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Keywords:

  • rainfall interception;
  • urban water balance;
  • urban heat balance;
  • saturation deficit;
  • ground heat flux;
  • COSMO

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[1] Rainfall interception (RI) over an outdoor urban-scale model was investigated from the perspectives of water and energy balance. On average, RI was 6% of the gross rainfall and smaller than typical values in forests. No correlation was found between RI and gross rainfall or rainfall duration unlike the correlations found in forests. Most RI occurred in the first several hours of rainfall, and then RI rapidly decreased with time during a rainfall event. RI was dependent on the saturation deficit at the beginning of the rainfall event. The latent heat for RI was approximately balanced by heat conduction from the concrete surfaces. Differences in the canopy structure are considered as possible reasons for the different behaviors of RI between the present site and forests. Accordingly, three aspects of the canopy structure, i.e., effective wet surface area, efficiency for scalar transfer, and canopy heat capacity, are discussed.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[2] The water vapor transfer process between cities and the atmosphere is an important element in urban meteorology and hydrology. The characteristics of urban latent heat flux on nonprecipitation days have been investigated in a number of field campaigns in urban areas [e.g., Oke, 1988; Grimmond and Oke, 1999a; Kanda et al., 2002; Moriwaki and Kanda, 2004; Grimmond et al., 2004; Christen and Vogt, 2004]. On the other hand, studies on the characteristics of latent heat flux during rainfall, especially rainfall interception (RI), are limited [Grimmond and Oke, 1991; Ragab et al., 2003; Gash et al., 2008]. Ragab et al. [2003] (hereinafter referred to as RAGAB) pioneered urban RI measurements. However, their focus was on “local RI” on the roofs of houses. No “bulk RI” measurements of entire urban canopies have yet been conducted. One reason for the scarcity of research on urban RI is the difficulty in making hydrological and meteorological measurements in real cities due to their complex geometries.

[3] In contrast to the limited observations of urban RI, many observations of RI have been conducted in forest regions [e.g., Zinke, 1967]. Rainfall interception typically ranges from 10 to 50% of gross rainfall in many forests [e.g., Hörmann et al., 1996]. Two mechanisms are known for RI in forests: (1) evaporation from the surfaces of leaves [Rutter et al., 1971; Gash, 1979; Gash et al., 1995], which is known as the aerodynamic mechanism, and (2) evaporation from small water droplets produced by the splash of raindrops that have collided with a canopy element [Murakami, 2006, 2007].

[4] The objective of this study is to investigate the magnitude and mechanisms of urban RI using data obtained from the Comprehensive Outdoor Scale Model (COSMO). COSMO is an idealized miniature city which has no vegetation, no human activity, and no heterogeneity of the surface geometry. The model has been created by arranging large concrete cubes on a concrete base to ensure thermal inertia similarity with real cities. The simple and idealized setup of COSMO allows for detailed examinations of the bulk RI of entire urban canopies for both the energy balance and the water balance.

2. Methodology

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

2.1. Site Description and Data

[5] The COSMO experimental site was located in the northern side of the Kanto Plain in Japan (39°04′N, 139°07′E) and was characterized by temperate climate with a rainy season in June and July and a dry season in winter. The dominant wind directions at the site were northwesterly in winter (October–April) and southeasterly in summer (May–September). Rice paddies (northwestern side) and sparse residences extended at least a few tens of kilometers around the site. The model consisted of cubic concrete blocks with 1.5 m height and 0.1 m wall thickness. The blocks were empty inside. A total of 512 blocks were regularly arranged on a flat concrete base with a surface area of 50 m × 100 m and thickness of 0.15 m (Fig.1). The street widths were 1.5 m throughout the model city. The typical Reynolds number of the airflow in COSMO was of the order of 105. The airflow in COSMO was dynamically similar to that in real cities [Kanda, 2006]. The concrete base was flat with a 1/200 inclination along the shorter axis to allow for drainage. The plane area aspect ratio was 0.25, and one of the two street directions pointed 43° counterclockwise from north. The same concrete material was used for the blocks and the basement, and all surfaces were painted with a dark gray paint. Therefore thermal and radiative properties of all surfaces were the same. More detailed descriptions of COSMO are given by Kanda et al. [2007], and Inagaki and Kanda [2008], and T. Kawai and M. Kanda (Energy balance obtained from the comprehensive outdoor scale model experiment: I. Basic features of the surface balance, submitted to Journal of Applied Meteorology, 2008). A portion of the COSMO site (6 m × 6 m) was used as a catchment for the current study. This catchment was enclosed by waterproof fencing (5 cm high), and all surfaces in the catchment were coated with a transparent water-impervious paint over the original paint. Thus infiltration into the concrete and horizontal water exchange between the catchment and its surrounding area were assumed to be zero. The runoff was collected and measured by a flowmeter (UIZ-TB1000, UIZIN, Ltd.) with a resolution of 1.0 L per tip (Figure 1). Total rainfall was measured at 1 m above the ground using a tipping-bucket rain gauge (TR-525M, Texas Electronics, Inc.) with a resolution of 0.1 mm per tip at a horizontal distance of 40 m from the catchment; the spatial variability of rainfall was assumed to be negligible. The data from the flowmeter and the rain gauge were recorded by a logger at 1-min intervals.

image

Figure 1. Schematic of outdoor urban-scale model site (top, side view; bottom, plan view). The shaded area (6 m × 6 m) is the catchment for the current study on rainfall interception. The numbers in parentheses represent the locations of the instruments: 1, rainfall gauge; 2, flowmeter; 3, three-cup anemometer and temperature and relative humidity sensors; and 4, ground heat flux and surface temperature sensors (heat flux plates).

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[6] Wind velocity was measured by a three-cup anemometer (03001-L, Campbell). Ambient temperature and relative humidity were measured by a temperature and humidity sensor (Hummitter 50U/50Y, Vaisala). These meteorological measurements were made at 1 Hz at 3 m above the ground and were recorded by a data logger as 1-min averages. Heat storage and surface temperature were directly measured in the present study. The conductive heat flux and the surface temperature for each of the surfaces constituting the idealized model city, i.e., the roof, floor, and four vertical walls, were directly measured using thin (300 × 300 × 0.4 mm in size) and highly accurate (instrumental accuracy within ±5%) heat flux plates (HF-300T, Captec) at 1-s intervals. A total of 164 heat flux plates were attached to a sample unit that consisted of a block and its surrounding streets for precise measurements.

[7] The present data set from COSMO allowed the investigation of RI from the perspectives of aerodynamics and heat balance.

2.2. Estimation of Rainfall Interception

[8] With the use of the simple catchment described in section 2.1, the water balance equation per unit horizontal area of COSMO can be written as

  • equation image

where P and Q are the rainfall and runoff, respectively (see Figure 2). All units are in volume of water per unit horizontal area (mm). RI was calculated for each rainfall event with equation (1). Two conditions needed to be met for the rainfall event to be included in the analysis: (1) Total precipitation was greater than or equal to 0.2 mm, that is, twice the rain gage resolution; and (2) no rainfall was observed in the 3-h period prior to the onset of the rainfall event to be defined. The second condition was applied to avoid the influence of runoff from a previous rainfall event.

image

Figure 2. Schematic of water balance in the Comprehensive Outdoor Scale Model (COSMO).

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[9] One component of RI is water storage capacity (St). To estimate St for COSMO, water was artificially poured onto the block surfaces and the floor. This experiment was conducted separately for the block roofs, block walls, and floor. The water remaining on the relevant surfaces was absorbed by towels and weighed. For the floor, St was calculated by subtracting the total amount of runoff from that of the poured water. To minimize the effect of evaporation, the measurements were made in the early morning, and the towels with absorbed water were stored in plastic bags. Furthermore, the experiment was performed at least five times for each relevant surface to reduce the measurement errors. The statistics of the measured values are shown in Table 1. The total value of St for COSMO was estimated to be 0.25 mm from

  • equation image

where Stroof, Stwall, and Stfloor are the storages for the roof (0.239 mm), wall (0.0087 mm), and floor (0.247 mm), respectively; Aroof, Awall, Afloor, and Ahoriz are the roof (9 m2), wall (36 m2), net floor (27 m2), and horizontal (36 m2) areas, respectively.

Table 1. Measured Values of St for Roofs, Walls, and Floorsa
 Roof × 10−1 (mm)Wall × 10−2 (mm)Floor × 10−1 (mm)
  • a

    Each value represents the measured value of St for a single surface (roof, wall, or floor). Total St = 0.25 mm and refers to the area-weighted average value of St (see equation (2)).

 2.490.802.87
 2.311.022.60
 2.400.802.23
 2.451.202.61
 2.331.022.04
 2.340.53
 0.76
 0.80
 0.89
Average2.390.872.47
Standard deviation0.070.210.30

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

3.1. Statistical Summary of RI and Rainfall Events

[10] Table 2 and Table 3 summarize the rainfall events in the period from September 2006 to January 2007. The ranges of total rainfall, maximum hourly rainfall, rainfall duration, and average wind velocity during rainfall are 0.2–134.5 mm, 0.1–10.5 mm h−1, 2–50 h, and 0.2–2.8 m s−1, respectively. The estimated values of RI ranged from 0 to 5.1 mm. On average, RI was 6% of the total rainfall. This value is smaller than the average value of RI estimated for the roofs of houses in the United Kingdom by RAGAB. The different values of RI between COSMO and RAGAB may offer insight into the difference between “bulk RI” of entire urban canopies and “local RI” of roofs (see section 4.2). The average percentage of RI relative to the total rainfall in COSMO is also significantly smaller than that reported for forests, 10–50%. The smaller value of RI from COSMO may be attributable to the difference in the canopy structure between COSMO and forests. In forest regions, high correlations between RI and certain rainfall quantities such as total rainfall [e.g., Rowe, 1983] and rainfall duration [e.g., Horton, 1919] have been observed. However, there was neither a clear dependency of RI on total rainfall (Figure 3) nor of RI on rainfall duration (Figure 4) in COSMO. The different behaviors of RI between COSMO and forests will be further discussed in section 4.1.

image

Figure 3. Relationship between rainfall interception (RI) and total rainfall. The x axis is logarithmic. Error bars represent the uncertainties associated with instrument accuracy. The data are classified by the tilt of the rainfall from the vertical direction. Data for which rainfall tilt could not be calculated due to a lack of wind speed data are shown as open circles. Negative values of RI are excluded.

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image

Figure 4. Relationship between RI and rainfall duration. Error bars represent the uncertainties associated with instrument accuracy. The data are classified by the tilt of the rainfall from the vertical direction. Data for which rainfall tilt could not be calculated due to a lack of wind speed data are shown as open circles. Negative values of RI are excluded.

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Table 2. Gross Rainfall, Maximum Hourly Rainfall, Mean Hourly Rainfall, Rainfall Duration, Gross Runoff, Runoff Fraction (Runoff as a Fraction of Total Rainfall), RI, RI Fraction (RI as a Fraction of Total Rainfall), and Mean Wind Speed During Rainfall for Each Rainfall Eventa
DOY_JSTRainfallGross Runoff (mm)Runoff FractionRI (mm)RI Fraction (1- Runoff Fraction)Mean Wind Speed (m s−1)
Gross (mm)Maximum Hourly (mm h−1)Mean Hourly (mm h−1)Duration (h)
  • a

    DOY and JST denote day of year and Japan Standard Time, respectively. NA, not available.

249_077.62.60.5162.470.335.10.671.1
252_010.30.20.220.000.000.31.000.6
254_044.21.61.142.610.621.60.381.3
254_170.50.30.320.000.000.51.001.5
255_030.30.20.220.000.000.31.000.4
255_0952.14.61.05050.000.962.10.040.9
260_1927.66.41.81526.800.970.80.030.7
261_131.21.20.621.110.930.10.072.2
270_134.33.72.224.301.000.00.001.7
274_1428.83.11.32224.120.844.70.161.2
275_1931.30.562.860.950.10.050.4
277_040.70.30.240.030.040.70.960.2
278_11134.510.53.341132.160.982.30.023.1
295_1933.510.41.91831.660.951.80.051.1
302_023.82.11.332.860.750.90.25NA
311_061.71.60.920.560.331.10.670.8
315_081.90.70.2120.920.481.00.520.9
319_187.64.31.176.780.890.80.111.3
323_1249.26.32.22248.470.990.70.012.5
324_162.92.60.482.670.920.20.080.6
327_220.40.10.170.000.000.41.000.7
330_2230.452.21430.891.02−0.5−0.022.1
331_185.51.40.3165.581.02−0.1−0.021.0
343_085.61.30.4144.720.840.90.16NA
346_141.41.20.531.140.810.30.19NA
347_160.20.20.140.060.280.10.72NA
348_1812.12.41.01212.030.990.10.01NA
006_0528.75.62.11429.221.02−0.5−0.022.8
017_183.41.10.492.940.870.50.130.8
021_242.30.80.551.920.830.40.170.8
Table 3. Cumulative Values of Gross Rainfall, Gross Runoff, and Gross RI and Average Values of RI Fraction and Runoff Fraction for the Rainfall Events in Table 2
Gross Rainfall (mm)Gross Runoff (mm)Gross RI (mm)Average RI FractionAverage Runoff Fraction
455.7428.8826.700.060.94

[11] Wind can tilt rainfall from the vertical direction, which is known as wind-driven rain (WDR) [Herwitz and Slye, 1995; Sevruk and Nespor, 1998; Blocken and Carmeliet, 2004]. In the presence of WDR, (1) the rainfall rate at the canopy surface becomes spatially heterogeneous, (2) local circulation may be induced by wind around the rain gauge, and (3) raindrops that have landed on the canopy surface may be transported away from the canopy by wind. Thus the presence of WDR can cause deviations in the values of RI estimated in a catchment. Accordingly, the rainfall events were classified into three groups based on the tilt angle of raindrops from the vertical direction to investigate the WDR effect on the relationship between RI and the total rainfall (Figure 3) and that between RI and rainfall duration (Figure 4). The tilt angle was calculated for each rainfall event using the mean wind velocity and the mean rainfall intensity given by Herwitz and Slye [1995]. No clear effects of WDR were observed on the relationship between RI and the total rainfall (Figure 3) or of that between RI and rainfall duration (Figure 4). This result may be explained by the influence of the WDR on both the capture rate of rainfall and the wind-induced loss of raindrops from the catchment area; that is, both P and Q in equation (1) are affected.

3.2. Seasonal and Temporal Changes of RI

[12] Rainfall interception tended to be larger in summer than in winter (Figure 5). The seasonality of RI appears to be related to that of available radiative energy.

image

Figure 5. Seasonal variation of RI. Day of year is indicated as DOY. The broken line is the water storage capacity of the site (0.25 mm). Error bars indicate the uncertainties associated with instrument accuracy.

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[13] To investigate the temporal changes of hourly RI, temperature difference between the surface and ambient air, and saturation deficit, rainfall events that satisfied the following conditions were selected for the analysis: (1) rainfall duration was more than 10 h and (2) the total RI was nonnegative. The ensemble-averaged values of the temporal change of hourly RI of the selected rainfall events indicate that most of the RI occurred in the first several hours of rainfall and that RI rapidly decreased with time (Figure 6a). In Figure 6a, a 5-h moving average was applied to both the rainfall and runoff data to reduce the time lag between rainfall and runoff.

image

Figure 6. Temporal variability of (a) hourly RI, (b) temperature difference between the surface and the ambient air, Tc − Ta, and (c) saturation deficit. Symbols and error bars indicate ensemble means and standard deviations, respectively. Rainfall events were included if (1) the duration was more than 10 h and (2) the total RI of the event was nonnegative. In Figures 6b and 6c, two rainfall events are excluded due to a lack of data.

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[14] To calculate the temperature difference between the ambient air and the surface, the ambient air temperature, Ta, from a height of 3 m and the complete surface temperature, Tc, were used. The complete surface temperature, Tc, is defined as the simple area-weighted average of the temperature of all surfaces of and surrounding a block (i.e., the four vertical walls, roof, and floor). Figure 6b shows the ensemble-averaged values of the temperature difference between the Ta and Tc and indicates that Tc is higher than Ta during rainfall in COSMO. This observation is attributable to the large heat capacity of the urban material.

[15] Subsequently, the saturation deficit was estimated from Ta, Tc, and RH with the following assumptions. First, the surface air was assumed to be saturated at Tc during rainfall because of the small value of St (section 2.2). The small value of St implies that the surface of the COSMO model can be wetted by a small amount of water, which creates a thin water layer on the smooth model surface. The temperature of this thin layer can reasonably be assumed to be equal to the temperature of the model surface, Tc. Second, RH was assumed to be 100% when the RH data from a height of 3 m exceeded 90%. This assumption was made because RH measurements in high-humidity conditions are considered unreliable. Figure 6c shows the ensemble-averaged values of the temporal change of the saturation deficit.

[16] The temporal changes of RI, temperature difference between the surface and the ambient air, and saturation deficit in Figure 6 appear to be correlated. This result indicates that RI was governed by the conventional aerothermodynamic mechanism.

3.3. Aerothermodynamic Evaluation of RI

[17] The direct application of an aerothermodynamic method to the prediction of RI is difficult because of the difficulty in obtaining accurate measurements of the saturation deficit during rainfall. As an alternative, RI was related to the saturation deficit at the beginning of the rainfall event (Figure 7). Figure 7 suggests a dependency of RI on the saturation deficit at the beginning of the rainfall event, which may also be inferred from Figure 6. This dependency implies the possibility that RI can be estimated by a modification of aerothermodynamic methods using the saturation deficit measured at the beginning of the rainfall event. This possibility will be discussed in section 4.3.

image

Figure 7. Relationship between RI and saturation deficit measured at the beginning of each rainfall event. Eleven rainfall events are excluded due to a lack of data.

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3.4. Energy Balance of RI

[18] The energy balance provides another perspective for the investigation of RI. To estimate the storage heat flux G, the conductive heat fluxes into the four vertical walls, roof, and floor were individually measured by heat plates (section 2.1), and their values were weighted on a unit horizontal surface area basis. Figure 8 shows the relationship between the latent heat flux equivalent to the observed RI and the measured storage heat flux G into the surface during rainfall. Negative values of G indicate that heat was transferred from the subsurface to the surface. The correlation between the latent heat flux and G (Figure 8) indicates that the energy necessary to evaporate RI was mainly supplied from the concrete substrate (correlation coefficient = −0.75). One possible reason for the deviation of the correlation coefficient from −1 is that the RI measurement site is not exactly collocated with the storage heat flux measurement site (Figure 1). The heat budget and RI are both affected by characteristics of the wind field. The wind field around the RI site may be different from that around the site with heat plates, especially in summer, because the fetch for the RI site becomes short due to the summertime prevailing wind direction. Heat balance during rainfall for both COSMO and forests is further discussed in section 4.1.3.

image

Figure 8. Relationship between the latent heat for RI (L × RI) and the total storage heat flux into the ground (G). Negative storage heat flux indicates that heat was transferred from the subsurface to the surface. Triangles indicate data that were affected by sunlight during rainfall. The dashed line is the 1:1 line. Three rainfall events are not included due to a lack of data.

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4. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

4.1. Difference in RI Between COSMO and Forests

[19] The value of RI as a percentage of total rainfall in COSMO was significantly smaller than the typical values in forests. A possible reason for the smaller RI in COSMO is the difference in canopy structure between COSMO and forests. Accordingly, three aspects of the canopy structure will be discussed: (1) complete surface area index (SAI), (2) scalar transfer efficiency in relation to roughness size, and (3) heat balance in relation to volumetric heat capacity of the roughness elements.

4.1.1. Complete Surface Area Index

[20] The complete surface area index (SAI) is the ratio of all surface areas to the horizontally projected ground surface area. In a forest, the SAI is twice the leaf area index (LAI). The SAI is a measure of the wettable surface area. Accordingly, a high correlation is found between SAI and St for a variety of forests that were studied in the literature (Figure 9a). In addition, SAI is well correlated to RI regardless of forest type or climate conditions (Figure 9b). Table 4 summarizes the values of SAI, St, and RI reported in the literature. Figure 9 and Table 4 suggest that the small value of SAI in COSMO is one of the reasons for the small value of RI in COSMO.

image

Figure 9. Relationship between surface area index (SAI) and (a) storage capacity (St) and (b) RI as a percentage of total rainfall. Detailed information on the reported values for forests is summarized in Table 4.

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Table 4. Leaf Area Index (LAI), Complete Surface Area Index (SAI), Water Storage Capacity (St), Rainfall Interception (RI) as a Percentage of Gross Rainfall, and Gross Rainfall (GR) as Reported in the Literaturea
LAISAISt (mm)RI (%)GR (mm)PeriodCanopy TypeCountryReference
  • a

    NA, not available.

10.220.41.421.4418.736 monthsPseudotsuga menziesiiUnited StatesPypker et al. [2005]
7.314.62.4638.581914 yearsLauraceae, etc.EcuadorFleischbein et al. [2005]
4.559.10.618.93160.82 yearsChamaecyparis obtusaJapanMurakami [2006]
2.054.10.9714.3867.132 monthsQuercus serrara, etc.JapanDeguchi et al. [2006]
3.486.961.2617.62990.0
8.617.23.324.01069.62 yearsPseudotsuga menziesiiUnited StatesLink et al. [2004]
12241.239NA18 monthsPseudotsuga menziesiiEnglandRutter et al. [1975]
5.110.21.0535Pinus nigra
6.613.20.828.413181 yearFraxinus ornus, etc.SloveniaŠraj et al. [2008]
6.913.80.7525.41212Carpinus orientaliscroaticus, etc.
4.59.01.1611.83273.8NANA (tropical rain forest)Colombian amazoniaMarin et al. [2000]
4.99.81.2812.23293.0    
5.611.21.3212.93158.4    
6.613.21.5517.23120.9    
2.34.60.5611.961310 monthsPinus pinasterFranceGash et al. [1995]
2.75.40.4117.11366.230 monthsPinus pinasterPortugalValente et al. [1997]
3.26.40.2110.81545.8 Eucalyptus globulus  
5.911.81.155285266 daysDacryodes excelsaPuerto RicoSchellekens et al. [1999]
4.59.02.3425.817950 daysPicea abies, etc.SwedenLankreijer et al. [1999]
5.611.31.225.4    above average
NA2.00.256.0428.885 monthsconcreteJapanthis study
4.1.2. Scalar Roughness Parameter

[21] The difference in water vapor transfer efficiency between COSMO and forests is discussed using an analogy to heat transfer. The aerodynamic resistance of heat transfer between the atmosphere and the surface is larger than that of momentum transfer. This enhancement of resistance for heat transfer is expressed as the ratio of the roughness length for momentum (z0) to that for heat (zT) [e.g., Brutsaert, 1982]:

  • equation image

The value of kB−1 is generally larger in urban areas than in forests [Voogt and Grimmond, 2000; Moriwaki and Kanda, 2006; Kanda et al., 2007; Kawai et al., 2009]. The value of kB−1 for COSMO is also larger than those for forests [Kanda et al., 2007]. These findings are also supported by the theoretical relationship between kB−1 and Reynolds number [Brutsaert, 1982]; the values of kB−1 are generally small for forest canopies and large for bluff obstacles such as urban canopies. Applying this idea to the evaporation process during rainfall, with the assumption that water vapor transfer is analogous to heat transfer, the larger value of kB−1 in COSMO and real cities is expected to yield a lower efficiency of water vapor transfer than in forests.

[22] The difference in kB−1 between COSMO and forests may be interpreted as a result of the difference in the size of the individual roughness elements. On small leaves, the boundary layers are not fully developed due to the short fetch and disturbances caused by moving leaves, i.e., the leading-edge effect [Oke, 1987]. As a result, the resistance between the leaf surface and the surrounding air is small for small leaves. Because forest canopies can be considered as an aggregation of small leaves that have small resistances, the value of kB−1 for forests is expected to be small, implying more efficient heat transfer. Further studies are required to investigate the validity of this speculation.

4.1.3. Heat Supply From Roughness Elements

[23] Energy balance requires that the energy loss equivalent to RI must be balanced by other energy flux terms. In forests, the possible heat sources for RI are sensible heat flux from the atmosphere [Stewart, 1977; Pearce et al., 1980; Kelliher et al., 1992; Asdak et al., 1998; Lankreijer et al., 1999] and net radiation (Rn) [e.g., Rutter et al., 1971; Gash, 1979; Kondo et al., 1992]. Leaves, which have a small volumetric heat capacity, cannot be a heat source for RI. However, the small volumetric heat capacity of leaves causes the leaf surface temperature to be lower than the ambient air, and the lower leaf temperature induces sensible heat supply from the atmosphere. Rn is supplied to the forest canopies during rainfall in daytime. The energy available from Rn is redistributed into sensible and latent heat terms, but not to the heat storage term due to the small heat capacity of forest canopies. Thus continuous heat supplies from both the sensible heat and Rn can sustain RI during rainfall, and this mechanism may account for the good correlation between RI and rainfall duration in forests. Gross rainfall amount generally increases with rainfall duration [Horton, 1919; Gash, 1979]. Therefore the relationship between RI and gross rainfall amount is essentially the same as the relationship between RI and rainfall duration.

[24] In contrast to forests, the latent heat necessary to balance RI in COSMO was mainly supplied from the concrete substrate (Figure 8) probably because the concrete has a large volumetric heat capacity. Large values of RI were observed mainly in the early stages of each rainfall event and the value of RI rapidly decreased with time (Figure 6a). The surface temperature in COSMO was always higher than that of the ambient air during rainfall (Figure 6b), which is opposite the situation found in forests. These results suggest that RI in COSMO was mostly determined by the saturation deficit or by the heat storage of urban materials at the beginning of the rainfall event; the influences of the rainfall duration and gross rainfall amount were quite small. This supposition is supported by the observations that the runoff water temperature at the beginning of a rainfall event was often warmer than that at the end of the rainfall event [Nakayama et al., 2007].

4.1.4. Effects of WDR on RI

[25] In addition to the three aspects of the canopy structure discussed in sections 4.1.1, 4.1.2, and 4.1.3, the effect of the canopy structure on the airflow pattern around the canopy may cause the canopy structure-dependent values of RI to vary because of the effects of WDR. Furthermore, WDR can cause a significant spatial heterogeneity of the throughfall and stemflow in forest regions, which leads to errors in the estimated value of RI [Herwitz and Slye, 1995]. While WDR has a significant influence on the estimated value of RI, most studies on RI in the literature have not taken WDR into consideration. Thus further studies on the effect of WDR on RI are considered necessary.

4.2. Difference in RI Between COSMO and RAGAB

[26] The value of RI as a percentage of total rainfall in COSMO, 6%, is much smaller than that reported in RAGAB, 23.9% for the 22° roof-slope case, and 33.8% for the flat roof case. In this section, causes of the difference in the urban RI between the present study, COSMO, and RAGAB are discussed.

[27] One possible reason for the difference in RI is the difference in the surfaces included in the control volume used for water balance between the two studies; RAGAB focused on the “local RI” of roofs whereas COSMO focused on the “bulk RI” of the entire urban canopy. The local RI of roofs can be larger than bulk RI for the following three reasons. First, the local rate of transfer for scalar quantities is larger on roofs than on other surfaces (e.g., walls or streets) [Narita, 2007]. Second, roofs are better located to receive solar radiation than other surfaces, and thus there is more available radiative energy on roofs than on other surfaces. Third, splash-loss of raindrops from the roof surfaces can increase with time and rainfall intensity in RAGAB. Because of the nature of the investigation, the catchment in RAGAB was not enclosed by a water-proof fence, and splash-loss likely increased in RAGAB with increasing time and rainfall intensity. In contrast, in COSMO, the splash-droplets that fall to the floor from the roofs and walls are counted as runoff or evaporation from the floor. The splash-loss of raindrops may have increased the measured values of the local RI with respect to the actual evaporation in RAGAB, and created a dependency of the local RI on the gross rainfall, similar to that observed in forests.

[28] Gash et al. [2008] used a model [Gash, 1979; Gash et al., 1995] to simulate the RI observed in RAGAB and concluded that the characteristics of urban RI are similar to those of forests. Gash et al. [2008] set the evaporation rate to a typical value used for RI simulations of forests in the UK based on the finding by Grimmond and Oke [1999b] that the momentum roughness lengths for cities are similar to those for forests. However, the scalar transfer efficiency strictly needs to be parameterized both by the momentum and scalar roughness lengths as discussed in section 4.1.2. Therefore, even though Gash et al. [2008] reproduced the observational results of RAGAB using a typical evaporation rate for forests, it does not necessarily imply that the mechanism for urban RI is the same as that for forests.

[29] Another possible reason for the difference in RI between COSMO and RAGAB is the difference in the values of St between the two studies. The value of St in COSMO is 0.25 mm, smaller than that of RAGAB, 0.55 mm. In COSMO, the impervious paint can decrease and the flat roof surfaces can increase the value of St with respect to that of RAGAB. However, the difference in the values of St is insufficient to fully explain the large difference in the values of RI between the two studies.

4.3. Proposal for a Simple RI Prediction Model for Urban Canopies

[30] A simple prediction model for urban RI is proposed using a modified bulk method. Using the original bulk equation, total RI for a rainfall event is expressed as

  • equation image

where t indicates the time since the onset of the rainfall event; and ρ, CH, U, and dq represent the air density, the bulk transfer coefficient, the wind velocity at a reference height, and the saturation deficit, respectively. An overbar indicates the average over the rainfall duration. CH can be theoretically determined in terms of surface geometry and the relation of kB−1 [Kanda et al., 2007; Kawai et al., 2009]. General values of St for urban materials are given by Kondo et al. [1992]; the value of St for asphalt is 0.26 mm and that for concrete is 1.1 mm. Saturation deficit, dq(t), is difficult to measure accurately in high-humidity conditions during rainfall. In the present study, RI was mostly determined in the first several hours of rainfall (Figure 6a), and rainfall duration was not correlated with RI (Figure 4). Therefore the saturation deficit measured at the beginning of the rainfall event (hereinafter designated as dqini) was used instead of equation image. Moreover, when duration exceeded a critical value, duration was set to that value. This approach is based on the assumption that the air is saturated after the critical time, and thus RI does not occur.

[31] Using the modified bulk transfer equation, RI is expressed as

  • equation image

where 0.66 is a constant determined from the best fit value of the COSMO data, equation image is the bulk transfer coefficient for heat determined by Kanda et al. [2007] from a data set from COSMO, and the critical value of duration is set to 10 h on the basis of Figure 6a. The value of RI was predicted for each rainfall event of COSMO with equation (5) and compared with the observed value (Figure 10). There was a good correlation between the observed and predicted values of RI (correlation coefficient = 0.85). Equation (5) can be used to approximate RI on urban canopies, although the constant value of 0.66 and the critical value of rainfall duration of 10 h may need to be adjusted.

image

Figure 10. Relationship between predicted and observed RI. Eleven rainfall events are not shown due to a lack of data. The dashed line is the 1:1 line.

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4.4. Considerations for Rainfall Interception in Real Cities

[32] It is expected that the fundamental mechanism of RI in COSMO is also valid in real cities since COSMO was designed to satisfy aerothermodynamic similarity with real cities [Kanda, 2006; Kawai et al., 2009]. Nevertheless, the highly idealized setup of COSMO is different from the complexity of real cities so that the findings in the present study may not be directly applicable to real cities. One difference between COSMO and real cities is storage, St. Real cities with the same value of SAI as COSMO would have a larger value of St than COSMO because real cites include multiple concave surfaces and vegetation. In addition, porous materials of building facades also increase St as they can absorb rainwater. Another difference between COSMO and real cities is the influence of anthropogenic heat emission [Moriwaki et al., 2008], which can be a heat source for RI. Thus (1) larger values of St due to concave surfaces and vegetation and due to uptake of water by the porous materials of buildings and (2) additional heat sources in real cities will increase the value of RI even if the cities have the same geometric parameters as COSMO.

5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[33] Rainfall interception (RI) was evaluated as the residual of the measured rainfall and the runoff at COSMO over a period of 5 months. On average, RI was 6% of the gross rainfall. There was no clear correlation between RI and total rainfall or between RI and rainfall duration. Most of RI occurred in the first several hours of a rainfall event, and RI rapidly decreased with time during rainfall. A similar trend was observed for the temperature difference between the surface and the ambient air and for the saturation deficit. There was a high correlation between RI and the saturation deficit measured at the beginning of a rainfall event. The latent heat required for RI was closely related to heat conduction from the substrate to the surface during rainfall. RI in COSMO behaved differently from that in forests due to differences in canopy structure. Three possible differences caused by the differing canopy structures include dissimilarities in (1) the complete surface area index (SAI), (2) scalar transfer efficiency in relation to roughness element size, and (3) heat balance in relation to volumetric heat capacity of roughness elements.

Notation
Afloor

net floor areas.

Ahoriz

horizontal areas.

Aroof

roof areas.

Awall

wall areas.

CH

bulk transfer coefficient for heat at the reference height.

dq

saturation deficit during rainfall.

dqini

saturation deficit at the beginning of the rainfall event.

duration

rainfall duration.

G

storage heat flux.

P

rainfall.

Q

runoff.

ρ

air density.

RI

rainfall interception.

Stfloor

storages for floor.

Stroof

storages for roof.

Stwall

storages for wall.

St

water storage capacity.

U

wind velocity at the reference height.

Ta

ambient air temperature.

Tc

complete surface temperature.

z0

roughness length for momentum.

zT

roughness length for heat.

kB−1

ln[z0/zT]: excess resistance for heat transfer.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[34] This research was supported by the Core Research for Evolution Science and Technology program of the Japan Science and Technology Cooperation and by a Grant-in-Aid for Developmental Scientific Research from the Ministry of Education Culture, Sports, Science and Technology of Japan.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information
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wrcr11856-sup-0001-t01.txtplain text document0KTab-delimited Table 1.
wrcr11856-sup-0002-t02.txtplain text document2KTab-delimited Table 2.
wrcr11856-sup-0003-t03.txtplain text document0KTab-delimited Table 3.
wrcr11856-sup-0004-t04.txtplain text document2KTab-delimited Table 4.

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