 -9.9 -39.0 temperature 1 -8.3 -34.4 2 -8.5 -37.7 4 -6.5 -31.3 8 -4.6 -23.6 Average canyon 0.5 -6.8 -27.3 air temperature 1 -6.9 -28.3 2 -5.2 -23.0 4 -3.9 -19.2 8 -3.0 -15.4 Mid-point facet 0 -0.3 -1.1 temperature 1 0.0 0.2 2 0.1 0.5 4 0.3 1 .2 8 0.1 0.6 Average facet 0 -0.2 -0.9 temperature 1 0.0 -0.1 2 0.0 0.2 4 0.2 0.7 8 0.2 1 .1 The percentage differences obtained when airport air temperature was used show maximum differences in LQ and L* for the hour after sunset in the H/W=1.0 canyon (Table 5.7). This coincides with observations that the maximum heat island develops shortly after sunset. The maximum difference in the 149 H/W=2.0 canyon is recorded at sunset, with a secondary maximum at two hours after sunset. Average canyon air temperatures reduce the percentage difference by 5 - 8%. The differences in the H/W=1.0 canyon using this approximation are almost constant with time, which might indicate a simple correction factor could be successfully employed to improve the surface temperature estimates. This finding is not reflected in the 2.0 canyon however, the differences exhibit a maximum for the hour after sunset and then reduced differences with time, similar to those recorded for the airport air temperature approximation used in the 1.0 canyon. Mid-point facet temperatures provide only minor differences in L0. Differences are greater for L* and show a consistent increase with time for both fluxes, due to overestimated surface temperature and therefore LQ on the upper portions of the walls. The use of average facet surface temperature further improves the percentage differences for nost times, with similar temporal changes and larger differences recorded for L*. It can be concluded from this analysis that: 1. Approximations to canyon facet temperatures which have as their basis in-canyon point or average surface temperatures will each significantly outperform air temperature-based estimates. 2. The use of the facet average temperature is slightly superior to the mid-point facet temperature in most cases. 150 3. Within-canyon air temperatures, averaged over the period of a complete traverse, yield superior modelled fluxes compared to unmodified airport air temperatures. The results apply to the mostly clear and calm conditions tested. 4. Further corrections in the form of temperature increments due to heat island and air and surface temperature difference effects could improve the results when air temperatures are used. 5. Results could also be enhanced by the use of a correction for the surface temperature based upon ^s for each grid-point and possibly the initial temperature distribution. 151 CHAPTER 6. CANYON TEMPERATURES, RADIATION, AND COOLING 6.1 INTRODUCTION Features of the temporal and spatial variation of surface and air temperatures and long-wave radiation within the model canyons are presented in this chapter. Cooling at various points within the canyon are compared to show differential rates dependent upon initial surface temperature and position. Cooling of the canyon, represented by the mid-point on the canyon floor, is compared to the cooling of the open concrete surface to examine the influence of canyon geometry. Results are compared with those of Oke (1981). The role of atmospheric controls on the cooling of the canyon and open site is considered. 6.2 SURFACE TEMPERATURE DISTRIBUTIONS 6.2.1 The Diurnal Variation of Surface Heating and Cooling in the Model Canyons In a North-South aligned canyon, marked changes in the surface temperature, Ts, take place during the period of one day. The following description may be assumed to be typical of days characterized by clear, fine weather with light winds. The data upon which the description is based was collected on August 3/4, from a canyon with a H/W of 1.0. This canyon was 152 constructed prior to sunrise on-Aug. 3, thus, the surface temperatures start from approximately equal values with no 'history' of the cooling from the previous night. The sequence of events in canyons with the same orientation but different H/W ratios will be similar but the period of receipt of direct radiation on the canyon facets will decrease as H/W increases. ...Beginning at sunrise, the East canyon wall slowly warms as the rising Sun irradiates it's back. As the altitude of the Sun increases, the inside top of the West wall begins to receive direct solar radiation (K^)and the surface temperature climbs sharply for the directly irradiated portion (Figure 6.1a). The East wall (Figure 6.1b) then warms more quickly as short-wave radiation is reflected by the West wall. Following exposure of the entire West wall to direct solar radiation in the late morning, the floor (Figure 6.1c) nearest the West wall begins to receive K^. A sharp peak in the temperature develops similar to that described for the top of the West wall earlier in the morning. As the entire floor becomes irradiated, the temperature distribution becomes less skewed. Figure 6.1c illustrates the temporal spacing of maximum surface temperature for points 1 and 5 on the canyon floor, where point 1 is nearest the West wall and 5 is near mid-canyon. The surface temperature of the open site has been plotted for comparison. Cooling of the West wall begins prior to solar noon as the angle of incidence of direct solar decreases. The initial cooling is followed by a period of relatively constant or 153 (a) West Wall (b) (c) o o 4> 3 "5 » OL E Q> o o 3 30 25 20 •t i ns 1 K 10 -* ! 1 1 1000 2000 Time (PDT) East Wall TJ600 1000 2000 Time (PDT) Canyon Floor 0600 45 o 40 3 "5 k_ ID 35 CL E V 1— 30 <D O a 25 3 v> 20 -><-'•-. «1 1 - 1 \ MS— i ; Open - / 1 ) 1 I 1 v> V \ 1 1 1 1 1 1 1 1000 2000 Time (PDT) 0600 Figure 6.1 Diurnal variation of selected surface temperatures in a canyon with H/W=1.0, Aug. 3/4. 154 slightly increasing surface temperatures which are maintained through most of the afternoon, resulting in distinct shoulders on the plots in Figure 6.1a. These are due primarily to radiation reflected from the East wall with some additional effect from heat conducted through the wall. Similar shapes of plots for were observed by Nunez (1975) and Nunez and Oke (1976). After solar noon, the East wall becomes the recipient of and therefore exhibits the highest temperatures. The rate of temperature increase is not as great as that observed on the West wall since substantial warming has already taken place by reflection from the opposite wall and some component of transmission of heat from the outside of the wall. Eventually, shadows are cast by the West wall which progress across the floor towards, and later up, the East wall. Points on the canyon floor and East wall experience rapid cooling once in shadow and again create a highly skewed spatial temperature distribution. As sunset approaches, only the top of the East wall and the back of the West wall receive direct radiation. The maximum surface temperature near the top of the East wall is recorded within 90 minutes before sunset and exceeds that of the open surface. Transmittance of heat through the West wall probably offsets some of the cooling on the inner facet. The presence of a large hangar to the northwest of the canyon site cast shadows over the canyon prior to local sunset and a short period of direct irradiance on the East wall is lost, so that cooling is slightly enhanced. 155 In the early evening, the West wall displays locally cooler temperatures near the top and bottom of.the wall, with those the base attributed to the proximity of the relatively cool canyon floor at this time. The temperature of the West wall exceeds the temperature of the lower half of the East, due to heating from behind. The top of the East wall undergoes rapid cooling and a 'cross-over' of the other plotted points is observed between one and two hours following sunset after which the top point displays the minimum Ts. A similar cross-over of the top point from the West wall is observed approximately one hour prior to sunset. A cross-over of points 1 and 5 on the canyon floor occurs in the hour before sunset. The cross-over points signal a reversal of the location of maximum and minimum temperature location upon the canyon facets and indicate that the cooling is strongly governed by position in the canyon, and therefore \ps. Continual cooling is observed to the end of the measurement period with the minimum temperature for all facets recorded just prior to sunrise. Rates of cooling over the facets converge as the initial temperature distribution of the facet is reversed. Points on the canyon floor and West wall display approximately equal rates of cooling four hours from sunset; the rates for the East wall are dependent upon position, indicating that the initial temperature distribution still affects the cooling rate of the points within the canyon. 156 6.2.2 Temperature Distributions on Canyon Facets Surface temperature distributions for a mid-canyon length cross-section are presented for three different H/W ratios; 2.0, 1.0 and 0.41. The meteorological conditions of the three days were generally clear and calm, however emphasis is placed upon differences in the shape of the profiles rather than absolute magnitudes, since direct comparison requires consistent, equal conditions for the full heating and cooling period. Canyon cross-section diagrams are used to present the spatial and temporal changes of the distribution of surface temperatures across the canyon facets. The facet temperature distributions for a canyon with a H/W of 2.0 are shown in Figure 6.2a. The distributions are markedly different at sunset; the West wall is characterized by an relatively straight temperature profile while the East wall exhibits high values of Ts near the top of the wall resulting from the irradiation prior to sunset. The West wall shows a small increase in temperature for points 7-9 which may indicate receipt of reflected radiation from the directly irradiated top portion of the East wall. The lowest three points are slightly warmer than the rest. The temperature difference from top to base over the West wall increases with time to just over 4°C 8 hours from sunset. The East wall exhibits a peak Ts at the top of the wall at sunset with the lower portion of the wall displaying a relatively straight profile because it has been shaded for a substantial period of time. By 4 hours after 157 Surfoee Temperature Focet Point: Floor Surface Temperati Sorfoc. Twr««r<*ur« Fac»t Pomt: Floor Surlace T«mp«.otir. A Suraef + 1 h + Sunset + 2 h X Sunset + 4 h « Sunset Figure 6.2 Spatial and temporal variation of surface temperature distributions in (top) a canyon with H/W=2.0, (middle) H/W=1.0 canyon, (bottom) 0.41 canyon. 158 sunset, the temperature profile of the East wall resembles that of the West wall, with surface temperatures warmer at the base of the wall. From sunset onwards, the minimum temperature on the floor occurs in the centre of the canyon. Surface temperatures on the West side are consistently slightly higher than those on the East side. Two reasons may account for this: a) the base of the West wall is slightly warmer than that of the East wall at sunset, which may reduce the rate of radiative cooling due to the warmer surroundings, and b) conduction of heat through the floor from areas to the West of the canyon. The distributions of Ts for the facets of an H/W=1.0 canyon are presented in Figure 6.2b. At sunset, the maximum temperature difference on the East canyon wall is approximately 6°C. In contrast to the H/W=2.0 canyon, the temperature profile decreases steadily towards the base of the wall, reflecting the later times at which the wall was shaded in the more open geometry. The position of the maximum Ts at sunset is one grid-point lower than the H/W=2.0 canyon. The West wall displays a very straight initial profile with no indication of the warmer temperatures near the top as in the H/W=2.0 case. The temperature difference between the base and top of the wall increases with time up to four hours after sunset after which it remains relatively constant at approximately 3°C. The temperature distribution across the canyon floor at sunset is marked by a slight dip near the West wall and a plateau of slightly higher temperatures from the canyon mid-159 point extending to the opposite wall. The dip is associated with the cooling of this section of the canyon which has been occurring since it was shaded shortly after solar noon. The higher temperatures towards the eastern side of the floor are a result of the later time at which they were shaded, although their cooling may also have been reduced by reflection and radiative warming from the warm East wall through the•afternoon and early evening. Four hours from sunset, the temperature distribution across the canyon floor exhibits a shallow concave curve with the points nearest the walls having the highest temperatures. By 8 hours after sunset this curve has further developed to show a minimum near the canyon centre. The third case illustrated is the smallest H/W built, 0.41 (Figure 6.2c). For this H/W the wall height was reduced by two blocks resulting in the loss of four thermocouples from each wall. The data presented are from Aug. 22/23 and the surface temperatures are not available at sunset. The walls again develop a shallow S-shaped temperature profile. The peak of Ts near the top of the East wall so apparent in the H/W=1.0 and 2.0 cases near the top of the East wall in the hour following sunset is much less evident, in it's place is a broad increase over points 3-5. Compared with the H/W=1.0 and 2.0 canyons, the location of the maximum Ts appears to be further from the top of the wall in the early evening. The canyon floor displays substantially warmer temperatures on the East side of the canyon in the early evening, resulting from the relatively late time at which they were shadowed by the West wall and possibly due to 160 some reflection of solar radiation and/or radiative warming from the East canyon wall. Warmer temperatures for points nearest the walls on each side of the canyon are clearly visible, the increase in surface temperature is approximately 1.5 °C over that at mid-canyon. Comparison of absolute temperatures is difficult because of varying conditions under which the canyons heated and cooled. Of interest is whether there exists a limit in terms of canyon H/W at which reduced cooling rates afforded by larger canyon H/W is overcome by lower absolute temperatures due to reduced solar input during the day. The data available cannot be used to determine this and this might better be tested under-more controlled conditions. 6.2.3 Cooling of Canyon Facets Following Sunset The previous section described the temperature distributions on canyon facets at given times. Here, the cooling of various points upon the facets is examined. The information is an expansion of the results discussed in 6.2.1 for times after sunset. For walls, three points per facet are plotted,(except for the H/W=0.41 case when only the_upper- and lowermost points are presented), representing the lower, mid, and uppermost portions of the wall (model points 1, 5, and 10 respectively). These points represent a range of sky-view factors from a minimum at the base of the wall to a maximum at the top. The canyon floor is represented by two points which also cover 161 almost the full range of \//s; point 1 near the base of the West wall, and point 5 near the midpoint of the canyon. Plots for three H/W ratios are presented: 1.0, 2.0, and 0.41 using the filtered surface temperatures for the same days as presented in the previous section. The filtered surface temperatures have been used for plotting. The plots clearly indicate the importance of position (and therefore \ps) upon the cooling. Points deep within the canyon exhibit a more linear cooling than more exposed points. The cooling of point 10 on the walls over that of the lower points is most clearly evident for the largest H/W ratio, 2.0 (Figure 6.3). The topmost point on the walls may even cool at a rate exceeding that of the open surface because of the higher surface temperatures just prior to sunset due to the more favourable angle of solar irradiation. Cooling continues throughout the night up to sunrise. The cooling rates over each facet become more equal approximately 4 hours after sunset. This is well illustrated by the plots of West wall cooling in Figures 6.4 and 6.5 for the H/W=1.0 and 0.41 canyons. The largest reduction in the cooling rate occurs for points near the top of the East wall due to their initially high surface temperature. There is no indication of a levelling-out of the cooling rates which might have suggested the approach of canyon temperatures to an equilibrium value. The reversal of the temperature profile on the East wall is seen to be completed by four hours after sunset. 162 West Wall 1 2 3 4 5 6 7 Time From Sunset (h) East Wall 1 2 3 * 5 6 7 Time From Sunset (h) Canyon Floor 01 2345678 Time From Sunset (h) Figure 6.3 Cooling of selected points on canyon facets; H/W=2.0 canyon, August 1/2. (a) West wall, (b) East wall, (c) Floor. 163 28 S 24 CL E £ 22 West Wall PI 1 PI s P» 10 \ ^ » ^ ^ -J 1 1 • —1_J 1 _1 .1 2 3 4 5 6 7 Time From Sunset (h) East Wall 1 2 3 4 5 6 7 Time From Sunset (h) Canyon Floor 2 3 4 5 6 7 Time From Sunset (h) Figure 6.4 Cooling of selected points on canyon facets: canyon H/W=1.0, August 3/4. (a) West wall, (b) East wall, (c) Floor. 164 West Wall 22 .. (J 21 o © w 3 20 O e> 19 o. E V 1— 18 €> o o 17 u 3 to 16 1 2 3 4 5 6 7 8 Time From Sunset (h) East Wall . 23 o 22 3 21 O a> a. 20 E 19 o 18 o o 17 i_ 3 IO 16 \ % *\ \ « i H! 1 1 I 1 * s _ V 1 1 1 1 2 3 4 5 6 7 8 9 Time From Sunset (h) Canyon Floor 1 2 3 4 5 6 7 8 Time From Sunset (h) Figure 6.5 Cooling of selected points on canyon facets; canyon H/W=0.41, August 22/23. (a) West wall, (b) East wall, (c) Floor. 165 For larger H/W, the mid-point of the floor is at all times cooler than points towards the walls. Cooling rates on the canyon floor are more equal within the H/W=2.0 canyon than in the more open canyons. 6.3 AIR TEMPERATURES 6.3.1 Average Canyon Air Temperatures Average canyon air temperatures, calculated over the period of one complete traverse are compared with the recorded air temperatures at Vancouver International Airport (Figures 6.6, 6.7). The canyon air temperatures are consistently warmer than those recorded at the airport, except for brief periods on Aug. 2/3 and 11/12 (Figure 6.7).In general, the canyon air temperature follows that observed at the airport. Differences between the two fluctuate with time; .of course the once hourly measurements from the airport do not resolve the smaller temporal fluctuations exhibited by the canyon temperature. Some of these fluctuations may arise from traverses which were stopped for a period before being completed. Considering the effects of wind direction it seems that for winds in the along-canyon direction the difference between the canyon and airport temperatures is reduced. The two H/W=2.0 canyon cases illustrate this trend. For most cases, a large air temperature difference occurs shortly after sunset (but this is often reduced, particularly when the wind shifts from westerly 166 T 1*—t*—i ^ p 0 2 4 6 8 10 Time From Sunset M 1*—I 1 1 1 1 1 1 1 r 0 2 <S 6 8 10 Time From Sunset (h) -1 1 1 1 1 1 1 1 i 1 r 0 2 A 6 8 10 Time From Sunset Ch) • Canyon Air Temperature A Airport Air Temperature * Wind Direction Figure 6.6 Average canyon air temperature and air temperatures recorded at Vancouver International Airport for (a) Aug. 1/2, (b) Aug. 3/4, (c) Aug. 22/23. 167 0 2 A 6 8 10 Time from Sunset (h) Time From Sunset (h) Figure 6.7 Average canyon air temperature and air temperatures recorded at Vancouver International Airport for (a) Auq 2/3 (b) Aug. 10/11, (c) Aug. 11/12. Symbols as per Figure 6 6 168 at sunset to a more northerly direction). The largest temperature difference observed is over 3 °C in the H/W=2.0 canyon on August 2/3 (Fig. 6.7a). When the wind was easterly, and the canyon geometry provided maximum shelter. For most of the 2.0 data the wind is northerly, and the winds tend to be channelled through the canyon so the sheltering effect of the large H/W is lost. Other large canyon-airport temperature differences are recorded in the H/W=1.0 canyon on Aug. 3/4 (Figure 6.6b) and the H/W=0.41 canyon on Aug. 22/23 (Figure 6. 6c ) . The control of geometry upon cooling can therefore have two types of effects upon the air temperature: larger aspect ratios reduce surface cooling and, depending upon wind direction, may provide greater shelter . 6.3.2 Spatial Distribution of Canyon Air Temperatures Canyon air temperatures at points 40-50mm above the surface of the canyon facets are presented for the same canyons as the surface temperature distributions (Figure 6.8). The temperatures have been corrected for cooling or warming which occurred during the traverse circut. Recall also that the traverse cannot include points in the corners of the canyon and there may be some bias due to incomplete traverses of grid-points near the ends of each canyon facet. Air temperatures for points across the canyon top are included. 169 Focot Point: Top 12 3 4 5 I ,1 ' ' Air Ttmptrott** Focot Point: Floor Air Tomperotu-4 Facet Point: Top 123456763 10 I 1 1 1 I i ' ' i I ' . ' ' „ 1 ' . 1 —H i i i i i—i—i—r—i i—i—i—i—r— .'.5 19 9 22.3 I 23456789 10 24.0 21.6 19.2 *• TimptrottM Focot Point: rioor Air Tomorqluro Foot Point: Top O Sunset A Sunset + 1 h + Sunset + 2 h X Sunset + 4 h « Sunset + 8 h Figure 6.8 Spatial and temporal variations of air temperature above canyon facets in (top) a canyon with H/W=2.0, (middle) H/W=1.0 canyon,' and (bottom) 0.41 canyon. 170 Air temperatures in each of the canyons are consistently lower than the corresponding surface temperatures. In general,spatial variations are minor over most facets. The H/W=2.0 and 1.0 canyons show a small increase of air temperature towards the base of the walls. The large increase of surface temperature noted for the top of the East wall near sunset in all canyons is shown only as a small increase of air temperature on the East side of the canyon top. In each case air temperatures over the East wall are slightly warmer at all times than over the West wall. The only notable spatial distributions across the canyon floor is an increase towards both walls for the sunset+8 h line in the 0.41 H/W canyon and possibly in the H/W=2.0 canyon. Temperatures over the floor are warmer than those at the canyon top with small differences in the H/W=0.41 canyon (0.2-0.6°C) and larger differences in the 1.0 and 2.0 canyons (0.2 - 1.9°C). The differences remain relatively constant with time in the H/W=2.0 and 0.41 canyon, however the differences are much smaller for times later at night in the H/W=1.0 canyon. This may be associated with an increased wind speed observed in the early morning of Aug. 4. Air temperatures across the canyon top are slightly warmer near the East wall in each of the canyons for most of the plotted times, which agrees with the observation of a warmer East wall. 171 6.4 Long-Wave Radiation Figures 6.9-6.11 present the fluxes of L*, L^,, and L0 modelled for points around the same H/W=2.0, 1.0 and 0.41 canyon cross-sections used to present air and surface temperatures. The modelled values use the Unsworth and Monteith (1975) radiance distribution. Use of modelled values allows all points around the cross-section to be shown at a given time. A separate cross-section is used to present each flux. L^ across the canyon top is not presented as it is constant for all points at each time. Incident long-wave on the canyon floor exhibits similar spatial variations in all three canyons with higher values near the base of the walls, especially later at night. Early in the evening there is a small tendency for L^ to be larger for points on the floor close to the West wall because these have the greatest view-factor for the top of the warm East wall. Larger variations across the floor occur with more open geometries; the H/W=2.0 canyon shows little variation due to the small i//s and the almost isothermal lower portions of the walls. The canyon walls for the H/W=1.0 and 2.0 cases display an increase of L^ towards the base of the walls; the increase is close to linear for the H/W=1.0 canyon but increases more rapidly near the top of the H/W=2.0 canyon. The shape of the profiles of L^ on the canyon walls is maintained throughout the night in each of the cases presented. The H/W=0.41 canyon displays an irregular pattern of L^ on the walls with a decrease noted for the mid-portion of each 172 August 1/2 1988 H/W 2.0 Figure 6.9 Spatial and temporal variations of modelled radiative fluxes in an H/W=2.0 canyon. Top - Li. middle -bottom - L*. 1 173 August 3/4 1988 H/W 1.0 Facet Point: Top Facet Point: Top O Sunset A Sunset + 1 h + Sunset + 2 h X Sunset + 4 h «> Sunset + 8 h Figure 6.10 Spatial and temporal variations of modelled radiative fluxes in an H/W=1.0 canyon. Top - L;, middle - L0, bottom - L*. 174 August 22/23 1988 H/W 0.41 Focet Point: top Facet Point: top O Sunset A Sunset + 1 h + Sunset + 2 h X Sunset + 4 h O Sunset + 8 h Figure 6.11 Spatial and temporal variations of modelled radiative fluxes in an H/W=0.41 canyon. Top - L^, middle bottom - L*. 175 wall. This feature is present for each of the times plotted and may be a result of numerical approximations in the model routines, as the Lj derived from the measurements of L* and LD made by the traversed radiometers exhibits smoother changes across the walls in a manner similar to the other canyons. The plots of LQ for the canyon walls and floor are identical in shape to those described for the canyon surface temperature. L0 on the canyon top shows an increase towards the East canyon wall at, and shortly after sunset in all three cases because of the very warm surface temperatures there. Later at night, L0 is slightly higher towards the middle of the canyon because the tops of the walls are the coolest portion of the canyon. The net radiation across the canyon floor shows higher values towards the walls in the H/W=1.0 and 0.41 canyons with the greatest differences in the early evening. The H/W=2.0 canyon is the reverse, with lower values at all times near the canyon walls. This indicates greater radiative cooling near the canyon walls. However, the surface temperature distributions and profiles of L0 show an increase towards the walls which becomes stronger with time which would support reduced cooling at these points. Measured data are not available for comparison with these points to confirm this feature. One possibility is that the surface temperature is anomolously warm on the floor near the walls due to conduction from outside the canyon. This might increase LQ for the point and result in a net decrease in L*. A second possibility lies in numerical errors within the model 176 which are greater for corner grid-points (Arnfield, pers. comm. 1989). The irregularities noted for L^ in the 0.41 canyon affect the profiles of L* on the walls. On the canyon top L* is reduced for points near the East wall in the early evening and close to both walls later on. Similar results for the canyon top are shown in the H/W=1.0 and 2.0 canyons. Of the three canyons, L* is smallest for the H/W=1.0 canyon in the first two hours after sunset. Later, the lowest values are recorded in the H/W=2.0 canyon and L* increases as H/W decreases. This is an indicator of the reduced cooling which occurs in canyons with greater H/W early in the evening. 6.5 SUMMARY OF RESULTS: TEMPORAL AND SPATIAL VARIATION OF IN-CANYON TEMPERATURES AND RADIATION The previous sections have outlined temporal and spatial variations of the in-canyon quantities of long-wave radiation, surface and air temperatures. A.summary of results is as follows: 1. During the day, surface temperatures are strongly affected by K^. This results in a spatially skewed temperature distribution across canyon facets which are sunlit, shaded or partially shaded. The time of maximum Ts varies across the facet as K; reaches.a maximum for a point. 177 2. Maximum surface temperatures on the top portion of the East wall are observed to be higher than that of the open site. Maximum Ts values increase for points higher on the walls and towards the middle of the canyon because of a longer exposure time for K^. 3. Temperature on the West wall displays a distinct shoulder from the late morning to early evening due primarily to reflected radiation from the opposite wall with a small component due to conduction of heat through the wall. This feature is not as well defined for the East wall in the morning. 4. Spatial distributions of temperature across canyon facets after sunset are conditioned by their initial (sunset) temperature and their position in the canyon. The role of \£s in shaping the temperature profiles related develops through the night as differential cooling takes place. 5. Very warm surface temperatures near the top of the East wall are observed well into the night. The position of maximum Ts on the East wall at sunset appears to be lower on the canyon wall as the H/W decreases. 6. Cooling rates are initially high, particularly for points with high surface temperatures at sunset. The rates tend to become more equal with time. Cooling is nearly linear for points 178 deep within the canyon. There is no reduction of the cooling rate to indicate the approach of an equilibrium temperature. 7. Air temperatures after sunset are always cooler than surface temperatures. Only minor spatial variations across individual facets are noted although this may be due in part to the traverse lengths which do not include temperatures for points in the canyon corners, where more change may be present. 8. Air temperatures are warmer over the East than the West wall and warmer over the floor than the top. Smaller vertical differences are observed in the more open canyons. No consistent variations with time were observed; wind speed and direction may reduce or increase differences. 9. Wind direction is shown to be an important controlling factor in the development of canyon "heat islands', and is capable of overcoming geometry influences. 10. Long-wave radiation at points within a canyon is directly related to the Ts and \[/s of the point measured. 11. Net long-wave at the canyon top is the lowest in the 2.0 canyon late at night, because of the reduced rate of cooling through the night. L* decreases towards the canyon walls in the H/W=2.0 canyon, which is not seen elsewhere. 179 6.6 CANYON VERSUS OPEN SITE SURFACE COOLING Control of surface cooling by surface geometry has been cited previously (Oke, 1981) as a possible cause of the surface urban heat island. Results are presented here comparing the cooling of the open site with that of the canyon. Canyon cooling is represented by a point or points at canyon mid-width on the floor. Use of the canyon floor mid-point facilitates comparison with other published results; other measures of cooling of the canyon could also be made, for example air temperature or net-radiation. Examples from each of the H/W ratios tested are presented in Section 6.6.1. The basis for selection was based upon homogeneity of conditions through the night and the achievement of the desired simulation conditions (see Chapters 1 and 2). The presentation format includes a plot of the decrease of surface temperature with time of the open site and the canyon. For H/W ratios of 2.0 and 1.33 the mid-point temperature on the canyon floor is used. For other canyons the average of the two points closest to the middle are used. The cooling curves are overlain by a plot of the open site net long-wave radiation, L*0. The time series of Ljct and wind speed (u) are plotted above the cooling diagram, using the same time scale to permit easy -inter-comparison of plots. Table 6.1 presents average meteorological statistics recorded at Vancouver International Airport for the period 0600 - 1800 (PDT) for each day shown. 180 Table 6.1 Daily Average Meteorological Conditions 0600-1800 (PDT) August, 1988. Date T xa max Td u Ca1 CO2 Ts Ts max Q* O* ^ max (°C) (°c) (°C) (km/h) (/10) (/10) (°C) (°C) (W m"2) 1 18.3 21 .6 11.7 8.7 2.2 2.2 31 .8 41.8 239 420 3 21.6 24.4 12.6 4.0 0.8 0.2 37.5 45.2 284 4103 8 17.8 20.9 11.4 7.5 9.8 9.4 24.3 29. 1 78 227 10 18.4 20.5 13.6 12.1 5.5 5.1 11 18.5 21 .2 13.8 9.6 3.8 1 .8 30.5 40. 1 228 415 12 17.8 21.0 12.0 6.6 0.5 0.5 30.7 40.4 230 405 14 17.6 20.8 12.3 6.8 8.9 6.9 20 16.8 19.5 10.5 10.2 7.3 6.4 22 18.7 21 .9 13.7 10.4 0.0 0.0 1. Ca - Cloud amount 2. Co - Cloud opacity 3. Averaging period 0710-1800 for Ts and Q* 181 Where available, net radiation and surface temperature data from the open site are also included. These, data are of use when defining the conditions during the period of canyon heating and for comparing the similarity of conditions between two days. 6.6.1 Canyon and Open Surface Cooling: Surface Geometry Controls Figures 6.12-6.17 present results for each of the H/W tested, along with an additional data set for the H/W=1.0 canyon comparing the variability of cooling under less than ideal conditions. Plots are presented in order of decreasing canyon H/W. A reduced rate of cooling with larger canyon H/W is immediately apparent. The difference between canyon and open surface temperatures increases with time from sunset, with the greatest rate of change near sunset in all cases. The difference of the slope of the two curves is reduced with time and with more open geometries (Figure 6.17). The total temperature decrease of the open site at 8 hours from sunset is approximately 8-9 °C for the data collected under xideal' conditions. Of the H/W ratios tested, the most poorly represented in terms of xideal' meteorological conditions is the 1.33 H/W ratio (Figure 6.13) and the 0.41 canyon (Figure 6.17), which although clear and calm at night, were preceded by less than ideal conditions in the day (see Table 6.1). 182 --I 1 1 1 1 1 1 1 1 r~ 0 1 23456789 Time From Sunset (h) Figure 6.12 Bottom: Comparison of canyon (solid line) and open site (alternating long and short dashed line) cooling overlaid with L*p (short dashed line). L^ct .(top) and wind speed (u), (middle; are also presented. Data from Aug. 1/2, H/W=2.0. 183 Figure 6.13 As per Figure 6.12. Data from Aug. 14/15, H/W-1.. 33. 184 Figure 6.14 H/W=1.0. As per Figure 6.12. Data from Aug. 3/4, canyon 185 Figure 6.15 As per Figure 6.12. Data from Aug. 8/9, canyon H/W=1.0. 186 £ —i 1 1 1 1 1 1 1 1 0.0 1.0 2.0 3.0 4.0 5.0 E.O 7.0 8.0 9.0 eg 1 £ 8H o 9_ tn o _J o o „ m Time From Sunset (h) —i 1 1 1 1 1 1 1 1 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 BO 9.0 Time From Sunset (h) V) c to £ o V) O « o « Q <D l_ "5 v. <D CL £ <D E Time From Sunset (h) Figure 6.16 As per Figure 6.12. Data from Aug. 11/12, canyon H/W=0.67. 187 Time From Sunset (h) Figure 6.17 As per Figure 6.12. Data from Aug. 20/21, canyon 188 In all cases, the cooling rates, both in and outside the canyon, at the end of the night are relatively large. The concrete base of the site, and the underlying material, thought to be sand, appears to draw upon a large store of heat and it's thermal admittance, u, is probably high, (range 150 -2,370 J m~2 s~1//2 K-1 with typical values of 1300 J m~2 s"1/2 K~1 Oke, 1981). The linearity of cooling inside the canyon agrees favourably with both the scale model and city data presented in Oke (1.981 )' (Figure 6.18). However, the relatively large rates of cooling measured at the open site are in greater contrast with wooden xrural' model results. Results from an open concrete slab used by Oke (1981) show better agreement, with a much more linear cooling than the wooden model (Fig. 6.18) and a much reduced difference between the rates of cooling measured at the start of the cooling period and those measured at the end. Of the example city-rural cooling rates presented, that of Uppsala shows the best agreement with respect to the rate of cooling late at night. Initial cooling rates for both canyon and open sites appear to be less than those of Oke (1981). It is possible that the shadows cast by the nearby hangar across the canyon prior to the local time of sunset are of some importance to the low initial rates of cooling. This may cause cooling to take place at a greater rate than would normally be the case before local sunset. The greater rates of cooling observed late at night are probably a function of the thermal properties of the concrete canyon floor. The wooden models of Oke (1981) tend to 'use up' their finite heat store and approach 189 12 -14 -O Montreal •> — -O Vancouw ' «v o Upptalt 10 12 TIME (h) Figure 6.18 Cooling of urban and rural surfaces observed from (a) scale models, (b) the cities of Montreal (H/W=3.29), Vancouver (H/W=1.50) and Uppsala (H/W=0.76). From Oke (1981). Field observations made by Oke and Maxwell (1975) (Montreal and Vancouver) and Hogstrom et al. (1978) (Uppsala). 190 Figure 6.19 Temporal changes of heat island intensity generated using (a) a scale model and (b) observed intensities from Montreal, Vancouver and Uppsala. From Oke (1981) . 191 an equilibrium temperature. This effect is reduced in the city-rural examples presented and further with the concrete material used here, indicating the thermal admittance of the concrete surface used in this study may exceed that of both the wooden models and urban areas presented in Oke (1981). Attempts to model the cooling using the radiative cooling model of Groen (1947) and a simple surface energy balance model (Lyons, Oke, and Steyn, pers. comm.) model based upon the force-restore method proposed by Blackadar (1976), Bhumralkar (1975) and Deardorff (1978) were largely unsuccessful. Imprecise knowledge of thermal properties of the material and of boundary conditions necessary for the energy balance model reduce the effectiveness of modelled results. The Groen formulation also requires that both L^ct and the rate of decrease of L* with temperature change remain constant through the night. Neither of which were observed to be the case. The Groen approach may also require an initial time other than sunset for the calculation of some parameters, Kondo and Haginoya (1989) suggest t=0 is approximately 30 min prior to sunset. Again, the shadows cast by the hangar over the site may change this time. The composite plot (Figure 6.20) of the temperature difference between the canyon and open site shows the distinct effects of the various canyon geometries later at night. Variations in the meteorological conditions on some days result in the merging of the three intermediate H/W geometries, early in the cooling period. Comparison of the temperature differences measured from-the model canyon with those for scale and real 192 Time From Sunset (h) Figure 6.20 Temporal development of the temperature difference between the mid-point of the canyon floor and the open concrete Temperature differences have been set to zero at sunset Data are from days with mostly clear conditions; H/W=2.0 Aug. 1/2 1.33 Aug. 14/15, 1.0 Aug. 3/4, 0.67 Aug. 11/12, 0.41 Aug. 20/21. 193 canyons in Oke (1981) (Figure 6.19) do not show the characteristic early increase to a maximum and then a linear decrease of temperature difference with time. The differences in Figure 6.20 increase throughout, but.at a decreasing rate with time. In the data here the rate of temperature decrease in the urban canyon never exceeds that of the open site. Therefore, the observation that the time of maximum intensity occurs later as the H/W increases (Oke, 1981) cannot be confirmed here, but the rate of increase in the temperature differences for all times increases with H/W, in agreement with those of Oke (1981). It should be noted that the heat island intensities measured in the three cities presented in Figure 6.19 are derived from air temperatures rather than surface temperatures as used in Oke (1981) and the present work. The overall effect of geometry upon the development of a canyon heat island is also shown in Figure 6.21 where the maximum temperature difference is plotted versus \j/s for the mid point of the canyon floor. The data are drawn from days which were mostly clear with light winds. Overall, a general linear trend is noted for the H/W tested, supporting the earlier results of Oke (1981). The regression relation obtained is Tmax = 6»60 " 7«30 ^s (6«1 ) with an r2 of 0.94 and a standard error of Tm=v of 0.36°C. 194 Canyon H/W 2.0 1.33 1.0 0.67 0.41 i • o 5 ATmax = 6.60 - 7.30^ - Open 4 O 2 r = 0.94 lyon - 3 • 8\ o \ D CJ X n 2 o \. E * I— <i 1 i i 0.3 0.4 0.5 0.6 0.7 0.8 Sky View-Factor Figure 6.21 Surface temperature differences between the canyon and open sites at eight hours after sunset for the five H/W tested. 195 6.6.2 Canyon and Open Surface Cooling: Atmospheric Controls The cooling of a surface is strongly controlled by the wind speed and radiation, the former aiding in the convection of heat from surfaces as turbulent sensible heat and the latter governs the rate of radiative heat transfer. The effects of L^ct and u upon the surface cooling is evident in several of the plots. An increase in u approximately 2 hours after sunset on Aug. 1/2 (Figure 6.12) is correlated with an increased rate of cooling of the open surface. A drop in windspeed on the evening of,Aug. 11/12 appears to be related to a reduced rate of surface cooling at this time although the effects are not large. The direction of influence of changes in u does not follow that commonly observed for rural areas at night in which an increase in u is associated with enhanced transfer of sensible heat towards the surface and a reduction of the cooling rate. The classic case is dependent upon the formation of an inversion layer above the surface, which has been observed not to occur within urban canyons (Nakamura and Oke, 1988). The effect of wind under these conditions would thus be to enhance the cooling of the surface by convective transfer of heat away from the surface in the form of turbulent sensible heat. Positive fluxes of turbulent sensible heat have been observed over urban areas (Yap and Oke, 1974; Ching et al., 1983; Cleugh and Oke, 1986). The dependence of surface cooling on L^ct is marked. Fluctuations of L^ct affecting the surface temperature are shown in Figures 6.1,3, 6.14 and 6.15. The effect increases with the ^s 196 of the surface, so that maximum effects are experienced by the open site. The data from August 8/9 (Figure 6.15) illustrate the much reduced rate of cooling under cloudy conditions, although the daytime heat input to the canyon was also reduced by cloud. Differences between the canyon and the open concrete are also reduced compared with Aug. 3/4 (Figure 6.14). -The evening of August 14/15 (Figure 6.13) indicates warming of the open site as Lict increases. This observation is suprising but not unique. Temperatures within the canyon were also observed to increase at these times. The net long-wave radiation of the surface remains negative so that radiative warming is not indicated. Explanation for the warming may be related to the method of mounting. If convergence of heat were to occur slightly below the surface due to a reduced rate of heat loss from the surface while heat continues to be conducted upwards through the concrete following the established subsurface temperature gradient (the thermocouple junctions were slightly buried) a rise in temperature might occur. The period of increase is short-lived after which temperatures again decrease, suggesting the re-establishment of a new sub-surface temperature gradient. Plots of L^ct with time on very clear nights (Figures 6.12, 6.14, 6.16, 6.17) indicate a slight decrease of the order of 10 - 20 W m~2 over the night, the shape of the decrease varies from near-linear (Figures 6.16,17), to variable (Figure 6.14) to greater rates of decrease with time (Figure 6.12). These observations, '• if typical of clear nights, are of importance 197 because several models of radiative cooling assume L^ct to be constant. The reduction of Ljct is expected because air temperature decreases in the lower atmosphere and this is the layer which contributes most to the incoming long-wave flux. Net long-wave over the open surface is always at a minimum at sunset under clear conditions. It then increases for the first part of the night at close to a linear rate after which the rate slows with time. 6.7 SUMMARY OF RESULTS: CANYON AND OPEN SURFACE COOLING 1. Increased canyon H/W reduces the rate of cooling observed at the mid-point of the canyon floor under ideal radiative cooling conditions. Under less than ideal conditions, the differences are much less. 2. The greatest difference in cooling rates between canyons is observed near sunset. The rates become more equal with time and are approximately linear at.the end of the night. 3. Cooling of the canyons and the open concrete at this site differ from results for other scale models and cities, and with that predicted by models. A number of factors may account for these differences including the use of surface as opposed to air temperatures, the thermal properties of the canyon floor, 198 shadowing of the site prior to local sunset, and difficulties in obtaining accurate model input data. 4. Composite plots of the increase in temperature difference between the canyon and open site shows the canyon 'heat island' grows most rapidly following sunset, but never stops increasing over the measurement period. The plot of maximum temperature difference versus i//s agrees well with earlier results, with a generally linear decrease over the range of H/W tested. 5. Increased wind speed at night appears to enhance cooling for both the open site and canyon suggesting the absence of inversion conditions over the site. 6. Increases of L^ct have a rapid and marked effect upon surface temperature and cooling rates, causing increases in surface temperature for points with large \ps in several cases. 7. L^ct decreases with time on very clear nights, however, the nature of this decrease is not consistent. L* shows minimum values near sunset after which it increases at a rate which decreases with time. 199 CHAPTER 7. CONCLUSIONS 7.1 ACHIEVEMENT OF THE RESEARCH OBJECTIVES In Chapter 1, three main objectives were outlined: (1) the validation of the Arnfield model (1976, 1982) for nocturnal long-wave radiative fluxes, (2) the investigation of model errors which result from using less than the full model input data set, and (3) the study of the effects of urban surface geometry upon the cooling of urban areas. For details of the results, refer to the individual chapter summaries. The first objective has been met, subject to the limitations of the methodology used to measure the independent long-wave fluxes and the noise incurred in the surface temperature measurements. Notable findings include: the increase in model accuracy for low numbers of grid-points when view-factors are re-calculated using the Nusselt Sphere method, a slight but consistent increase in accuracy of L^ and L* when the Unsworth and Monteith (1975) radiance distribution is specified, and very good results overall when modelling fluxes at the canyon top, which form the lower boundary conditions for larger scale atmospheric processes. Four approximations to the full model input for surface temperature were made. These were based upon: (1) air temperature measurements made within and (2) outside the canyon, and on (3) average and (4) facet mid-point temperatures. 200 Temporal and spatial variations within the canyon were presented. It was concluded that surface temperature-based estimates were superior to those based upon air temperatures; the greatest differences were obtained when using unmodified screen-level air temperature estimates taken independently at Vancouver International Airport. The use of such data, commonly available in climate archives, for this scale of urban modelling is not advocated. A substantial data base of canyon and open site cooling using different canyon H/W values and under varying weather conditions was gathered. Spatial and temporal variations of radiative fluxes and air and surface temperatures were presented. Surface geometry has a clear influence under conditions when radiative cooling dominates with the greatest difference in cooling rates between canyon H/W observed near sunset. When conditions deteriorate, surface geometry effects are reduced. Comparison with previous results and models shows differences which may be due to the use of surface as opposed to air temperatures, thermal properties of the materials used, and local site factors. 7.2 RECOMMENDATIONS AND FUTURE RESEARCH This research has validated the urban canyon radiation model of Arnfield (1976, 1982) to the scale of individual grid-points using a unique methodology. The success of the validation of 201 this model also supports other models which are based upon similar principles. The methodology employed is recommended as an alternative to obtaining measurements in real cities, which are complicated by logistical difficulties, in cases where such measurements can be made without undue scaling restrictions. Scaling restrictions need to be further investigated in order for more direct comparisons to be made with field observations and for this approach to be used to study turbulent fluxes. The validation of the full energy balance within urban canyons should be made. The accuracy of some numerical methods of calculating view-factors should be examined. If errors can be reduced, lower numbers of grid-points can be used to achieve a given accuracy, with consequent reductions in computational time required for models. The development of approximations to model input should be made with the goal of achieving reasonably accurate model results with currently available data sources. It has been shown that airport air temperatures, which are often the data available in climate archives, did not represent canyon surface temperatures well. Correction of these temperatures based upon known heat island intensities and the temporal and spatial variations of surface temperature in urban canyons could be attempted in model form, before passing the results to models such as that of Arnfield (1976, 1982). Cooling models (Brunt, 1941; Groen, 1947; Lyons, Oke and Steyn pers. comm.) did not agree well with measured results for 202 both open and canyon sites although not all the model input data was available. Further work on the accuracy and the assumptions of these models would be helpful. The model canyons undergo significant cooling prior to sunset, further research should ensure measurements are available from this period of time. The relation between canyon H/W, surface temperatures, and penetration of into the canyon to cooling could be further investigated, perhaps under more controlled conditions to determine whether a particular H/W exists after which lower absolute surface temperatures that are due to increased shading within the canyon are not offset by reduced cooling at night. 203 REFERENCES Aida, M. 1982. 'Urban Albedo as a Function of the Urban Structure - A Model Experiment', Boundary-Layer Met. 23, 405-413. Aida, M. and Gotoh, K. 1982. 'Urban Albedo as a Function of the Urban Structure - A Two-Dimensional Numerical Simulation', Boundary-Layer Met. 23, 415-424. American Society of Heating, Refrigerating and Air-Conditioning Engineers 1981. ASHRAE Handbook, ASHRAE Inc. Atlanta, Ga. Arnfield, A.J. 1976. 'Numerical Modelling of Urban Surface Radiative Parameters', in Papers in Climatology: the Cam Allen Memorial Volume, J.A. Davies (ed.), Discussion Paper No. 7, Dept. of Geography, McMaster University. Arnfield, A.J. 1982. 'An Approach to the Estimation of the Surface Radiative Properties and Radiation Budgets of Cities', Phys. Geogr. 3, 97-122. Arnfield, A.J. 1988. 'Validation of an Estimation Model for Urban Surface Albedo' Phys. Geog. 9, 361-372. Barnes Engineering Co. Instruction Manual for the Model PRT-4A Portable Radiation Thermometer, Barnes Engineering Co., Stamford, Conn. Barring, L., Mattsson, J.O., and Lindqvist, S. 1985. 'Canyon Geometry, Street Temperatures and Urban Heat Island in Malmo, Sweden*, /. CLimatol. 5, 433-444. Bhumralkar, CM. 1975. 'Numerical Experiments on the Computation of Ground Surface Temperature in an Atmospheric General Circulation Model', /. Appl. Met. 14, 1246-1258. Blackadar, A.K. 1976. 'Modeling the Nocturnal Boundary Layer', in Proc. of the Third Symposium on Atmospheric Turbulence, Diffusion and Air Quality, American Meteorological Society, Boston, Mass. 46-49. 204 Bornstein, R.D. 1986. 'Urban Climate Models: Nature, Limitations and Applications', in Urban Climatology and It's Application with Special Regard to Tropical Areas, T.R. Oke (ed.). W.M.O. No. 652, 237-276. Bornstein, R.D. and Oke, T.R. 1981. 'Influence of Pollution on Urban Climatology', Advances in Environmental Science and Engineering 2, 171-202. Bruhl, Ch. and Zdunkowski, W. 1983. 'An Approximate Calculation Method for Parallel and Diffuse Solar Irradiances on Inclined Surfaces in the Presence of Obstructing Mountains or Buildings', Arch. Met. Geoph. Biocl. Ser. B 32, 111-129. Brunt, D. 1941. Physical and Dynami cal Meteorology, Cambridge University Press, London. Brutsaert, W. 1982. Evaporation into the Atmosphere, D. Reidel Publishing Co., Dordrecht. Buettner, K.J.K. and Kern, CD. 1965. 'The Determination of Infrared Emissivites of Terrestrial Surfaces', /. Geophys. Res. 70, 1329-1337. Campbell Scientfic, 1984. 2IX Mi crol ogger Instruction Manual, Campbell Scientfic Inc., Logan, Utah. Ching, J.K.S., Clark, J.F., and Godowitch, J.M. 1983. 'Modulation of Heat Flux by Different Scales of Advection in an Urban Environment', Boundary-Layer Met. 25, 171-191. Cleugh, H.A. and Oke, T.R. 1986. 'Suburban-Rural Energy Balance Comparisons in Summer for Vancouver, B.C.', Boundary-Layer Met. 36, 351-369. Cole, R.J. 1976. 'The Longwave Radiative Environment Around Buildings', Building and Environment 11, 3-13. Davies, J.A., Robinson, J., and Nunez, M. 1971. 'Field Determinations of Surface Emissivity and Temperature for Lake Ontario', /. Appl. Met. 10, 811-819. 205 Deardorff, J.W. 1978. 'Efficient Prediction of Ground Surface Temperature and Moisture, With Inclusion of a Layer of Vegetation', J. Geophys. Res. 83, 1889-1903. The Eppley Laboratory. Instrumentation for the Measurement of t he Components of Solar and Terrestrial Radiation, The Eppley Laboratory Inc., Newport, R.I. Estournel, C, Vehil, R., Guedalia, D., Fontan, J., and Druilhet, A. 1983. 'Observations and Modeling of Downward Radiative Fluxes (Solar and Infrared) in Urban/Rural Areas', J. Clim. Appl. Met. 22, 134-142. Fairey, P. and Kalaghchy, S. 1982. 'Evaluation of Thermocouple Installation and Mounting Techniques For Surface Temperature Measurement in Dynamic Environments',in Seventh National Passive Solar Conference, J. Hayes and CB. Winn (eds.). American Solar Energy Society Inc. 801-805. Flueck, J.A. 1978. 'The Role of Statistics in Weather Modification Experiments' Atmos.-Ocean 16, 377-395. Fritschen, L.J. and Gay, L.W. 1979. Environmental Instrumentation, Springer-Verlag, New York. Fuchs, M. and Tanner, CB. 1966. 'Infrared Thermometry of Vegetation', Agron. J. 58, 597-601. Fuggle, R.F. and Oke, T.R. 1976. 'Long-Wave Radiative Flux Divergence and Nocturnal Cooling of the Urban Atmosphere. I. Above Roof-Level', Boundary-Layer Met. 10, 112-120. Groen, P. 1947. 'Note on the Theory of Nocturnal Radiational Cooling of the Earth's Surface', /. Meteorol. 4, 63-66. Hamming, R.W. 1983. Digital Filters, Prentice-Hall, Englewood Cliffs, N.J. Hogstrom, U., Taesler, R., Karlsson, S., Enger, L. and Hogstrom, A-S. Smedman. 1978. 'The Uppsala Urban Meteorology Project', Boundary-Layer Met. 15, 69-80. 206 Huband, N.D.S. 1985. 'An Infra-Red Radiometer for Measuring Surface Temperature in the Field. Part II. Calibration and Performance', Agric. For. Meteorol. 34, 227-233.. Idso, S.B. and Cooley, K.R. 1971. 'The Vertical Location of Net Radiometers. I. The Effects of the Underlying Air Layer', /. Meteor. Soc. Japan 49, 343-349. Idso, S.B. and Cooley, K.R. 1972. 'The Vertical Location of Net Radiometers. II. The Effects of the Net Radiometers Shadow', • /-. Meteor. Soc. Japan 50, 49-57. Idso, S.B. 1987. 'The C02/Trace Gas Greenhouse Effect: Theory Vs. Reality', Theor. Appl. Climatol. 38, 55-56. Johnson, G.T. and Watson, I.D. 1984. 'The Determination of View-Factors in Urban Canyons', /. Clim. Appl. Met. 23, 329-335. Johnson, G.T. and Watson, I.D. 1987. 'Modelling the Radiative Heating and Cooling of Urban Canyons', in Proc. International Conference on Model Ii ng and Simulation, 14-16 Oct. 1987, Melbourne. Kondo, J. and Haginoya, S. 1989. 'Characteristic Heat Transfer Coefficients Near the Ground at Night During Strong Winds' Bounday-Layer Mel. 46, 169-180. Landsberg, H.E. 1981. The Urban Climate, Academic Press, New York. Latimer, R.J. 1972. Radiation -Measurement , International Field Year for the Great Lakes Technical Manual No. 2. National Research Council of Canada, Ottawa. Lorenz, D. 1966. 'The Effect of the Long-Wave Reflectivity of Natural Surfaces on Surface Temperature Measurements Using Radiometers', J. Appl. Met. 5, 421-430. Lyons, T.J. 1983. 'Comments on 'Canyon Geometry and the Nocturnal Urban Heat Island: Comparison of Scale Model and Field Observations'', Climatol. 3, 95-101. 207 Monteith, J.L. 1972. Survey of Instruments for Micro-Meteorology, Blackwell, Oxford. Nakamura, Y. and Oke, T.R. 1988. 'Wind, Temperature and Stability Conditions in an East-West Oriented Urban Canyon', Aimos. Environ. 22, 2691-2700. Nunez, M. 1975. The Energy Balance of an Urban Canyon, Ph.D. Thesis, University of British Columbia, Vancouver. Nunez, M. and Oke, T.R. 1976. 'Long-Wave Radiative Flux Divergence and Nocturnal Cooling of the Urban Atmosphere. II. Within an Urban Canyon', Boundary-Layer Met. 10, 121-135. Nunez, M. and Oke, T.R. 1977. 'The Energy Balance of an Urban Canyon', J. Appl. Met. 16, 11-19. Oke, T.R. 1974. Review of Urban CIimal ol ogy 1968-1973, W.M.O. Tech. Note No. 134, World Meteorological Organization, Geneva. Oke, T.R. 1976. 'The Distinction Between Canopy and Boundary Layer Urban Heat Islands', Atmosphere 14, 268-277. Oke, T.R. 1978. Boundary Layer Climates, Methuen and Co. Ltd., London. Oke, T.R. 1979. Review of Urban CI imat ol ogy 1973-1976, Tech. Note No. 169, W.M.O., Geneva. Oke, T.R. 1981. 'Canyon Geometry and the Nocturnal Urban Heat Island: Comparison of Scale Model and Field Observations', J. CI imat ol-. 1, 237-254. Oke, T.R. 1982. 'The Energetic Basis of the Urban Heat Island', Quart. J. R. Met. Soc. 108, 1-24. Oke, T.R. 1984. 'Towards a Prescrpition for the Greater Use of Climatic Principles in Settlement Planning', Energy and Build. 7, 1-10. Oke, T.R. 1988. 'Street Design and Urban Canopy Layer Climate', Energy and Build. 11, 103-113. 208 Oke, T.R. and Maxwell, G.B. 1975. 'Urban Heat Island Dynamics in Montreal and Vancouver*, Atmos. Environ. 9, 191-200. Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. 1986. Numerical Recipes, Cambridge University Press, Cambridge. Schuring, D.J. 1977. Scale Models in Engineering: Fundamentals and Applications, Pergamon Press, Oxford. Schwerdtfeger, P. 1976. Physical Principles of Micro-Meteorological Measurements, Elsevier Scientific Publishing Co., Amsterdam. Siegel, R. and Howell, J.R. 1972. Thermal Radiation and Heat Transfer, McGraw-Hill, New York. Sievers, U. and Zdunkowski, W.G. 1985. 'A Numerical Simulation Scheme for the Albedo of City Street Canyons', Boundary-Layer Met. 33, 245-257. Sievers, U. and Zdunkowski, W.G. 1986. 'A Microscale Urban Climate Model', Beitr. Phys. Atmosp. 59, 13-40. Skoglund, V.J. 1967. Similitude: Theory and Applications, International Textbook Co., Scranton, Penn. Steven, M.D. and Unsworth, M.H. 1979. 'The Diffuse Solar Irradiance of Slopes Under Cloudless Skies', Quart. J. R. Met. Soc. 105, 593-602. Steven, M.D. and Unsworth, M.H. 1980. 'Angular Distribution and Interception of Diffuse Solar Radiation Below Overcast Skies', Quart. J. R. Met. Soc. 106, 57-61. Steyn, D.G. 1980. 'The Calculation of View Factors From Fish-Eye Lens Photographs', Atmos.-Ocean 18, 254-258. Steyn, D.G. and Lyons, T.J. 1985. 'Comments on 'The Determination of View-Factors in Urban Canyons'', /. Clim. Appl. Met . 24, 383-385. 209 Terjung, W.H. and Louie, S.S-F. 1973. 'Solar Radiation and Urban Heat Islands', Annals Assoc. Amer. Geog. 63, 181-207. Terjung, W.H. and Louie, S.S-F. 1973. 'Solar Radiation and Urban Heat Islands', Annals Assoc. Amer. Geogrs. 63, 181-207. Terjung, W.H. and Louie, S.S-F. 1974. 'A Climatic Model of Urban Energy Budgets', Geog. Anal. 6, 341-367. Terjung, W.H. and O'Rourke, P.A. 1980a. 'Simulating the Causal Elements of Urban Heat Islands', Boundary-Layer Met . 19, 93-118. Terjung, W.H. and O'Rourke, P.A. 1980b. 'Influences of Physical Structures on Urban Energy Budgets', Boundary-Layer Met. 23, 415-424. Terjung, W.H. and O'Rourke, P.A. 1981. 'Energy Input and Resultant Surface Temperatures for Individual Urban Interfaces, Selected Latitudes and Seasons', Arch. Met. Geoph. Biocl. Ser. B. 29, 1-22. Thurow, C. 1983. Improving Street Climate Through Urban Design, Plan. Advisory Service Report No. 376, American Planning Association, Chicago. Todhunter, P.E. and Terjung, W.H. 1988. 'Intercomparison of Three Urban Climate Models', Boundary-La yer Met. 42, 181-205. Tuller, S.E. 1973. 'Microclimatic Variations in a Downtown Urban Environment', Geog. Annaler Ser. A. 54, 123-125. Unsworth, M.H. and Monteith, J.L. 1975. 'Longwave Radiation at the Ground: I. Angular Distribution of Incoming Radiation', Quart. J. R. Met. Soc. 101, 13-24. Venikov, V.A. 1969. Theory of Similarity and Simulation, Macdonald and Co. Publishers Ltd., London. Verseghy, D. 1987. On t he Me asurernent and Modelling of Radiative Exchange for Building Surfaces, Ph.D. Thesis, Univeristy of Toronto, Toronto. 210 Wakefield, P.M. 1987. URBMAT: An Urban Canyon Sampling Format for Nocturnal Long Wave Radiation Regime Modelling, M.A. Thesis, University of Victoria, Victoria. Willmott, C.J. 1981. 'On the Validation of Models', Phys. Geogr. 2, 184-194. Willmott, C.J. 1984. 'On the Evaluation of Model Performance in Physical Geography', in Spatial Statistics and Models, G.L. Gaile and C.J. Willmott (eds.). D. Reidel, Dordrecht. Yamashita, S., Sekine, K., Shoda, M., Yamashita, K., and Hara, Y. 1986. 'On Relationships Between Heat Island and Sky View Factor in the Cities of Tama River Basin,Japan', Atmos. Environ. 20, 681-686. Yap, D.H. and Oke, T.R. 1974. 'Sensible Heat Fluxes Over an Urban Area - Vancouver, B.C.', /. Appl. Met. 13, 880-890. Zdunkowski, W. and Bruhl, Ch. 1983. 'A Fast Approximate Method for the Calculation of the Infrared Radiation Balance Within City Street Cavities', Arch. Mel. Geoph. Biocl., Ser. B 33, 237-241. 211 APPENDIX A. SPECIFICATION OF SENSOR TRAVERSING SPEED AND v DELAY INTERVAL A.1 INTRODUCTION The sensor traversing speed and the delay interval were determined from an analysis of sensor response to anticipated changes in the outgoing and net long-wave flux densities across canyon facets. The approach is based upon the response of a temperature sensor to changes in environmental temperature as described in Fritschen and Gay (1979). A prerequisite for the analysis is an estimate of the time constant for the miniature net radiometers used. No value is available for the exact model used in this work, but Monteith (1972) lists the response time of a previous Swissteco miniature net radiometer (Model S1) as 98 percent equilibrated to a step change in 25 s. Using these data and t = (1 - e_t/T) (A.1) where t is the elapsed time and the right hand side is the adjustment completed to a step change, a time constant r, of 6.3905 s was calculated. The approach of Fritschen and Gay (1979) assumes a stationary instrument responding to a temporal change in the environmental temperature. Here, the determination of sensor traversing speed assumes spatial changes in radiation to be much greater than 212 temporal changes for any particular point; ie. the change in LQ or L* across a canyon facet is much larger than any change induced by heating or cooling in the time it takes to traverse the facet. The response of the instrument is therefore a function of distance, but is easily converted to time when divided by the traversing speed. The equation governing sensor response is dQ/dt = -1/T (Q - QA) (A.2) where dQ/dt is the change of measured radiation with time (here time is the time necessary to traverse a facet and represents spatial rather than temporal changes) and QA is the actual or true radiation. If changes in QA over the facets are known, the sensor response may be calculated for the traverses across the canyon facets. To represent QA modelled distributions of LQ and L* were generated using the Arnfield model and canyon temperature data collected in October, 1987 for a H/W=1.0 canyon (see Figure A.1). To a first approximation,.the net and outgoing radiation distribution on the walls for most times after sunset may be represented by a ramp change, and that of the top and floor by a portion of a periodic or sinusoidal change (if not represented by a ramp change). 213 October 10/11 1987 H/W 1.0 O Surest A Sunset + 1 h + Sunset + 2 h X Sunset + 4 h O Sunset + 8 h Focel Point: Top Figure A.1 Modelled distributions of L* (bottom) over canyon facets. Oct. 10, (top), Lo (middle) and 1987. 214 A. 2 CANYON WALLS 1 With a constant or ramp change of L0 or L*, the change of the radiation sensed by the radiometer over time (ie. distance/speed) may be written dQ/dt = - 1/T (Q - Bt) (A.3) where Q represents the radiation measured by the sensor, B is the rate of change of the true radiation QA with time t, and T is the instrument time constant. It is assumed that Q is equal to QA at the start of the traverse. The general solution of (A. 3.) is Q = B(t - T) + Ce_t/T (A.4) and if Q = QA at the start of the traverse then C = BT and Q - QA = -BT(1 - e_t/T). (A.5) When t >> r, (ie. the traversing time is much greater than the instrument time constant), (A.5) may be reduced to Q - QA = -BT. (A.6) Given the change of L0 or L* over the wall and the speed of traverse, the slope, B, may be calculated. Specifying the length 215 of traverse and instrument time constant, various speeds or times of traverse may be tested for the difference between Q and QA. Two such tests are presented in Table A.1 and cases from each test are illustrated in Figure A.2. Table A.1 True and Measured Radiation For a Sensor Traversed Across a Canyon Wall. Change in Flux Density of Radiation Over a Wall: (a) 15 W m~2, (b) 30 W m ~2 Traverse Time (s) Speed (m s~I) X10~2 Slope B (W m"2 s 1) (W m z) (a) 300 0.335 0.05 0.32 240 0.419 0.0625 0.40 180 0.558 0.0833 0.53 120 0.838 0.125 0.80 60 1 .675 0.25 1 .60 (b) 300 240 180 120 60 0.335 0.419 0.558 0.838 1 .675 0.10 0.125 0. 167 0.25 0.50 0.64 0.80 1 .07 1 .60 3.20 With greater changes of radiation over the facet, and with faster traversing times, it is apparent that the difference between the true and measured radiation grows. The traversing times tested were chosen somewhat arbitrarily but are constrained by a lower limit governed by the maximum speed of the traversing unit and the increase in vibrations of the sensors at those speeds, and an upper limit restricted by the total amount of time needed to complete an entire traverse. To 216 SENSOR RESPONSE TO A RAMP CHANGE 0 5 10 15 20 25 30 Time From Start ot Traverse (s) Figure A.2 Sensor response to a ramp change in LQ or L* over a wall. Total change over the wall is 30 Wm"2. Solid lines -actual radiation, dashed line - measured radiation. Traverse times are: A - 60 s, B - 180 s, C - 300 s. 217 keep the difference (Q - QA) below 1 W m~"2 for the changes tested, a speed of over three min m~1 is necessary. A.3 CANYON TOP AND FLOOR For the sinusoidal change the governing equation, (A.2), may be .rewritten as dQ/dt + Q/T = (Q./iOsinwt (A.7) where CJ represents the angular frequency of oscillation CJ = 27T/Period (A.8) and the amplitude of the oscillations. The solution of the first order linear differential equation with the constant solved for Q = QA = 0 = t as before, yields Q = Q1wT[1 + (cjT)2]"1/2e"t/T + Q, [ 1 + (CJT)2]-1/2 sin(uJt - arctanwr). (A.9) As illustrated in Figure A.3, the measured signal will be both attenuated and lagged behind the true signal. The attenuation factor a = [1 + (CJT)2]-1/2 (A.10) 218 SENSOR RESPONSE TO A SINUSOIDAL CHANGE Time From Start of Traverse (s) Figure A.3 Sensor response to Solid lines - actual radiation radiation. Traverse times are: for a 1 m canyon width. a sinusoidal change in LQ or L*. , dashed lines - measured A - 60 s, B - 180 s, C - 300 s 219 and the lag L = arctancjT (A. 11) when t >> T , and the lag time = L/OJ. The attenuation, lag and lag time calculated at several traversing speeds are presented for radiation data of a given amplitude in Table A.2. Table A.2 Attenuation and Lag Time of Canyon Floor/Top Data for Various Traverse Times Amplitude: 10 W m~2 One-half period represents the distribution Traverse Time Period Attenuation Factor Lag Lag Time (s) (s) (s) 300 600 0.998 0.067 6.381 240 480 0.997 0.083 6.375 180 360 0.994 0.111 6.364 120 240 0.986 0.166 6.332 60 120 0.948 0.323 6.167 For traverse times of 3 minutes or greater per metre the amount of attenuation is negligible and the lag time is only very slowly changing. For traverses of 2 minutes or less per metre, the attenuation becomes more pronounced and lag times decrease. Given a lag time of 6.4 s and a speed of traverse of 0.55X10~2 m s~1, a measurement made at a particular point would be lagged by approximately 35.6 mm in distance. 220 A.4 DELAY INTERVAL The determination of sensor traversing speed based upon sensor response to the distribution of radiation across the canyon facets assumes QA = Q at the start of a traverse across each facet. To achieve this, upon completion of a traverse and rotation of the sensors at each corner, the instruments must remain stationary for a period of time in order to equilibrate to the radiative balance of the new facet. The difference in radiative balance between the two facets is equivalent to a step changeUsing the time constant of the radiometers, the time needed to adjust to a given fraction of the new level of radiation may be determined from (A.1). Changes between facets are assumed to be greater than temporal changes occurring during the delay time. The CTS has a built in delay of 27 s which is invoked after each instrument rotation. This provides an adjustment of 0.985. The largest changes in radiation occur during instrument rotation to and from the canyon top, with much smaller changes occurring between the walls and floor. Table A.3 presents the adjustment to a step change completed with increasing time using (A.1) for a time constant of 6.3905 s. 221 Table A.3 Adjustment Completed to a Step Change in Radiation Using a Miniature Net Radiometer. Elapsed Time (s) Adjustment Completed 5 0.543 10 0.791 15 0.904 20 0.956 25* 0.980 27* 0.985 30 0.991 35 0.996 * Delay built into CTS A.5 CONCLUSIONS This analysis servesonly as a guide to choosing an appropriate traversing speed and delay interval and does not provide any form of correction factor. It is based on simple approximations to the actual radiation distributions will occur across canyon facets and is a compromise between factors. Based on the results of the preceeding calculations, a traversing speed of approximately 5.5 cm s~1 (3 min m~1) was chosen to best provide a speed which would allow complete canyon traverses in a short time, while not incurring large lags or attenuations of the measured signals. Errors incurred by the chosen speed and assumptions of radiation distributions are discussed in Appendix 222 APPENDIX B. DATA PROCEDURES B.1 DESCRIPTION OF RECORDED DATA The data recorded by the CR21X micrologger may be divided into two categories: traversed and stationary. Traversed data includes the radiation and temperature measurements made by the traversing sensors: L*, Lc, Tc, and Ta. These data are recorded as samples at a fixed time interval (either 1 or 2 s). Also 1 recorded is a number representing the state of the traverse; 1 represents measurements taken during a delay period, 0 represents those made during a traverse. Stationary data include: surface temperature, Lict, wind direction, and L*0. The stationary data are sampled at fixed intervals (15 s during traversing) and averages are recorded at intervals of 1 - 3 min during traversing operations. B.2 ASSIGNMENT OF TRAVERSED DATA TO GRID-POINTS Traverse/delay information provided by the recorded 0 or 1, together with estimates of the speed of traversing for each facet allow each sample to be equated to a distance from the start of the traverse of each facet. Thence, using the start and end location of the traverse in relation to the facet dimensions, and grid-point dimensions, each sample may be assigned to a grid-point. 223 Once a facet number and point number have been assigned to each sample, they may be condensed into averages over any number of grid-squares. This assumes that the average of samples across the grid-quare is a good approximation of the value at the grid-point, which is the location of the modelled value. B.3 SIGNAL FILTERING THE SURFACE TEMPERATURE Figure B.1a presents surface temperatures measured on the evening of Aug 1/2. When compared with Figure B.1b for the evening of August 25/26 it is clear that there is a noise component in the former data above that which might normally be expected. Results indicate the measurement of the delay voltage and the use of an A/C adapter to power the 21X are the principal causes. The noise is most obvious in the surface temperature data, but can be found in the traverse data as well. It seems likely that the noise is similar to AC noise (ie. 60 Hz), unfortunately this cannot be ascertained because the recorded signal is sampled at a much slower rate (usually 15 second intervals) and averaged over a 1, 2 or 3 minute period. Since the noise is outside the Nyquist critical frequency (in this case 1/6 min.) it becomes folded or aliased into the frequency range -fc < f < fc. Given the sensitivity of the Arnfield model to even small changes in the input surface temperature (Chapter 3) it is desirable to reduce the effects of noise in the cooling curves. 224 IS -• 1 1 ' ' ' • 1 ' 0 1 2 S « St 7 6 Tim* From Sunsvt (h) Figure B.1a Surface temperatures, evening of Aug. 1/2. 2* 23 • Floor H> S ? 22 • 3 • E • 20 ^^j. WoB 8 IP 5 • u o T 1» 3 </> • 18 IP 17 •J ' 0 2 4 6 8 Tlm« From Sun*«l (h) Figure B.lb Surface temperatures, evening of Aug. 25/26. 225 It was decided not to modify the traverse data as the level of noise is not as great and some degree of smoothing is achieved when the traverse data is reduced to values for each grid-point. B.3.1 Methods Used •One of a number of possible alternatives to smooth the temperature data is to construct a low-pass filter. The method, stated simply, requires the definition of a set of filter coefficents, followed by the transformation of the data to the frequency domain, where they are multiplied by the filter coefficients and re-transformed to the time-domain. The critical operation is the definition of the filter coefficients. To define the coefficients a stop/pass frequency is chosen to filter only the frequencies which define the noise. A plot of the power spectral density of the detrended temperature data can be used to investigate the frequencies at which noise exists. From the sampling theorem, two points/cycle are the minimum needed to define a sine wave of the Nyquist critical frequency (0.5 x sampling interval). To ensure the noise defined by consecutive samples is well defined (the highest frequency visible noise) the input data were resampled using linear interpolation between true data points. The total number of points is now 2xN-1 (no extrapolation). Resampling also has the advantage of allowing more frequencies to be defined in the power spectrum when using Fourier Transform methods of computing the power spectral density. 226 A plot of the power spectral density obtained using the Maximum Entropy Method (Press et al. 1986) of the rescaled and detrended temperature data from August 1/2 (West Wall IP 1-5) is shown in Figure B.2. The frequency scale is based upon the data being sampled one time unit apart. The large peak evident near zero is probably a result of the detrending of the data (Hamming, 1983); accurate detrending of the data was made diffcult by true variations in the cooling curve; up to a third order polynomial has been subtraced from the data. The time series of the first point on the West wall had the most linear decrease of temperature and was therefore detrended most successfully (Figure B.3). A separate plot of it's power spectrum is shown in Figure B.4. The high frequency noise defined by consecutive original points is evident at a frequency of 0.25. Definite peaks are also present at frequencies of 0.062, .094, and 0.117, with the peak at 0.094 containing almost twice the power of the other peaks. The noise defined by this peak can also be seen in the time series plot. Note that because the data are sampled at different rates and/or averaged over different lengths of time, the power spectra involve different aliasing of the noise and shift the location of apparent noise peaks. With longer averaging periods, the high frequency noise is reduced. Filter coefficients may now be defined for a given stop/pass frequency estimated from the power spectrum. Figure B.5 plots the transfer function values for positive frequencies of a low-227 0.20 h Figure B.2 Power spectrum of rescaled and detrended data for points 1 to 5 on the West wall on Aug. 1/2. 228 o o D "o OJ CL E OJ O O D if) ~o OJ TJ C OJ ~a> Q -0.1 -0.3 100 200 300 400 Time 500 Figure B.3 Detrended surface temperature of point 1 on the West wall; Aug. 1/2. Time is in units of samples from the start of recording. 229 Frequency Figure B.4 Power spectrum of rescaled and detrended surface temperature shown in Figure B.3. 230 LOW PASS FILTER SF=0.03 Frequency Figure B.5 Transfer function of a low-pass filter with a stop frequency (SF) of 0.03 for different truncations of the Fourier series. 231 pass filter which passes frequencies up to 0.03. The curves are obtained from the Fourier series for H(f) = 1 , 0 < |f| < 0.03 (B. 1) H(f) = 0, 0.03 < |f| <0.5 (B.2) and assumes that the transfer function is symmetric about f=0. The series, truncated to k terms is k H(f) = 2Fs + I (2/rrk) sin27rkfs cos27rkf (sin (jrk/n)/vrk/n) 2 (B.3) n=1 where the squared sine term is a smoothing term (Hamming, 1983). Figure B.5 shows that after approximately 40 terms, the transfer function is very close to the ideal curve (1 up to the stop frequency 0 after). The ideal curve may be used but the impulse response can, and in this case does, have ringing at frequencies corresponding to the sharp edges of the filter (Press et al. 1986). Figure B.6 illustrates the original and filtered data using 40 terms to approximate the transfer function for stop frequencies of 0.2, 0.075, and 0.03. A simple linear detrending and rescaling of the original data was performed. Clearly, removal of only the higher frequencies does not adequately smooth the fluctuations. This is not unexpected since the high frequency noise aliased into the data when sampled will have components even at low frequencies. The danger of setting the 232 cutoff frequency at too low a frequency is the loss of some true information; while 0.03 may seem low in this regard, it does not appear unreasonable in visual terms. The data need not be rescaled to use the filter, however, note that the stop frequency is two times that used previously when using the assumption of data sampled one time unit apart in both the original and rescaled data. A second method of determining a filter for noisy data is that of optimal or Wiener filtering. Following the procedures outlined in Press et al. 1986, the power spectrum of the data is plotted using a log scale and an extrapolation of the signal and noise portions of the plot are made (Figure B.7). The filter function is defined as F(f) = |S(f)|2/( |S(f)|2 + |N(f)|2 (B.4) where |S(f)|2 and |N(f)|2 are derived from |S(f)|2 + |N(f)|2 Pc(f) = |C(f)|2 0<f<fc (B.5) with Pc the power spectral density of the measured signal C. S(f) and N(f) are the signal and noise frequencies respectively. The approach is not sensitive to the method used to obtain the power spectrum (Press et al. 1986); it only requires the general shape of the noise and signal region of the plot. Except for a few small peaks, Figure B.7 exhibits a generally flat tail of noise. This method assumes that the signal and noise are 233 Figure B.6 Filtered surface temperature on Aug. 1/2 using various low-pass filters. Plus signs - measured surface temperature, short dashed line - SF = 0.2, long dashed line - SF = 0.075, solid line - SF = 0.03. Time has units of samples from the start. 234 io7 F 106 -105 . Frequency Figure B.7 Power spectral density of surface temperature (point 1 on the West wall) for Aug. 1/2. The straight horizontal line represents the average 'tail* of noise. The signal+noise curve has been extrapolated. 235 uncorrelated, an assumption partially violated here, as evidenced by a portion of the signal peaking at the higher frequencies. However, due to aliasing, the character of the noise is made more 'white' as it is folded into the spectrum (Hamming, 1983). Continuing, we can define the filter function (Figure B.8). Note that it's shape bears marked resemblance to the low pass filter function constructed earlier, differing only in the stop frequency. Given this similarity, a low-pass filter was constructed to approximate the optimal filter. A stop frequency of 0.015 was selected based upon the plot of the optimal filter function. Data from other days yielded similar results. Using 105 terms, the transfer function closely approximates the optimal filter. Using the low-pass filter as a representation of the optimal filter, the original data from Figure B.6 are filtered and the results are shown in Figure B.9. B.4 EXTRAPOLATION OF ADDITIONAL SURFACE TEMPERATURES ON CANYON WALLS The addition of an extra grid-point near the top of the walls in the modified Arnfield model (Chapter 3) requires two additional surface temperatures. Measured data are not available for these grid-points, therefore the temperature must be estimated by empirical or theoretical means. In the absence of an analytical function to describe the temperature of the 236 Figure B.8 Filter function derived from an optimal filter (solid line), compared to a low-pass filter (dashed line) using 105 terms and a stop frequency of 0.015. 237 24.0 Figure B.9 Filtered surface temperature using an 'optimal' low-pass filter. Top: Aug. 1/2. Bottom: The first 75 measurement intervals of Aug. 1/2 for comparison with Fig. B.6. 238 additional grid-points, interpolation/extrapolation methods may be used. The problem in this case is one of extrapolation, and is made more difficult by the differences of the structure and position of the capping blocks compared to the remainder of the canyon walls. Recall that the capping block is a solid slab placed across the-upper row of concrete blocks. It is probable that, due to the variation in the thermal properties and position of the capping blocks, the extrapolation of the temperature distribution curve over the wall to the capping block will not be smooth. A low order extrapolation of the temperature over the top portion of the wall has been selected to estimate these temperatures. Profiles of the surface temperature distribution up and down the canyon walls (Chapter 5) illustrate a significant alteration in shape between the walls and over time. In particular, the distribution of temperature up the East wall after sunset shows a large peak near the top of the wall. In such cases the temperature to be extrapolated is related to only one or two grid-points lower than itself and a low order of extrapolation is necessary. Later at night the temperature distribution is much smoother and a higher order of extrapolation can be specified. Polynomial extrapolation assumes the temperatures of the known points are correct so that in data where noise was originally present the filtered data are used in the extrapolation procedure. The sensitivity of the extrapolation to the order used for a selection of data is presented in Chapter 239 3. While the probability of errors is high, the points to be extrapolated are only used to prevent excess errors in the modelled radiation for the tenth grid-point on each wall and are not used as a point in the validation of the measured and modelled data. The closest points affected by extrapolation errors (corner points on the canyon top) are also usually omitted (depending on length of traverse). No effect on neighbouring points on the wall is achieved in the model (see sensitivity tests, Chapter 3). The small area of the extra grid-point also reduces the errors which it may cause in other modelled points, relative to the error of a normal grid-point. 240 APPENDIX C. CALIBRATION OF THE BARNES PRT-4A INFRARED THERMOMETER A calibration curve for an infrared (IR) thermometer may be obtained by measuring the instrument output for various known temperatures of a blackbody surface. The calibration curve should cover the range of temperatures expected to be encountered in the field. The calibration curve was created and confirmed two methods. In the first, a stirred, constant temperature water bath was used as a test surface (Huband, 1985). The emissivity of water itself is high (0.972 Davies et al. 1971; 0.993 Buettner and Kern, 1965) and when combined with the polished metal surfaces of the bath produces an effective emissivty of the water-bath system of near unity (Fuchs and Tanner, 1966). A profile of six thermocouples was placed in the bath to obtain a vertical transect of temperature was across the water/air boundary so that surface temperature could be determined by interpolation. The IR thermometer was mounted over the bath and viewed the water surface though an aperture cut in the styrofoam insulating cover of the bath. To obtain points at lower temperatures a low temperature water bath filled with a water-glycol mixture was used. A second method, derived from Fuchs and Tanner (1966), was used to confirm the curve obtained from the water bath. Three thermocouples (30 awg) were cemented in shallow grooves cut in a plywood plate.-which was painted flat black. A small cone with a 241 polished aluminum inner surface was constructed and the IR thermometer was used to view the surface though the apex of the cone. The cone increases the effective surface emissivity so that the surface under the cone behaves approximately as a blackbody when the temperature of the cone equals that of the surface. Surface temperature measurements made with the thermocouples may then be compared to the instrument output. Figure A3.1 illustrates the results from the two procedures. The data from the first method (open squares) are fit by a curve using a second order polynomial (solid) and the dest-fit straight line (dashed). The difference between the two lines is minor over most of the range of surface temperatures encountered in the field. The points from the second method are also included for comparison (crosses). Use of the polynomial relation is recommended for very high or low surface temperatures. 242 T. = -13.318 • 1.2747 (rnV) - 0.004 (nM>) 10 20 30 40 Instrument Output (mV) Figure C.1 Calibration curve for Barnes Model PRT-4A Infrared Thermometer. 243 APPENDIX D. ERRORS D.1 INTRODUCTION This appendix describes the errors in the measured variables used for model input and model validation. The bounds of error placed upon those variables used in model input can be used in conjunction with the sensitivity analysis of Chapter 3 to determine effects on modelled radiation. The instrumentation errors have been collected from many sources: original calibration certificates, manufacturer's specifications and various texts. For some instrumentation, there is documentation to list the component errors which together comprise a total error in the measurement. The absolute component errors may be summed or combined using a root mean square (RMS) approach. The errors of functions which consists of several variables have been calculated using probable error analysis as described in Fritschen and Gay (1979). For a function Y consisting of variables x1f x2 ... xn, the general equation for the absolute error of Y is EY = Ex. 6Y/6x] + Ex2 SY/6x2 + ... +' Exn•6Y/6xn (D. 1 ) where the Ex^ are the absolute errors of each of the variables. Absolute error provides a 'worst case' error estimate where all 244 errors act in the same direction to provide a maximum error. The probable error of Y assumes the errors of the x^ are normally distributed and that some compensation of the individual errors is likely to occur. The formula for the probable error of Y is PeY = [(Pex, 6Y/6xr)2 + ... + (Pexn 8Y/6xn)2] 1/2. (D.2) The differentials of Y with respect to each of the x^ are substituted into (2) and typical values of the variables are used to generate PeY. The values of Pex^ are the errors in the variables, typically the RMS error, and are obtained from component instrument errors, or estimated by other means. D.2 SURFACE TEMPERATURE ERRORS Errors to be considered when making a surface temperature measurement using a 21X micrologger with a built-in reference temperature include: the reference temperature, the thermocouple output, the voltage measurement used to estimate the temperature, the reference and output linearization, method of attaching the thermocouple to the surface and noise (Campbell Scientific, 1984). Table D.1 summarizes the component errors of a surface temperature measurement taken during the day under high solar radiation (Case 1), and under typical nighttime conditions (Case 2). 245 Table D.1 Error Summary: Surface Temperature Error Description Amount of Error (°C) Case 1 Case 2 Percent 1 of Total Error 2 Reference Temperature 0.6 0.7 28 39 Thermocouple Output - ANSI Standard 1.0 1.0 - 1% Slope Error 0.2 0.04 9 2 Voltage Measurement 0.06 0.07 3 4 Reference Linearization 0.001 0.001 <1 <1 Output Linearization 0.001 0.001 <1 <1 Mount ing 0.75 0.5 36 28 Noise 0.5 0.5 24 28 Sum RMSE 2.91 I 2.11 2 1 .47 \ 1 . 10 2 2.77 1 .81 1 .41 1 .00 Using ANSI standard error Assuming 1% slope error Reference temperature errors consist of errors in the thermistor used to measure the reference temperature within the 21X (±0.2 °C in the range 0-40 °C) and differences in temperature along the terminal strip on top of the 21X (generally less than 0.3 °C when the insulating terminal strip cover is used). The first error is essentially fixed with respect to the data collected however the second error will become smaller or larger depending upon how closely the multiplexer terminal strip temperature matches the 21X when the 21X reference temperature is used. Errors across the 21X terminal strip cover are further reduced by placing the entire 246 data logger within an insulating box, which minimizes temperature gradients around the data logger. Thermocouple output errors are entered as either the ANSI standard which is the manufacturers standard for type-T thermocouple wire or as the product of the slope error of the Seebeck coefficient with the difference in temperature between the surface temperature and measurement temperature. When expressed in the latter form, errors will become small as the surface temperature and reference temperature tend to converge. Voltage meaurement is generally 0.05% of the full scale range used to measure the thermocouple voltage. In all cases the 5 mV range was used, which in the environmental range of temperatures converts to a temperature error of 0.6 - 0.7°C. Reference and output linearization errors occur as a result of approximations to the conversion of voltage to temperature, and are negligible compared to the other errors. Mounting errors include conduction errors, radiation errors etc. which result from the presence of a thermocouple on the measurement surface. Each of these component errors can be estimated from formulas (eg. Fritschen and Gay, 1979) when precise information is available on the heat transfer properties of the surface, thermocouple and surroundings. Here, an estimate of the error has been made using the range of temperature differences about the 1:1 line of the comparison of surface temperature accuracy shown in Chapter 2. Errors are likely to be higher in the daytime due to larger radiation errors. 247 The final error component listed is noise. Plots of unfiltered temperature indicated fluctuations about the mean of up to 0.5 °C. While the errors in the filtered data are thought to be much less, this term has been retained as a cautionary measure. Using the 1% slope error in place of the ANSI error, it is clear that the error in temperature measurements is made up primarily of reference temperature errors, mounting errors, and noise. It is likely that errors in the reference temperature and noise are often less than is presented in Table D.1, thereby improving the error estimate. Total error estimates for nighttime temperatures range from 2.77 °C (absolute sums with ANSI standard error) to 1.00 °C (RMSE with a 1% slope error). D.3 EMISSIVITY ERRORS Surface emissivity was estimated using the governing equation listed in Table D.2b. Ts and Tr,each consist of a single measurement while T^ was obtained by sampling T^ at several zenith angles and multiplying the view-factor for the portion of sky viewed with the value of T^-. Component errors are shown in Table D.2a. 248 Table D.2a Error Summary: Emissivity (Ts, Tk, Tr) Error Description Amount Of Error Infrared Thermometer 0. 5 ° C 1 Voltage Measurement 0. 03 °C 2 Sum 0. 53 UC RMSE 0. 50 °c Reference: Barnes Engineering Co. Reference: Campbell Scientific (1984) Substituting typical values of Tr, Ts and Tk (293.66, 294.16, and 281.16 K respectively) into the equation for Pee (Table D.2b) a probable error of 0.06 in the surface emissivity is obtained when the error of Tr, Ts, and Tk are set to 0.5 K each. Table D.2b Probable Error Analysis: Emissivity Governing Equation: e = (Tr4 - Tk4) / (Ts4 - Tk4) Probable Error of e: Pee = [(PeTr 6e/6Tr)2 + (PeTs 6e/5Ts)2 + (PeTk 6e/8Tk)2]0•5 Partial Errors: 6e/5Tr = 4 Tr3/(TS4 - Tk4) 6e/6Ts = -4 Ts3 (Tr4 - Tk4)/(TS4 - Tk4) 6e/5Tk = 4 Tk3 (Tr4 - TS4)/(TS4 - Tk4) Because Tk is taken at discrete zenithal and azimuthal angles it is an approximation to the true hemispherical average and the errors will be- greater than for Tr and Ts. Analysis of the 249 partial errors reveals that the change in emissivity with respect to is minor (±0.003 for typical values used); thus the estimate of probable error remains satisfactory for greater errors in T^.. D.4 RADIATION ERRORS D.4.1 Lict Errors The instrument used to measure L^ct was an Eppley Precision Infrared Radiometer (pyrgeometer), Model PIR. Table D.3a provides a summary of errors of this instrument and the recording system used (21X Micrologger). Table D.3a Error Summary: L^ct Error Description Amount of Error Calibration 2 % 1 Temperature Dependence Linearity Cosine Response Recorder Errors 2 % (-20°C - 40°C) 2 1 % (0 - 700 W m~2) 2 insignificant for diffuse sources; <5 % from normalization 2 0.05 % of FSR Sum " 5.05 % (diffuse source) RMSE 3.00 % Reference: Latimer (1972). Reference: Eppley Instrument Manual. 250 The probable error analysis recognizes the governing- equation is simply the instrument output multiplied by the calibration i coefficient (Table D.3b). Table D.3b Probable Error Analysis: L^ct Governing Equation: L^c^ = C (IO); C = Calibration Coefficient IO = Instrument Output Probable Error of L^ct: PeLict = [(PeC 6Lict/8C)2 + (PelO 8Lict/«IO)2]0•5 Partial Errors: 6Lict/6C = IO 6Lict/5IO = C The component error of the instrument calibration is treated separately from the other errors. For the instrument used the calibration coefficient is 215.98 W m~2 mV-1, the error in C is 2%, and the error in the instrument output is 2.24% (RMSE). Therefore an instrument output of 1.6 mV (typical nighttime value) yields a probable error estimate of 10.37 W m-2. D.4.2 L*0 Errors Net radiation over the open site was measured using a miniature net radiometer. The instrument and recording errors are listed in Table D.4. 251 Table D.4 Error Summary: L*D Error Description • Amount of Error Calibration 2.5 % Temperature Dependency 0.012 % Balance 1.0% Recording Errors 0.05 % of FSR Sum 3.562 % RMSE 2.693 % Reference: Original Manufacturer's Specifications The probable error analysis is similar to that for Lict. The calibration constant for L*0 was 164.93 W m~2 mV_1, the error of calibration is 2.5% and the remainder of the instrument error is 1.0% (RMSE). For an instrument output of -0.1 mV, the probable error of L*D is 0.4 W m~2; for an output of -0.8 mV the error is approximately 3.6 W m~2. D.4.3 L* Errors Errors in the radiative fluxes measured by the traversed instruments have two additional errors to those listed in Table D.4. These result from the traversing procedure and are composed of errors resulting from the finite initial delay length, and the errors of instrument response to changes of radiative fluxes over canyon surfaces. The error to the inital delay has been calculated as 1.5 %, which is the adjustment remaining to a step 252 change after a delay length of 27 seconds (Table A1.3). The design error for a change in L* of 30 W m~2 over a 1 m canyon facet traversed in 180 seconds is approximately 3 percent. A worst case error of 10 % has been identified by using the observed changes in L* between adjacent points on the canyon walls. The error summary of L* is presented in Table D.5. Table D.5 Error Summary L* (Traversed) Error Description Amount of Error Calibration 2.5 % Temperature Dependency 0.012 % Balance 1.0% Recording Errors 0.05 % of FSR Initial Delay 1.5% Response to Change in LD 3 % (design) 10 % (worst case) Sum 8.06% (design), 15.06% (worst case) RMSE 4.30% 10.46% A probable error analysis of ,L* yields errors ranging from 0.7 - 1.7 W m~2 for an instrument output of -0.1 mV, and between 5.7 - 13.9 W m~2 for an output of -0.8 mV using the worst case RMS error for the instrument output (Note: Table D.5 gives the total errors including the calibration component). 253 D.4.4 Lc Errors Use of a blackbody cavity with a minature net radiometer to measure L0 incurs additional errors due to the need for a temperature measurement. The component errors are listed in Table D.6a. Table D.6a Error Summary LQ (Traversed) Error Description Amount of Error Calibration 2.5 % Temperature Dependency 0.012 % Balance 1.0% Recording Errors 0.05 % Of FSR Initial Delay 1.5% Response to Change in LQ 3 % (design) 10 % (worst case) Reference Temperature 0.4 °C Thermocouple Output ANSI Standard 1% Slope Error 1 .0 °C 0.02 °C Voltage Measurement 0.07 °C Reference Linearization 0.001 °C Output Linearization 0.001 °C Sum (radiation errors) 8.06% design 15.06 % worst RMSE (radiation errors) 4.30 % 10.46 % case Sum (thermocouple errors) 0.49 °C 1% slope 1.47 °C ANSI RMSE (thermocouple errors) 0.41 °C error 1.08 °C 254 The thermocouple errors are based upon a cavity temperature of 20.0 °C, a reference temperature of 18.0 °C and a temperature gradient across the terminal strip of 0.2 °C. A probable error analysis is presented in Table D.6b. In general, the instrument output is small at night during traversing (except at the canyon top) so that the probable error is dominated by the Tc errors. Probable errors range from worst case estimates of over 10 W m-2 at the canyon top to less than 3 W m~2 for design radiation errors and thermocouple errors using a 1% slope error (Table D.6c). Table D.6b Probable Error Analysis: L0 Governing Equation: L0 = C (IO) + aTc4 Probable Error of Lc: PeLD = [(PeC 6L0/6C)2 + (PelO 6Lo/6I0)2 + (PeTc 6L0/6TC)2 + (Pea 6L0/6a)2]0*5 Partial Errors: 6L0/6C = IO 6LQ/6I0 = C 5L0/6TC = 4aTc3 6LQ/5a - 0 255 Table D.6c Typical Probable Errors: LQ Tc 10 10 L0 measured PelO PeTc PeLn (°C) (W m 2.) (mV) (W m-2) (mV) (°C) (W m 2) 289.6 -80.4 -0.516 318.1 -0.018 0.41 4.1 1 -0.052 1.08 10.3 2 289.8 1.9 -0.013 401.9 0.0004 0.41 2.3 0.0013 1.08 5.9 290.2 25.8 0.166 427.7 0.0058 0.41 2.5 0.0168 1.08 6.6 PelO calculated using RMSE design (3.5%) PelO calculated using RMSE worst case (10.46%) 256 APPENDIX E. MODEL INPUT Input to the model for a typical nocturnal run is listed in Table E.1. Parameters listed fully define nocturnal radiative conditions. Model values needed for daytime runs, eg. standard irradiance of short-wave and diffuse radiation, solar azimuth and zenith angle are not listed. In addition to the listed input data, modifications to the model require that the canyon location (facet number and point) and value of the measured observations of Lc and L* be entered. 257 Table E.I Model Input for Nocturnal Model Runs. Model Name Definition Comments H W L THETA E T LD various ID IT IF IP JRAD IRADL P1L P2L P3L RSTOP IVFIN IVFOT ICHEK Canyon height Canyon width Canyon half-length Canyon orientation Emissivity Temperature Lict View-factors Date Time (PDT) Facet Number Point Number Defines radiation budget components to be calculated Identifies the rad iance distribution for sky derived long wave Radiance distribution parameter 1 Radiance distribution parameter 2 Radiance distribution parameter 3; Zenithal optical water path (u) convergence criteria for canyon multiple reflection routines source.of view-factors file to save view factors sets check to avoid re calculating variables arbitrary units ?« n ndegrees from north measured; array measured; array measured; at plane of canyon top arrays for pairs of canyon facets time written from data logger. End of the averaging period used. From 1 to 4:1 Wall A, 2 Wall B, 3 Floor, 4 Canyon Top From 1 to 10 for each facet array options: isotropic, Unsworth and Monteith (UM) (1975) Intercept c of the UM formula Slope from UM formula (cm), optional; for use with long-wave rad. dist.of Unsworth and Monteith (1975) in units of Wm-2 internal calculation or read from external file 258 APPENDIX F. ADDITIONAL VALIDATION DATA SETS F.1 AUGUST 2/3 The complete validation data set collected on August 2/3, 1988, from a canyon with a H/W of 2.0. Table F.1 Model Performance Statistics: August 2/3, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Statistic L* Isotropic L0 Li L* UM Lo Li n 1 1 24 1 1 24 1 1 24 1 1 75 1 175 1 1 75 0 (W m t.) -32. 6 429.3 396. 7 -30. 4 420. 1 389. 8 P (W m 2) -30. 9 430.8 400. 0 -29. 5 421 .2 391 . 7 s0 (W m 2) 26. 9 11.9 31 . 6 25. 9 10.2 29. 5 sp (W m~z) 28. 2 11.8 31 . 6 26. 8 10.1 29. 3 RMSE (W m~2) 4. 9 4.0 5. 6 3. 3 3.2 3. 7 RMSEs (W m"2) 2. 0 1 .7 3. 3 1 . 1 1 .2 1 . 9 RMSEu (W m 2) 4. 5 3.6 4. 5 3. 1 3.0 3. 2 MSEs/MSE 0. 17 0.18 0. 35 0. 1 1 0.14 0. 26 MSEu/MSE 0. 83 0.82 0. 65 0. 89 0.86 0. 74 MAE (W m-2) 4. 3 3.1 4. 7 2. 8 2.5 3. 0 MBE (W m 2) 1 . 8 1 .5 3. 3 0. 8 1 . 1 1 . 9 r2 0. 98 0.91 0. 98 0. 99 0.91 0. 99 d 0. 99 0.97 0. 99 0. 99 0.98 0. 99 a (W m~2) 3. 0 24.9 7. 2 1 . 7 23.5 6. 9 b 1 . 04 0.95 0. 99 1 . 03 0.95 0. 99 259 F.2 AUGUST 8/9 The complete validation data set collect on August 8/9, 1988, from a canyon with a H/W of 1.0. Table F.2 Model Performance Statistics: August 8/9, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Statistic Isotropic UM L* Lo Li L* LQ Li 64 1064 1064 1064 1064 1064 14.6 415. 9 401 .3 -14.6 415.9 401 .3 14.1 417.2 403. 1 -14.3 417.2 402.9 11.0 6.2 11.6 11.0 6.2 11.6 8.2 5.5 9.1 9.4 5.4 9.5 3.6 1 .9 4.0 3.0 2.0 4.1 3.0 1.6 3.4 1.9 1.6 3.1 2.0 1.0 2.2 2.3 1 .2 2.7 0.69 0.71 0.72 0.40 0.64 0.57 0.31 0.29 0.28 - 0.60 0.36 0.43 3.2 1 .6 3.2 2.5 1.7 3.3 0.5 1 .3 1 .8 0.4 1 .3 1 .7 0.94 0.97 0.94 0.94 0.95 0.92 0.96 0.98 0.96 0.98 0.97 0.96 -3.5 55.8 99.6 -2.2 63.7 89.7 0.73 0.87 0.76 0.83 0.85 0.78 n 0 P (W nT2) (W m 2) (W m"2) (W m~2) RMSE (W m2) RMSEs (W m 2) RMSEu (W m 2) MSEs/MSE MSEu/MSE MAE MBE r2 d (W m 2) (W m 2) a b (W m 2) 260 F.3 AUGUST 11/12 The complete validation data set collect on August 11/12, 1988, from a canyon with a H/W of 0.67. Table F.3 Model Performance Statistics: August 11/12, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Isotropic UM Statistic L* L6 Li L* L0 Li n 0 (W m~2) P (W m_2) s0 (W m_2) sp (W m z) RMSE (W m~2) RMSEs (W m_2) RMSEu (W m 2) MSEs/MSE MSEu/MSE MAE (W m~2) MBE (W m 2) r2 d a (W m~2) b 975 975 -42.7 411.3 -47.6 412.9 27.0 13.0 23.0 13.2 9.1 3.5 6.8 1.6 6.0 3.1 0.56 0.21 0.44 0.79 6.4 2.4 -4.9 1.6 0.93 0.95 0.97 0.98 -12.3 7.4 0.83 0.99 975 975 368.5 -42.7 365.3 -47.2 27.4 27.0 24.2 24.1 6.9 6.9 4.9 5.5 4.9 4.2 0.50 0.64 0.50 0.36 5.1 5.2 -3.2 -4.5 0.96 0.97 0.98 0.98 46.3 -9.5 0.87 0.88 975 975 411.3 368.5 412.9 365.7 13.0 27.4 13.2 25.1 3.6 5.1 1.7 3.8 3.2 3.4 0.22 0.56 0.78 0.44 2.5 4.0 1.6 -2.8 0.94 0.98 0.98 0.99 8.9 31.4 0.98 0.91 261 F.4 AUGUST 14/15 The complete validation data set. collect on August 14/15, 1988, from a canyon with a H/W of 1.33. Table F.4 Model Performance Statistics: August 14/15, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Statistic L* Isotropic L* UM n 0 P (W m~2) (W m 2) (W m2) (W m 2) RMSE (W nT2) RMSEs (W m~2) RMSEu (W m~2) MSEs/MSE MSEu/MSE MAE MBE r2 d (W nT2) (W m~2) a b (W rn"2) 960 960 960 960 960 960 -25. 1 408. 7 383. 5 -25. 1 408. 7 383. 5 -28. 2 410. 9 382. 7 -28. 1 410. 9 382. 8 23. 7 9. 5 25. 7 23. 7 9. 5 25. 7 22. 1 8. 7 24. 2 22. 3 8. 7 24. 0 6. 3 3. 6 4. 4 5. 0 3. 7 3. 6 3. 7 2. 5 2. 0 3. 4 2. 5 2. 0 5. 1 2. 6 3. 9 3. 6 2. 7 3. 0 0. 34 0. 48 0. 21 0. 46 0. 46 0. 31 0. 66 0. 52 0. 79 0. 54 0. 54 0. 69 4. 8 2. 7 3. 6 3. 8 2. 8 3. 0 -3. 0 2. 2 -o. 8 -2. 9 2. 2 -0. 7 0. 95 0. 91 0. 97 0. 97 0. 90 0. 98 0. 98 0. 96 0. 99 0. 99 0. 96 0. 99 -5. 4 •54. 0 26. 8 -4. 8 56. 3 27. 3 0. 91 0. 87 o. 93 0. 93 0. 87 0. 93 262 F.5 AUGUST 22/23 The complete validation data set collect on August 22/23, 1988, from a canyon with a H/W of 0.41. Table F.5 Model Performance Statistics: August 22/23, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Statistic Isotropic UM L* L0 Li L* Lo Li 865 865 865 865 865 865 -48.8 413.1 364.3 -48.8 413. 1 364.3 -51.8 412.3 360.4 -51 .5 412.3 360.8 22.5 8.7 22.6 22.5 8.7 22.6 18.3 8.6 19.1 20.4 8.5 21.1 7.2 3.1 7.0 4.6 3.1 5.2 5.7 1 . 1 5.5 3.6 1 . 1 3.9 4.4 2.9 4.2 2.9 2.9 3.4 0.63 0.13 0.62 0.61 0.13 0.56 0.37 0.87 0.38 0.39 0.87 0.44 5.2 2.2 5.0 3.5 2.3 4.2 -3.0 -0.8 -3.8 -2.7 -0.8 -3.5 0.94 0.89 0.95 0.98 0.88 0.98 0.97 0.97 0.97 0.99 0.97 0.99 -13.4 29.0 60.5 -7.8 30.3 24.7 0.79 0.93 .0.82 0.90 0.93 0.92 n 0 P (W m~2) (W m~2) (W m~2) (W m 2) RMSE (W m~2) RMSEs (W nT2) RMSEu (W m~2) MSEs/MSE MSEu/MSE MAE MBE r2 d (W m 2) (W m 2) a b (W m"2) 263 F.6 AUGUST 23/24 The complete validation data set collect on August 23/24, 1988, from a canyon with a H/W of 0.67. Table F.6 Model Performance Statistics: August 23/24, Individual Validation Points, Isotropic and Unsworth and Monteith (1975) Radiance Distribution. Statistic Isotropic UM L* Lo Li L* Lo Li 956 956 956 956 956 956 0 (W m t) --40.8 420.4 379.6 -40.8 420.4 379.6 P (W m 2) -44.3 419.7 375.4 -43.9 419.7 375.8 s0 (W nT2) 24.8 9.4 25.7 24.8 9.4 25.7 sp (W m l) 19.9 9.1 21.6 20.8 9.1 22.5 RMSE (W m~2) 8.5 3.2 7.7 6. 1 3.2 5.8 RMSEs (W m"2) 6.6 1 .0 6.2 5.3 1 .0 5.1 RMSEu (W m"2) 5.4 3.0 4.5 3.2 3.0 2.7 MSEs/MSE 0.60 0.10 0.65 0.75 0.10 0.77 MSEu/MSE 0.40 0.90 0.35 0.25 0.90 0.23 MAE (W m"2) 6.6 2.3 5.8 4.9 2.4 4.8 MBE (W nT2) -3.5 -0.6 -4.2 -3.2 -0.6 -3.8 r2 0.93 0.89 0.9 0.98 0.99 0.99 d 0.96 0.97 0.9 0.98 0.97 0.99 a (W m~2) -12.8 34.6 63.7 -10.1 35.9 46. 1 b 0.77 0.92 .0.8 0.83 0.91 0.87 264 APPENDIX G. STATISTICAL INDICES OF MODEL PERFORMANCE G.1 SUMMARY UNIVARIATE STATISTICS Observed 0, and predicted P, means and standard deviations, _ n 0 = ( Z 0^ n~1 (G.1) i = 1 _ n P = ( I Pi) n"1 (G.2) i = 1 so [n (I Oi2) - (2 Oi)2 n_1 (n-1)-1]0-5 (G.3) i=1 i=1 sD = [n (I Pi2) - (Z Pi)2 n_1 (n-1)_1]°-5 (G.4) * i=1 i=1 G.2 COEFFICIENTS OF LEAST-SQUARES LINEAR REGRESSION The intercept a, and slope b. n n n n (Z PA MI O,-2) - (Z OiMZ Oi Pi) i = 1 i=1 i = 1 i = 1 a = (G.5) n n n (Z Oi2) - (Z Oi)2 i=1 i=1 n n n n (Z OiPi) - (Z OiMZ Pi) i=1 i=1 i=1 b = (G.6) n (Z Oi2) - (Z Oi)2 i=1 i=1 265 G.3 MEASURES OF ERROR The root mean square error, RMSE, systematic and unsystematic portions of the RMSE (RMSES and RMSEU respectively); mean absolute error, MAE, and mean bias error, MBE. RMSE = [n~1 I (Pi - Oi)2]0'5 (G.7) i = 1 RMSES= [n~1 Z (Pi - Oi)2]0'5 (G.8) i = 1 RMSEu = [n~1 Z (Pi - Pi)2]0-5 (G.9) i = 1 where Pi = a + bOi, (G.10) and a and b are the coefficients of simple linear regression. 11 MAE = n"1 Z |Pi - Oi| (G.11) n Z i = 1 n MBE = n 1 Z (Pi - Oi) (G.12i = 1 266 4 INDICATORS OF CORRELATION The coefficient of determination, r , and index of agreement, n n n [n (Z Oi Pi) - (Z OiMZ Pi)]2 i=1 i=1 i=1 r2 = __ (G.13) [n (Z Oi2) - (Z O,)2 ] [n (Z Pi2) - (Z Pi)2] i = 1 i = 1 i = 1 i = 1 Z (Pi - Oi)2 i = 1 d = (G.14) where £ [|Pil + |OiN2 i=1 Pi = Pi - 0 (G.15) Oi = Oi - 0. (G.16

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0097570/manifest

Comment

Related Items