A Method of Aggregating Heterogeneous Subgrid Land-Cover Input Data for Multiscale Urban Parameterization

Stephen R. Shaffer School of Mathematical and Statistical Sciences, and Julie Ann Wrigley Global Institute of Sustainability, Arizona State University, Tempe, Arizona

Search for other papers by Stephen R. Shaffer in
Current site
Google Scholar
PubMed
Close
,
Mohamed Moustaoui School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona

Search for other papers by Mohamed Moustaoui in
Current site
Google Scholar
PubMed
Close
,
Alex Mahalov School of Mathematical and Statistical Sciences, and Julie Ann Wrigley Global Institute of Sustainability, Arizona State University, Tempe, Arizona

Search for other papers by Alex Mahalov in
Current site
Google Scholar
PubMed
Close
, and
Benjamin L. Ruddell Fulton Schools of Engineering, Arizona State University, Tempe, Arizona

Search for other papers by Benjamin L. Ruddell in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

A method of representing grid-scale heterogeneous development density for urban climate models from probability density functions of subgrid-resolution observed data is proposed. Derived values are evaluated in relation to normalized Shannon entropy to provide guidance in assessing model input data. Urban fraction for dominant-class and mosaic urban contributions is estimated by combining analysis of 30-m-resolution National Land Cover Database 2006 data products for continuous impervious surface area and categorical land cover. The aim of the method is to reduce model error through improvement of urban parameterization and representation of observations employed as input data. The multiscale variation of parameter values is demonstrated for several methods of utilizing input. This approach provides multiscale and spatial guidance for determining where parameterization schemes may be misrepresenting heterogeneity of input data, along with motivation for employing mosaic techniques that are based upon assessment of input data. The proposed method has wider potential for geographic application and complements data products that focus on characterizing central business districts. It utilizes observations to obtain a parameterization of urban fraction that is dependent upon resolution and class-partition scheme, thus providing one means of influencing simulation prediction at various aggregated grid scales.

Denotes Open Access content.

Corresponding author address: Stephen R. Shaffer, School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk PSA 216, Tempe, AZ 85287-1804. E-mail: stephen.shaffer@asu.edu

Abstract

A method of representing grid-scale heterogeneous development density for urban climate models from probability density functions of subgrid-resolution observed data is proposed. Derived values are evaluated in relation to normalized Shannon entropy to provide guidance in assessing model input data. Urban fraction for dominant-class and mosaic urban contributions is estimated by combining analysis of 30-m-resolution National Land Cover Database 2006 data products for continuous impervious surface area and categorical land cover. The aim of the method is to reduce model error through improvement of urban parameterization and representation of observations employed as input data. The multiscale variation of parameter values is demonstrated for several methods of utilizing input. This approach provides multiscale and spatial guidance for determining where parameterization schemes may be misrepresenting heterogeneity of input data, along with motivation for employing mosaic techniques that are based upon assessment of input data. The proposed method has wider potential for geographic application and complements data products that focus on characterizing central business districts. It utilizes observations to obtain a parameterization of urban fraction that is dependent upon resolution and class-partition scheme, thus providing one means of influencing simulation prediction at various aggregated grid scales.

Denotes Open Access content.

Corresponding author address: Stephen R. Shaffer, School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk PSA 216, Tempe, AZ 85287-1804. E-mail: stephen.shaffer@asu.edu

1. Introduction

State-of-the-art mesoscale atmospheric models incorporate urban areas with physics-based parameterizations of processes that are not explicitly resolved at model grid scales (Chen et al. 2011). Current schemes partition urban-classified model grid cells, or mosaic urban “tiles,” into urban and nonurban contributions that are computed separately (Kusaka and Kimura 2004a; Li et al. 2013). The urban parameterization term accounting for development density, or urban fraction furb (note that the variables used in this paper are collected and defined in the appendix), is of primary importance to urban modeling since it defines the ratio of urban and nonurban contributions when aggregating the fields (i.e., sensible and latent heat fluxes, upward longwave radiation flux, albedo, and emissivity) to the model grid (Loridan and Grimmond 2012; Chen et al. 2011; Loridan et al. 2010). The urban contribution accounts for buildings and roads (e.g., Kusaka and Kimura 2004a; Grimmond et al. 2010), and the nonurban component, termed natural, is by default “grassland” to represent, for example, grass-covered urban parks (Kusaka and Kimura 2004a; Li et al. 2013). Loridan and Grimmond (2012) recommended that default parameters have higher values of furb together with a default natural class that has increased evaporation (“cropland/natural vegetation mosaic”). The role of furb was shown in Shaffer et al. (2015) to influence bias of various land–atmosphere interaction and surface energy balance terms within an arid city such as Phoenix, Arizona. For example, lower furb causes an overestimation of the latent heat flux. In addition, there may be multiple urban and nonurban land-cover types within an aggregated urban grid cell, suggesting that a mosaic approach may be of benefit when applied to urban areas (Li et al. 2013).

Ching (2013) summarized issues with state-of-the-art urban modeling and recommended that further guidance was needed when determining and aggregating development density from subgrid-resolution data. In this paper, we develop a method of parameterizing urban fraction for heterogeneous mosaic representations along with a means of assessing the representativeness of this parameterization. Monaghan et al. (2014) recently studied the influence of homogeneous development density versus heterogeneous development density , with values of being determined from the National Urban Database and Access Portal Tool (NUDAPT; Ching et al. 2009), for a single dominant urban class. Other recent studies have examined heterogeneous grid-scale representations of urban areas obtained from subgrid-scale remote sensing data (e.g., Comarazamy et al. 2010, 2013), although not accounting for nonurban subgrid areas within urban tiles.

A method is proposed to assess probability density functions (PDF) of subgrid development density along with suggesting the use of the PDF’s mode to determine the spatially aggregated parameter from finer-resolution observations, in concert with assessment of normalized Shannon entropy h. Shannon introduced the notion of entropy to measure the density of information (Billingsley 1965), and the concept was extended by Kolmogorov and Sinai for general nonlinear dynamical systems (Cornfeld et al. 1981). The normalized Shannon entropy provides a quantitative approach for evaluating the partitioning and representation of mosaic land-cover input data. The proposed method also provides guidance from an input-data perspective for multiscale and spatial evaluation of categorical partitioning schemes and motivates the use of mosaic methods, instead of a dominant-class approach, to accurately represent subgrid heterogeneity.

2. Methods

a. Finescale urban land-cover data

To demonstrate the proposed method we utilize two 2006 National Land Cover Database (NLCD) products: the 30-m-resolution land-cover-class product (hereinafter C), which is composed of categorical data (Fry et al. 2011), and the percent-developed-imperviousness product (hereinafter Ψ), which is composed of continuous data (Xian et al. 2011). NLCD partitions the urban environment into four urban land-cover classes (Curb, with CurbC)—as developed open space (DOS), developed low intensity (DLI), developed medium intensity (DMI), and developed high intensity (DHI)—on the basis of thresholds of Ψ (Homer et al. 2004):
e1

b. Assessment of subgrid land-cover entropy

Consider observations Ψ(γ), treated as a random variable, with γ as the fine grid, and Γ as the aggregated grid. From the PDF , for all γ within Γi,j, at all grid points in Γ denoted p(Ψ), and with Ψ having Ns states (i.e., with Ψ ∈ [1, 2, …, 100], Ns = 100), normalized Shannon entropy is defined as
e2
Here h depends explicitly upon Γ, with ΔΓ and positioning of Γ with respect to γ as implicit parameters that will influence the partitioning and aggregation of Ψ. Also, h ∈ [0, 1], where small hi,j) indicate that has a distribution near the mode of pi,j, denoted μi,j (or simply μ), whereas hi,j = 1 indicates that each state is equally probable. With additional categorical observations Curb(γ), we similarly construct the conditional PDF p(Ψ | Curb), for each Curb, along with a conditional h,
e3

c. Urban fraction parameter

Within the Weather Research and Forecasting (WRF) Model framework (Skamarock and Klemp 2008; Michalakes et al. 2004; Skamarock et al. 2008), land surface models (LSM; e.g., Chen and Dudhia 2001; Niu et al. 2011; Li et al. 2013) are coupled with urban schemes (e.g., Kusaka and Kimura 2004a; Martilli et al. 2002; Salamanca and Martilli 2010) on the basis of the urban fraction parameter furb. In current applications, the total aggregate variable Vtotal for grid cells with urban contribution furb > 0 is produced for a variable V (e.g., sensible heat flux) by a convex combination:
e4
Here, Vurban is computed by an urban scheme for a particular Curb and Vnonurban is computed by the LSM. The Vnonurban contribution is set by the natural class, which is typically set to cropland/natural vegetation mosaic or grassland by default as within the original implementation (Kusaka and Kimura 2004b; Chen et al. 2011; Li et al. 2013). An approach such as Eq. (4) precludes interactions between elements (trees shading buildings, etc.). Equation (4) suggests a linear sensitivity to the value of furb. Thus, model predictions will depend upon the selection of furb.

d. Dominant subgrid approach to spatially heterogeneous furb

The current approach for obtaining domainwide spatially heterogeneous development density is by considering a weighted sum of the normalized area fraction α of each Curb within an aggregated grid cell Γ:
e5
This is prescribed to a single dominant Curb based upon α within each Γ for use within Eq. (4). For instance, the NUDAPT approach for obtaining from NLCD Curb data employs the weights w(Curb) = (0.5, 0.5, 0.9, 0.95). These weights represent the impervious fraction of an urban class, which is represented within the WRF urban schemes as buildings and roads. The WRF urban framework then converts these four NLCD urban classes into categories of low-intensity residential (LIR), high-intensity residential (HIR), and commercial/industrial/transportation (CIT; Ching 2013; Anderson et al. 1976), after identifying LIR = DOS ∪ DLI, HIR = DMI, and CIT = DHI (Glotfelty et al. 2013). Other urban-scheme parameters are derived (estimated) from additional data sources (Burian and Ching 2009; Glotfelty et al. 2013). We suggest an alternate approach for determining within Eq. (5) by deriving the weights for each Curb from the conditional PDF of subgrid observations such as with the NLCD Ψ:
e6
That is, as the most probable Ψ value (i.e., mode) of p(Ψ | Curb), denoted .

e. Mosaic subgrid approach to spatially heterogeneous furb

Assessing of the input data motivates investigating mosaic methods based upon reduced , given a partitioning scheme such as the categorical-data Curb. The present mosaic subgrid approach within WRF (Li et al. 2013) considers Nt homogeneous noninteracting subgrid tiles and aggregates contributions—for example—for a variable V, based upon normalized (for Nt) tile areal fraction α with class C, by
e7
Here, the tiles have been ranked by α, and therefore Nt = 1 reproduces the dominant case. When cCurb, Eq. (4) is employed with furb = 0.5, 0.9, or 0.95 for LIR, HIR, or CIT, respectively. Again, Vnonurban is obtained from the LSM for a natural class, and for Curb from NLCD the nonurban class (or impervious-cover contribution from Ψ) is not available.
We investigate an alternate approach for determining within Eq. (4) for mosaic subgrid aggregation within Eq. (7):
e8
with the rhs as described above for Eq. (6).

f. Verification experiments

A series of numerical experiments were conducted with the Advanced Research WRF Model to test the dominant and mosaic approaches to , as described above. Four telescoping nested domains were employed with grid spacing ΔΓ reduced by a factor of 3, such that the innermost nest D4 had ΔΓ = 1 km. Domain D4 contained the entire Phoenix metropolitan area (PMA) within the interior of the domain to avoid lateral boundary issues (e.g., Warner et al. 1997). The first three domains were run with concurrent one-way nesting during premonsoon summer 2012 for the 3-day period beginning at 1800 UTC 17 June 2012 [see the Shaffer et al. (2015) Yonsei University–MM5 cases using modified morphological and material values for Phoenix (PHX-A/B) and their section 2b for details], with the outer domain initialized with NCEP Final Analysis (FNL; NCEP 1999) 6-hourly data. The 5-min-history archive interval on D3 was employed to provide consistent initial and lateral boundary forcing for the current set of experiments. We show several cases that test variations only for the innermost domain D4. The Noah LSM (Chen and Dudhia 2001) was employed for parameterizing the land surface of nonurban classes, with the Single Layer Urban Canopy Model (SLUCM; Kusaka and Kimura 2004a) scheme for urban classes, within either the dominant or mosaic-tiling approaches.

A subset of the 2006 NLCD Curb and Ψ datasets (described in section 2a) were obtained such that they contained the entire PMA. Since the NLCD Curb data do not retain classification for nonurban contributions of urban-classified cells, default natural settings (cropland/natural vegetation mosaic) were employed. Nonurban C were obtained via Moderate Resolution Imaging Spectroradiometer (MODIS) 20-category 30-arc-s data modified for the Noah LSM, as discussed in Shaffer et al. (2015). For all simulations, urban areas outside the NLCD data subset were reclassified as open shrubland, the predominant nonurban C (within MODIS). Dominant Curb was determined by maximum α for the NLCD Curb dataset excluding DOS. To avoid parameter tuning, the default urban parameter values (invariant for all cases) are used except for furb, as described below.

The cases tested for are summarized in Table 1. For the dominant approach [Eq. (5)], SLUCM was adapted within WRF to enable input of user-defined values. The mosaic implementation was tested, also with default urban table values, and with modifications to input for use as described with Eq. (8) within Eq. (7) replacing the hard-coded values of 0.5, 0.9, and 0.95 for furb. A case was tested with Nt = 3. To simplify the demonstration of the proposed methods, only the dominant μ, , and mosaic wmos cases will be shown in this paper.

Table 1.

Summary of cases for testing the dominant scheme [Eq. (6)] and the mosaic scheme.

Table 1.

g. Verification with observations

Observations of near-surface air temperature were obtained with the West Phoenix Flux Tower [WPHX-FT; described in Chow et al. (2014) and equipped with Vaisala, Inc., model HMP45AC temperature–relative humidity sensors within a radiation shield, with 1-Hz sampling], along with micrometeorological stations that are deployed within the Flood Control District of Maricopa County (FCDMC) Automated Local Evaluation in Real Time system (hereinafter ALERT; data were obtained at http://www.fcd.maricopa.gov/Weather/weather.aspx). The ALERT stations use either Vaisala HUMICAP model HMP155 humidity and temperature probes within a radiation shield or Hydrolinx Systems, Inc., model 2048RH/T relative humidity and temperature sensors (as indicated in Table 2), with 15-min sampling. These data were averaged to 30-min intervals, along with 5-min instantaneous WRF output for the grid cell containing the station.

Table 2.

Summary of station metadata. WPHX-FT is the only station not from the FCDMC ALERT system. Temperature-sensor types are indicated with a superscript in the sensor-identifier (ID) column: V is Vaisala HMP155 and H is Hydrolinx 2048RH/T. Note that the XRD site elevation slopes down to a catch basin east of the station.

Table 2.

A subset of 11 ALERT stations was selected for analysis on the basis of the criteria of being within the PMA study area and within modified urban-classified WRF grid cells. Basic station metadata are summarized in Table 2. No corrections were applied for sensor height, in comparison with the WRF 2-m diagnostic temperature T2m. Standard statistical measures (Willmott 1981; Willmott et al. 1985) employed were ordinary least squares regression between observed and predicted values, mean bias error (MBE), and mean absolute error (MAE), along with the modified index of agreement for MAE d1 (a dimensionless statistical measure of relative average error), root-mean-square error (RMSE), systematic (linear model bias) and unsystematic (model precision) RMSE (RMSEs and RMSEu, respectively, where RMSE2 = ), and index of agreement for RMSE d2. Comparisons were made with the composite diurnal variation for the 3-day study period at each station and across all stations (ALERT and WPHX-FT), for each simulation case.

3. Results and discussion

a. Multiscale analysis of input data

The NLCD 2006 data described in section 2a for Ψ and C are presented in Figs. 1a and 1b for a particular 9 km × 9 km subset of the PMA containing the WPHX-FT (Chow et al. 2014). The probability distribution of Ψ is assessed for each Curb (Figs. 1c,d). For this particular PMA subset, μ = 57% with a largest-area Curb of DMI. Conditional PDFs, or p(Ψ | Curb), are shown for each Curb (Fig. 1d) for the data in Figs. 1a and 1b. Apparent in Figs. 1c and 1d is that the limits of Ψ for each Curb [Eq. (1)] are not strictly valid. There may be misclassification or other differences between these data, or processing differences between the two NLCD datasets (Ψ and Curb). In the analysis that is presented here, no modifications are made to account for these inherent NLCD data discrepancies.

Fig. 1.
Fig. 1.

Analysis of NLCD 2006 data of a 9 km × 9 km subset of the PMA (containing the West Phoenix Flux Tower at 33.484°N, 112.143°W, labeled WPHX FT Subset and denoted by a solid black circle), for maps of the (a) categorical C and (b) continuous Ψ and for (c) the distribution of cumulative count of Ψ colored by C, with count per C and total count indicated, and (d) PDFs p(Ψ | Curb) for Curb = DOS, DLI, DMI, and DHI. The same C color scheme is used for (a),(c), and (d). Conditional PDFs are constructed by partitioning Ψ with C. Assessing distributions of Ψ for each C reveals bias of methods that use just one of these data products to derive furb and reveals furb parameterization bias for each C.

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

The merging of DOS with DLI to form LIR (e.g., Figs. 1c,d) overestimates both the area and development density and changes the Curb partition [Eq. (1)]. This result indicates that urbanization within for LIR is overrepresented in simulations that use the method of single dominant Curb Eq. (5). Furthermore, the NUDAPT approach, with w(DOS ∪ DLI) = 0.5, additionally overrepresents the density in addition to α. Given the many parameters in the urban models (e.g., Grimmond et al. 2011), deficiencies in may be masked by bias in other model input values, especially when employing an approach that uses a single dominant class.

The multiscale influence of horizontal aggregate length ΔΓ is examined in Fig. 2 with center Γ0 at the WPHX-FT. For these analyses, ΔΓ varies from 30 to 9990 m. The roles of ΔΓ on h [Eq. (2)] for p(Ψ) and on [Eq. (3)] for p(Ψ | Curb) are shown (Fig. 2a) for the four Curb. For this aggregated gridcell center, the DOS have low for ΔΓ < 600 m, owing to the low number of DOS-classified fine-grid cells within this ΔΓ range. The for all Curb seem to converge to distinct values, principally dependent upon Curb for ΔΓ > 1 × 103–3 × 103 m, and upon partition [Eq. (1)] of Ψ. This large ΔΓ behavior suggests that there may exist a “citywide” maximum entropy for p(Ψ | Curb). The increase of with ΔΓ also indicates that the of each PDF becomes less representative of the distribution. Partitioning p(Ψ) by Curb, as p(Ψ | Curb), reduces relative to h.

Fig. 2.
Fig. 2.

Multiscale evaluation with fixed Γ0 at WPHX-FT with Curb and Ψ from NLCD 2006 data products for (a) h for p(Ψ) with Eq. (2) (black) and for p(Ψ | Curb) with Eq. (3) (colored by Curb; bottom legend) and for (b) furb (top legend) from using just Curb with Eq. (5) with w(Curb) = (0.50, 0.50, 0.90, 0.95) (labeled NUDAPT), and following thresholds of Ψ as in Eq. (1), with w(Curb) = (0.20, 0.50, 0.80, 1.0) (labeled Max Ψ) and for w(Curb) = (0.20, 0.50, 0.80, 0.95) (labeled w/DOS). (c) The furb estimated by mean, median, and mode with Eq. (6), for just using p(Ψ) (labeled All Ψ) and p(Ψ | Curb) (bottom legend). Thresholds of Ψ per Eq. (1) are indicated by the dash–dotted horizontal lines (colored by Curb) in (b) and (c). The Curb color scheme in (a) and (c) is the same as in Figs. 1a, 1c, and 1d. The exhibits limiting values (ΔΓ > ~3 km), which are reduced for categorical partitioning, indicating improved parameterization of furb, which varies with ΔΓ, along with skewness of p(Ψ | Curb).

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

The multiscale role of ΔΓ on derived furb is presented (Fig. 2b) for the corresponding distributions with h (Fig. 2a) that are discussed above. Shown are derived for the approach using a single dominant Curb following Eq. (5) with w(Curb) = (0.50, 0.50, 0.90, 0.95) (labeled as NUDAPT), for following thresholds of Ψ as in Eq. (1) with w(Curb) = (0.20, 0.50, 0.80, 1.0) (labeled as Max Ψ), and for w(Curb) = (0.20, 0.50, 0.80, 0.95) (labeled as w/DOS). Also shown are furb estimated by mean, median, and mode [Eq. (6)], for just using p(Ψ) [labeled as p(Ψ)] and p(Ψ | Curb) (labeled by Curb). All furb are ΔΓ dependent. The NUDAPT furb values are ~0.1% above those obtained with limits given in Eq. (1), which differ by less than 2% for ΔΓ of less than approximately 3 km (Fig. 2b). The w/DOS values reduce from ~84% below 1 km to ~80% for ΔΓ of less than approximately 3 km and then decrease to ~73% for ΔΓ ≈ 9 km. The w/DOS furb are 0.02%–0.15% above the mean and median p(Ψ) method by Eq. (5) but are 0.1%–0.2% below μ[p(Ψ)] for ΔΓ > ~1 km, which varies between μDMI and μDHI as Γ increases. For this Γ0, the Curb of DOS has at Ψ = 1%, which indicates a very low contribution from impervious surface components as would be provided by urban schemes. The furb values decrease with ΔΓ > 500 m for the p(Ψ) single-class method but remain bounded [by Eq. (1)] with skewed distribution (for this Γ0) for p(Ψ | Curb) mosaic methods.

b. Spatial analysis of input data

To examine the spatial distribution of h values so as to assess , and that of partitioning for Curb, this analysis will focus on a fixed ΔΓ (990 m), which is comparable to the typical finescale (1 km) of mesoscale simulation studies. The approach using a single dominant Curb [Eq. (5)] is presented for the region containing the PMA (Fig. 3). An estimate of by the μ of p(Ψ) is shown as a map in Fig. 3a. The urban-core area is present in Fig. 3a, but fringe areas that incorporate DOS with low Ψ values are absent. The corresponding h (Fig. 3b) indicates that p(Ψ) is near μ outside the urban core, but p(Ψ) are less represented by μ within the urban-core areas. These large h values indicate increased heterogeneity of Ψ with urban-core areas and motivate investigating mosaic approaches.

Fig. 3.
Fig. 3.

Maps of derived (%) aggregated to ΔΓ = 990 m for the PMA by (a) mode of p(Ψ) and by Eq. (5) for (c) w(Curb) = (0.50, 0.50, 0.90, 0.95) NUDAPT method and (d) w(Curb) = (0.20, 0.50, 0.80, 0.95) NUDAPT method following Eq. (1). (b) The h (dimensionless) for p(Ψ) corresponding to the in (a). Just μ for p(Ψ) alone as in (a) underestimates the extent of the urban C and has large h for much of the urban area as in (b). The NUDAPT approach overestimates the urban area and furb when combining DOS with DLI [(c) vs (d)].

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

The method of a single dominant Curb in Fig. 3a for μ of p(Ψ) underestimates the extent of the urban area relative to the NUDAPT approach (Fig. 3c) for weights w(Curb) = (0.50, 0.50, 0.90, 0.95) in Eq. (5). A modified approach satisfying Eq. (1) with w(Curb) = (0.20, 0.50, 0.80, 0.95) is presented in Fig. 3d. As with Γ0 = WPHX-FT (Fig. 1 and Fig. 2), the NUDAPT approach of combining DOS and DLI overestimates the areal extent of LIR (Fig. 3c), along with w(Curb) overestimating . Rural fringe areas (Fig. 3d) show the largest reduction of (over Fig. 3c), with some urban-core areas also affected because of the many golf courses and parks within the region (e.g., DOS and low Ψ in Figs. 1a,b).

Analysis at ΔΓ = 990 m of by Eq. (6) [for an aggregation approach following Eq. (7)] is presented in Fig. 4, with the corresponding in Fig. 5, for Curb being DOS (Figs. 4a and 5a), DLI (Figs. 4b and 5b), DMI (Figs. 4c and 5c), and DHI (Figs. 4d and 5d). The values follow the partition of Ψ for each Curb as per Eq. (1), with tile aggregation using the respective subgrid areal fractions as per, for example, Eq. (7). Heterogeneous structure is present within for each Curb, with indicating that DLI and DMI have the highest heterogeneity for much of the metropolitan area (Fig. 5). The (Fig. 5) also indicate locations within the city where the p(Ψ | Curb) are less represented by , and improvement of class partitioning may be required. In contrast, the NUDAPT method employs values at or above upper bounds given in Eq. (1), which vary from , for many scales (Fig. 2b) and across the entire domain (Figs. 4a–d). Such bias raises concern for potential “parameter tuning” of other urban model input values that are not readily surveyed.

Fig. 4.
Fig. 4.

Similar to Fig. 3, but showing a map of [Eq. (6)] for a mosaic approach [Eq. (7)] with Curb being (a) DOS, (b) DLI, (c) DMI, and (d) DHI. The spatial pattern of most probable Ψ for each Curb shows where each class contributes to the aggregated model output [Eq. (7)]. Note that α(Γ | Curb) can be similarly displayed, with the product giving the weight of each Curb in Eq. (7).

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

Fig. 5.
Fig. 5.

As in Fig. 4, but following Eq. (3) for with Curb being (a) DOS, (b) DLI, (c) DMI, and (d) DHI. Spatial guidance for categorical partition [Eq. (1)] and parameterization of furb [Eq. (6)] indicates that DOS and DHI have lower than do DLI and DMI, where urban-core areas and roadway corridors have increased , indicating locations of increased heterogeneity within p(Ψ | Curb) and where the parameterization [Eq. (6)] may be less representative of the subgrid development density distribution or an alternate partitioning scheme to Eq. (1) may be needed.

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

c. Evaluation of method within WRF

Evaluation with many stations across the PMA, where station locations, dominant C, and terrain elevation are shown in Fig. 6, with details given in Table 2, was done to assess the impact on a typically observed meteorological variable for the methods of determining a spatially heterogeneous furb. Figure 7 and Fig. 8 show diurnal variation (in 30-min intervals averaged over the 3-day study period) of the near-ground air temperature T2m for these stations, for the Max Ψ, , and wmos cases. Diurnal variations of statistical measures across all stations are shown for these model cases in Fig. 9, and overall statistical measures across all stations for the entire study period are presented in Table 3 for the model cases given in Table 1.

Fig. 6.
Fig. 6.

Maps of WPHX-FT and ALERT station locations (black circles; yellow circles are within grid cells with furb > 0 and are used for analysis, with station ID string as in Table 2) within the Phoenix metropolitan study area, along with (a) dominant land-cover class (described in text) and (b) terrain elevation (color bar). Also shown in (b) is the boundary of grid cells with = 0.01 (red contour).

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

Fig. 7.
Fig. 7.

Diurnal 30-min T2m during 17–20 Jun 2012 for from Eq. (5) with w = μ and α from Ψ > 0 (green squares), with and α from max αc (red times signs), and for from Eq. (7) (orange circles), along with observed values (Obs) at (a) WPHX-FT, (b) DGO, (c) DMS, (d) FHF, (e) GCC, and (f) GLN. See Fig. 6 for ALERT locations.

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

Fig. 8.
Fig. 8.

As in Fig. 7, but for ALERT stations (a) MKN, (b) O64, (c) P2B, (d) PJX, (e) WBG, and (f) XRD.

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

Fig. 9.
Fig. 9.

Diurnal plots of statistical measures (Willmott 1981; Willmott et al. 1985) for each simulation case (Table 1) over all 12 stations (Table 2) for near-ground air temperature: (a) MAE, (b) index of agreement for RMSE d2, (c) MBE, (d) RMSE, (e) systematic error RMSEs, and (f) unsystematic error RMSEu. See Table 3 for daily totals. The d1 statistic showed a ranking of models that was similar to that for d2 (but with lower values) and so is not shown.

Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-16-0027.1

Table 3.

Statistical measures (Willmott 1981; Willmott et al. 1985) for each simulation case (Table 1) over all 12 stations (Table 2) for the 3-day study period for near-ground air temperature. Here, a, b, and r2 are the intercept, slope, and correlation coefficient, respectively, for an ordinary least squares regression between observed and predicted values. For simulation vs observations, MBE and MAE are the mean bias and absolute errors and d1 is the modified index of agreement for MAE. Also given are the systematic, unsystematic, and total RMSE and the index of agreement d2.

Table 3.

Figure 7 shows that T2m is often underestimated for Max Ψ and cases, with increased negative MBE (Fig. 9c) during nighttime (Table 1) and largest overall MBE (Table 3). The wmos case shows improvement at most stations (Figs. 7, 8), with improved overall statistical measures during the entire day (Fig. 9) with the exception of midafternoon, for which some measures (e.g., RMSEs; Fig. 9e) degrade between 1030 and 1630 LST. Regardless, the overall performance of wmos is comparable to mosaic (Table 3), and both are correspondingly much better than the dominant methods.

Accounting for the stated thresholds (Max Ψ) given by Eq. (1) shows a decrease in performance, which is attributable to the relative contributions of Noah and SLUCM [Eq. (4)]. We note that the default WRF SLUCM model parameters were recommended by Loridan and Grimmond (2012) on the basis of optimization [following Loridan et al. (2010)] of surface energy balance terms (net radiation Q*, sensible heat flux QH, and latent heat flux QE) for many cities and that because we here modify the furb values, together with the parameters not being adjusted for Phoenix (e.g., Shaffer et al. 2015) or specifically for each station, such a decrease in model performance may be anticipated.

We hypothesize that the fact that the mosaic cases for the proposed modified scheme do not show improved performance over the default mosaic (not shown) is likely due to a combined effect of both urban-class parameter values (we simply employed default values) and the default selection of the natural class. As discussed by Loridan and Grimmond (2012), there are several factors involved with the derivation of default parameters, where higher furb values were selected together with a natural class with increased evaporation (cropland/natural vegetation mosaic), which provided better agreement with their observations. Lower values of furb were shown by Shaffer et al. (2015) to cause an overestimation of the latent heat flux within arid cities such as Phoenix. Here again, the natural class is uniformly set to the default class rather than being derived from observations of C and is expected to introduce such a bias in latent heat flux, and in turn, the near-ground air temperature, as observed for the selected meteorological stations. We note that some stations were near grass (parks) or croplands while others were in xeric vegetation settings (open shrubland). No correction for station-setting bias was employed here.

The widely used NLCD C unfortunately does not retain nonurban-class contribution within urban-classified grid cells. Furthermore, other NLCD classes are categorically the majority at Δγ. Thus, higher-resolution categorical observations, such as the National Agricultural Imagery Program (NAIP), which has Δγ = 1 m for the PMA (Li et al. 2014), would enable deriving percent contributions of these nonurban classes and would allow for determining gridded values of majority natural class within each urban tile. Such an approach should reduce bias for both default and modified mosaic approaches. As discussed previously regarding the input data, the weights of 0.5, 0.9, and 0.95 for the default mosaic are actually overestimating the actual development density (or plan areal fraction of built environment). The fairly robust evaluation of default mosaic may result from compensation from bias of other urban parameter values and requires further evaluation, which is beyond the scope of this paper (e.g., see Loridan and Grimmond 2012). Generalization of urban class with more gridded parameters and for more classifications or for classification schemes that differ from Eq. (1) should also be explored.

4. Conclusions

Incorporating spatially heterogeneous development density allows for improvement of urban parameterization, including for methods that use a single dominant Curb. A more accurate representation of should improve urban modeling efforts since model output is sensitive to furb [e.g., Eqs. (4) and (7)]. Furthermore, is less than h and indicates a more representative parameterization of than furb. Employing data products (e.g., NLCD) derived from satellite observations, in principle, enables deriving from globally available data and is desirable for application of the method to developed areas worldwide. Skewed distributions of p(Ψ) and p(Ψ | Curb) motivate consideration of the subgrid PDF and determining alternative methods of representing subgrid flux contributions, such as the most probable value. Employing a categorical partitioning scheme and conditional PDFs enable determining for mosaic methods.

The normalized Shannon entropy provides a quantitative means for assessing the representation of subgrid PDFs of development density. Spatial analysis of h is useful for determining where distributions of subgrid development density are not well represented by the mode of a PDF and also for determining where a categorical partitioning scheme may be misrepresenting urban heterogeneity. Assessing h also provides important guidance for determining possible sources of bias (e.g., of ) when making comparison with observations (in situ or remotely sensed) within the urban area. Large h values indicate increased subgrid heterogeneity, which may result in reduced confidence for the parameterization () of a particular Curb. The increase of with ΔΓ also indicates that the of each PDF becomes less representative of the distribution, which is improved by partitioning p(Ψ) by Curb, as p(Ψ | Curb), with a reduced relative to h.

These analyses of input data motivate employing a mosaic urban approach, along with investigating categorical partitioning schemes, informed by conditional h, which enable one to assess the partitioning of urban tiles at each model grid cell. Additional classes are sensible provided they are physically based and will guide parameter selection within urban models. These results also motivate investigating alternate partitioning schemes to categorically segregate C for model physical parameters, the spatial variations of which are not easily derived from remote observations. Supplementary datasets may enable refinement of the process of estimating, for example, material property parameters, particularly albedo, as was done here with Ψ for . The NLCD 2006 Ψ and C products together are not sufficient to determine aggregated nonurban C since any NLCD grid cell with Ψ > 0 will be classified as urban. Employing higher-resolution C data (e.g., NAIP; Li et al. 2014) would enable the construction of a fractional contribution for each C at various aggregated scales, rather than attributing grassland to the nonurban C.

Multiscale analyses of h indicate citywide maximum values at large scales (>~3 km), which are also dependent upon class partitioning. Note that citywide Ψ distributions also depend upon the city, as shown in Zhang et al. (2012). The also depends upon ΔΓ and Γ0. No significant variation of model prediction across scales from 9 km to 333 m was found by Shaffer et al. (2015), owing to homogeneous scale-independent values of furb. Employing a resolution-dependent furb that is based upon improved parameterization of input data provides one means of influencing simulation prediction at various aggregated grid scales, which is of particular importance for models with variable grid size within a domain (e.g., Skamarock et al. 2012).

The multiscale methods presented herein can be applied for more general numerical prediction models for mixed land use and land cover, such as within urban environments. Here we tested with WRF employing Noah with SLUCM for dominant and mosaic approaches with the NLCD datasets. These selections were made to address an important weakness in the current approach of deriving grid-scale urban fraction from 30-m NLCD data in the widely used WRF-Urban model. Alternate models, datasets, class-partitioning schemes, and flux-aggregation approaches could be similarly examined with these methods.

Acknowledgments

This work was supported by grants awarded to Arizona State University (ASU) from the National Science Foundation (NSF) under Grant DMS 1419593, U.S. Department of Agriculture and National Institute of Food and Agriculture (USDA-NIFA) Grant 2015-67003-23508, and NSF Grants EF 1049251 and EAR 1204774. We acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by the National Center for Atmospheric Research’s Computational and Information Systems Laboratory, sponsored by the NSF, along with support from ASU Research Computing. West Phoenix Flux Tower data are available from Central Arizona Phoenix Long-Term Ecological Research (site manager Phil Torrant) with funding provided by Grant CAP3: BCS-1026865 and by NSF via EaSM Grant EF-1049251. We thank Daniel Henz for supplying the Flood Control District of Maricopa County ALERT system station data (available at http://www.fcd.maricopa.gov/Weather/weather.aspx). We also thank the three anonymous reviewers for feedback that improved the paper.

APPENDIX

Summary of Nomenclature

C

Land-cover class

Curb

Urban land-cover class

furb

Urban fraction parameter

Heterogeneous development density

Heterogeneous development density for mosaic approach

h

Normalized Shannon entropy

Conditional normalized Shannon entropy

Ns

Number of states (of p)

Nt

Number of tiles for mosaic approach

p()

Probability density function

Q*

Net radiation

QE

Latent heat flux

QH

Sensible heat flux

V

Generic model variable

Vtotal

Total aggregated V

Vurban

Urban contribution of V

Vnonurban

Nonurban contribution of V

w

Weighting coefficient

α

Normalized area fraction

Γ

Aggregated grid

Γ0

Center of aggregated grid cell

γ

Fine grid

ΔΓ

Aggregated grid length scale

Δγ

Fine-grid length scale

μ

Mode of p(Ψ)

Mode of p(Ψ | Curb)

Ψ

Percent developed imperviousness

REFERENCES

  • Anderson, J. R., E. E. Hardy, J. T. Roach, and R. E. Witmer, 1976: A land use and land cover classification system for use with remote sensor data. U.S. Geological Survey Professional Paper 964, 28 pp. [Available online at http://pubs.usgs.gov/pp/0964/report.pdf.]

  • Billingsley, P., 1965: Ergodic Theory and Information. Wiley Series in Probability and Mathematical Statistics, Vol. 1, John Wiley and Sons, 193 pp.

  • Burian, S., and J. Ching, 2009: Development of gridded fields of urban canopy parameters for advanced urban meteorological and air quality models. U.S. Environmental Protection Agency Tech. Rep. EPA/600/R-10/007, 73 pp. [Available online at https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=213904.]

  • Chen, F., and J. Dudhia, 2001: Coupling and advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, doi:10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, F., and Coauthors, 2011: The integrated WRF/urban modelling system: Development, evaluation, and applications to urban environmental problems. Int. J. Climatol., 31, 273288, doi:10.1002/joc.2158.

    • Search Google Scholar
    • Export Citation
  • Ching, J. K. S., 2013: A perspective on urban canopy layer modeling for weather, climate and air quality applications. Urban Climate, 3, 1339, doi:10.1016/j.uclim.2013.02.001.

    • Search Google Scholar
    • Export Citation
  • Ching, J. K. S., and Coauthors, 2009: National Urban Database and Access Portal Tool. Bull. Amer. Meteor. Soc., 90, 11571168, doi:10.1175/2009BAMS2675.1.

    • Search Google Scholar
    • Export Citation
  • Chow, W., T. Volo, E. Vivoni, G. Jenerette, and B. Ruddell, 2014: Seasonal dynamics of a suburban energy balance in Phoenix, Arizona. Int. J. Climatol., 34, 38633880, doi:10.1002/joc.3947.

    • Search Google Scholar
    • Export Citation
  • Comarazamy, D. E., J. E. González, J. C. Luvall, D. L. Rickman, and P. J. Mulero, 2010: A land–atmospheric interaction study in the coastal tropical city of San Juan, Puerto Rico. Earth Interact., 14, doi:10.1175/2010EI309.1.

    • Search Google Scholar
    • Export Citation
  • Comarazamy, D. E., J. E. González, J. C. Luvall, D. L. Rickman, and R. D. Bornstein, 2013: Climate impacts of land-cover and land-use changes in tropical islands under conditions of global climate change. J. Climate, 26, 15351550, doi:10.1175/JCLI-D-12-00087.1.

    • Search Google Scholar
    • Export Citation
  • Cornfeld, I., S. Fomin, and Y. G. Sinai, 1981: Ergodic Theory. Springer-Verlag, 486 pp.

  • Fry, J., and Coauthors, 2011: Completion of the 2006 National Land Cover Database for the conterminous United States. Photogramm. Eng. Remote Sens., 77, 858864.

    • Search Google Scholar
    • Export Citation
  • Glotfelty, T., M. Tewari, K. Sampson, M. Duda, F. Chen, and J. Ching, 2013: NUDAPT 44 documentation. National Center for Atmospheric Research Research Applications Laboratory Doc., 9 pp. [Available online at http://www.ral.ucar.edu/research/land/technology/urban/NUDAPT_44_Documentation.pdf.]

  • Grimmond, C. S. B., and Coauthors, 2010: The International Urban Energy Balance Models Comparison Project: First results from phase 1. J. Appl. Meteor. Climatol., 49, 12681292, doi:10.1175/2010JAMC2354.1.

    • Search Google Scholar
    • Export Citation
  • Grimmond, C. S. B., and Coauthors, 2011: Initial results from phase 2 of the International Urban Energy Balance Model Comparison. Int. J. Climatol., 31, 244272, doi:10.1002/joc.2227.

    • Search Google Scholar
    • Export Citation
  • Homer, C., C. Huang, L. Yang, B. K. Wylie, and M. Coan, 2004: Development of a 2001 National Land-Cover Database for the United States. Photogramm. Eng. Remote Sens., 70, 829840, doi:10.14358/PERS.70.7.829.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., and F. Kimura, 2004a: Coupling a single-layer urban canopy model with a simple atmospheric model: Impact on urban heat island simulation for an idealized case. J. Meteor. Soc. Japan, 82, 6780, doi:10.2151/jmsj.82.67.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., and F. Kimura, 2004b: Thermal effects of urban canyon structure on the nocturnal heat island: Numerical experiment using a mesoscale model coupled with and urban canopy model. J. Appl. Meteor., 43, 18991910, doi:10.1175/JAM2169.1.

    • Search Google Scholar
    • Export Citation
  • Li, D., E. Bou-Zeid, M. Barlage, F. Chen, and J. A. Smith, 2013: Development and evaluation of a mosaic approach in the WRF-Noah framework. J. Geophys. Res. Atmos., 118, 11 91811 935, doi:10.1002/2013JD020657.

    • Search Google Scholar
    • Export Citation
  • Li, X., S. W. Myint, Y. Zhang, C. Galletti, X. Zhang, and B. L. Turner, 2014: Object-based land-cover classification for metropolitan Phoenix, Arizona, using aerial photography. Int. J. Appl. Earth Obs. Geoinf., 33, 321330, doi:10.1016/j.jag.2014.04.018.

    • Search Google Scholar
    • Export Citation
  • Loridan, T., and C. Grimmond, 2012: Multi-site evaluation of an urban land-surface model: Intra-urban heterogeneity, seasonality and parameter complexity requirements. Quart. J. Roy. Meteor. Soc., 138, 10941113, doi:10.1002/qj.963.

    • Search Google Scholar
    • Export Citation
  • Loridan, T., and Coauthors, 2010: Trade-offs and responsiveness of the single-layer urban canopy parametrization in WRF: An offline evaluation using the MOSCEM optimization algorithm and field observations. Quart. J. Roy. Meteor. Soc., 136, 9971019, doi:10.1002/qj.614.

    • Search Google Scholar
    • Export Citation
  • Martilli, A., A. Clappier, and M. Rotach, 2002: An urban surface exchange parameterization for mesoscale models. Bound.-Layer Meteor., 104, 261304, doi:10.1023/A:1016099921195.

    • Search Google Scholar
    • Export Citation
  • Michalakes, J., J. Dudhia, D. Gill, T. Henderson, J. Klemp, W. Skamarock, and W. Wang, 2004: The Weather Research and Forecast Model: Software architecture and performance. Use of High Performance Computing in Meteorology: Proceedings of the Eleventh ECMWF Workshop, W. Zwieflhofer and G. Mozdzynski, Eds., World Scientific, 156168, doi:10.1142/9789812701831_0012.

  • Monaghan, A. J., L. Hu, N. A. Brunsell, M. Barlage, and O. V. Wilhelmi, 2014: Evaluating the impact of urban morphology configurations on the accuracy of urban canopy model temperature simulations with MODIS. J. Geophys. Res. Atmos., 119, 63766392, doi:10.1002/2013JD021227.

    • Search Google Scholar
    • Export Citation
  • NCEP, 1999: National Centers for Environental Prediction FNL Operational Model Global Tropospheric Analyses, continuing from July 1999 (updated daily). National Center for Atmospheric Research Computational and Information Systems Laboratory Research Data Archive, accessed 16 October 2012, doi:10.5065/D6M043C6.

  • Niu, G.-Y., and Coauthors, 2011: The community Noah land surface model with multiparameterization options (Noah-MP): 1. Model description and evaluation with local-scale measurements. J. Geophys. Res., 116, D12109, doi:10.1029/2010JD015139.

    • Search Google Scholar
    • Export Citation
  • Salamanca, F., and A. Martilli, 2010: A new building energy model coupled with an urban canopy parameterization for urban climate simulations—Part II. Validation with one dimension off-line simulations. Theor. Appl. Climatol., 99, 345356, doi:10.1007/s00704-009-0143-8.

    • Search Google Scholar
    • Export Citation
  • Shaffer, S., W. Chow, M. Georgescu, P. Hyde, G. Jenerette, A. Mahalov, M. Moustaoui, and B. Ruddell, 2015: Multiscale modeling and evaluation of urban surface energy balance in the Phoenix metropolitan area. J. Appl. Meteor. Climatol., 54, 322338, doi:10.1175/JAMC-D-14-0051.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 34653485, doi:10.1016/j.jcp.2007.01.037.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. National Center for Atmospheric Research Tech. Note NCAR/TN-475+STR, 113 pp., doi:10.5065/D68S4MVH.

  • Skamarock, W. C., J. B. Klemp, M. G. Duda, L. Fowler, S.-H. Park, and T. D. Ringler, 2012: A multi-scale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 30903105, doi:10.1175/MWR-D-11-00215.1.

    • Search Google Scholar
    • Export Citation
  • Warner, T. T., R. A. Peterson, and R. E. Treadon, 1997: A tutorial on lateral boundary conditions as a basic and potentially serious limitation to regional numerical weather prediction. Bull. Amer. Meteor. Soc., 78, 25992617, doi:10.1175/1520-0477(1997)078<2599:ATOLBC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Willmott, C. J., 1981: On the validation of models. Phys. Geogr., 2, 184194.

  • Willmott, C. J., S. G. Ackleson, R. E. Davis, J. J. Feddema, K. M. Klink, D. R. Legates, J. O’Donnell, and C. M. Rowe, 1985: Statistics for the evaluation and comparison of models. J. Geophys. Res., 90, 89959005, doi:10.1029/JC090iC05p08995.

    • Search Google Scholar
    • Export Citation
  • Xian, G., C. Homer, J. Demitz, J. Fry, N. Hossain, and J. Wickham, 2011: Change of impervious surface area between 2001 and 2006 in the conterminous United States. Photogramm. Eng. Remote Sens., 77, 758762.

    • Search Google Scholar
    • Export Citation
  • Zhang, P., M. L. Imhoff, L. Bounoua, and R. E. Wolfe, 2012: Exploring the influence of impervious surface density and shape on urban heat islands in the northeast United States using MODIS and Landsat. Can. J. Remote Sens., 38, 441451, doi:10.5589/m12-036.

    • Search Google Scholar
    • Export Citation
Save
  • Anderson, J. R., E. E. Hardy, J. T. Roach, and R. E. Witmer, 1976: A land use and land cover classification system for use with remote sensor data. U.S. Geological Survey Professional Paper 964, 28 pp. [Available online at http://pubs.usgs.gov/pp/0964/report.pdf.]

  • Billingsley, P., 1965: Ergodic Theory and Information. Wiley Series in Probability and Mathematical Statistics, Vol. 1, John Wiley and Sons, 193 pp.

  • Burian, S., and J. Ching, 2009: Development of gridded fields of urban canopy parameters for advanced urban meteorological and air quality models. U.S. Environmental Protection Agency Tech. Rep. EPA/600/R-10/007, 73 pp. [Available online at https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=213904.]

  • Chen, F., and J. Dudhia, 2001: Coupling and advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, doi:10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, F., and Coauthors, 2011: The integrated WRF/urban modelling system: Development, evaluation, and applications to urban environmental problems. Int. J. Climatol., 31, 273288, doi:10.1002/joc.2158.

    • Search Google Scholar
    • Export Citation
  • Ching, J. K. S., 2013: A perspective on urban canopy layer modeling for weather, climate and air quality applications. Urban Climate, 3, 1339, doi:10.1016/j.uclim.2013.02.001.

    • Search Google Scholar
    • Export Citation
  • Ching, J. K. S., and Coauthors, 2009: National Urban Database and Access Portal Tool. Bull. Amer. Meteor. Soc., 90, 11571168, doi:10.1175/2009BAMS2675.1.

    • Search Google Scholar
    • Export Citation
  • Chow, W., T. Volo, E. Vivoni, G. Jenerette, and B. Ruddell, 2014: Seasonal dynamics of a suburban energy balance in Phoenix, Arizona. Int. J. Climatol., 34, 38633880, doi:10.1002/joc.3947.

    • Search Google Scholar
    • Export Citation
  • Comarazamy, D. E., J. E. González, J. C. Luvall, D. L. Rickman, and P. J. Mulero, 2010: A land–atmospheric interaction study in the coastal tropical city of San Juan, Puerto Rico. Earth Interact., 14, doi:10.1175/2010EI309.1.

    • Search Google Scholar
    • Export Citation
  • Comarazamy, D. E., J. E. González, J. C. Luvall, D. L. Rickman, and R. D. Bornstein, 2013: Climate impacts of land-cover and land-use changes in tropical islands under conditions of global climate change. J. Climate, 26, 15351550, doi:10.1175/JCLI-D-12-00087.1.

    • Search Google Scholar
    • Export Citation
  • Cornfeld, I., S. Fomin, and Y. G. Sinai, 1981: Ergodic Theory. Springer-Verlag, 486 pp.

  • Fry, J., and Coauthors, 2011: Completion of the 2006 National Land Cover Database for the conterminous United States. Photogramm. Eng. Remote Sens., 77, 858864.

    • Search Google Scholar
    • Export Citation
  • Glotfelty, T., M. Tewari, K. Sampson, M. Duda, F. Chen, and J. Ching, 2013: NUDAPT 44 documentation. National Center for Atmospheric Research Research Applications Laboratory Doc., 9 pp. [Available online at http://www.ral.ucar.edu/research/land/technology/urban/NUDAPT_44_Documentation.pdf.]

  • Grimmond, C. S. B., and Coauthors, 2010: The International Urban Energy Balance Models Comparison Project: First results from phase 1. J. Appl. Meteor. Climatol., 49, 12681292, doi:10.1175/2010JAMC2354.1.

    • Search Google Scholar
    • Export Citation
  • Grimmond, C. S. B., and Coauthors, 2011: Initial results from phase 2 of the International Urban Energy Balance Model Comparison. Int. J. Climatol., 31, 244272, doi:10.1002/joc.2227.

    • Search Google Scholar
    • Export Citation
  • Homer, C., C. Huang, L. Yang, B. K. Wylie, and M. Coan, 2004: Development of a 2001 National Land-Cover Database for the United States. Photogramm. Eng. Remote Sens., 70, 829840, doi:10.14358/PERS.70.7.829.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., and F. Kimura, 2004a: Coupling a single-layer urban canopy model with a simple atmospheric model: Impact on urban heat island simulation for an idealized case. J. Meteor. Soc. Japan, 82, 6780, doi:10.2151/jmsj.82.67.

    • Search Google Scholar
    • Export Citation
  • Kusaka, H., and F. Kimura, 2004b: Thermal effects of urban canyon structure on the nocturnal heat island: Numerical experiment using a mesoscale model coupled with and urban canopy model. J. Appl. Meteor., 43, 18991910, doi:10.1175/JAM2169.1.

    • Search Google Scholar
    • Export Citation
  • Li, D., E. Bou-Zeid, M. Barlage, F. Chen, and J. A. Smith, 2013: Development and evaluation of a mosaic approach in the WRF-Noah framework. J. Geophys. Res. Atmos., 118, 11 91811 935, doi:10.1002/2013JD020657.

    • Search Google Scholar
    • Export Citation
  • Li, X., S. W. Myint, Y. Zhang, C. Galletti, X. Zhang, and B. L. Turner, 2014: Object-based land-cover classification for metropolitan Phoenix, Arizona, using aerial photography. Int. J. Appl. Earth Obs. Geoinf., 33, 321330, doi:10.1016/j.jag.2014.04.018.

    • Search Google Scholar
    • Export Citation
  • Loridan, T., and C. Grimmond, 2012: Multi-site evaluation of an urban land-surface model: Intra-urban heterogeneity, seasonality and parameter complexity requirements. Quart. J. Roy. Meteor. Soc., 138, 10941113, doi:10.1002/qj.963.

    • Search Google Scholar
    • Export Citation
  • Loridan, T., and Coauthors, 2010: Trade-offs and responsiveness of the single-layer urban canopy parametrization in WRF: An offline evaluation using the MOSCEM optimization algorithm and field observations. Quart. J. Roy. Meteor. Soc., 136, 9971019, doi:10.1002/qj.614.

    • Search Google Scholar
    • Export Citation
  • Martilli, A., A. Clappier, and M. Rotach, 2002: An urban surface exchange parameterization for mesoscale models. Bound.-Layer Meteor., 104, 261304, doi:10.1023/A:1016099921195.

    • Search Google Scholar
    • Export Citation
  • Michalakes, J., J. Dudhia, D. Gill, T. Henderson, J. Klemp, W. Skamarock, and W. Wang, 2004: The Weather Research and Forecast Model: Software architecture and performance. Use of High Performance Computing in Meteorology: Proceedings of the Eleventh ECMWF Workshop, W. Zwieflhofer and G. Mozdzynski, Eds., World Scientific, 156168, doi:10.1142/9789812701831_0012.

  • Monaghan, A. J., L. Hu, N. A. Brunsell, M. Barlage, and O. V. Wilhelmi, 2014: Evaluating the impact of urban morphology configurations on the accuracy of urban canopy model temperature simulations with MODIS. J. Geophys. Res. Atmos., 119, 63766392, doi:10.1002/2013JD021227.

    • Search Google Scholar
    • Export Citation
  • NCEP, 1999: National Centers for Environental Prediction FNL Operational Model Global Tropospheric Analyses, continuing from July 1999 (updated daily). National Center for Atmospheric Research Computational and Information Systems Laboratory Research Data Archive, accessed 16 October 2012, doi:10.5065/D6M043C6.

  • Niu, G.-Y., and Coauthors, 2011: The community Noah land surface model with multiparameterization options (Noah-MP): 1. Model description and evaluation with local-scale measurements. J. Geophys. Res., 116, D12109, doi:10.1029/2010JD015139.

    • Search Google Scholar
    • Export Citation
  • Salamanca, F., and A. Martilli, 2010: A new building energy model coupled with an urban canopy parameterization for urban climate simulations—Part II. Validation with one dimension off-line simulations. Theor. Appl. Climatol., 99, 345356, doi:10.1007/s00704-009-0143-8.

    • Search Google Scholar
    • Export Citation
  • Shaffer, S., W. Chow, M. Georgescu, P. Hyde, G. Jenerette, A. Mahalov, M. Moustaoui, and B. Ruddell, 2015: Multiscale modeling and evaluation of urban surface energy balance in the Phoenix metropolitan area. J. Appl. Meteor. Climatol., 54, 322338, doi:10.1175/JAMC-D-14-0051.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 34653485, doi:10.1016/j.jcp.2007.01.037.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. National Center for Atmospheric Research Tech. Note NCAR/TN-475+STR, 113 pp., doi:10.5065/D68S4MVH.

  • Skamarock, W. C., J. B. Klemp, M. G. Duda, L. Fowler, S.-H. Park, and T. D. Ringler, 2012: A multi-scale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 30903105, doi:10.1175/MWR-D-11-00215.1.

    • Search Google Scholar
    • Export Citation
  • Warner, T. T., R. A. Peterson, and R. E. Treadon, 1997: A tutorial on lateral boundary conditions as a basic and potentially serious limitation to regional numerical weather prediction. Bull. Amer. Meteor. Soc., 78, 25992617, doi:10.1175/1520-0477(1997)078<2599:ATOLBC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Willmott, C. J., 1981: On the validation of models. Phys. Geogr., 2, 184194.

  • Willmott, C. J., S. G. Ackleson, R. E. Davis, J. J. Feddema, K. M. Klink, D. R. Legates, J. O’Donnell, and C. M. Rowe, 1985: Statistics for the evaluation and comparison of models. J. Geophys. Res., 90, 89959005, doi:10.1029/JC090iC05p08995.

    • Search Google Scholar
    • Export Citation
  • Xian, G., C. Homer, J. Demitz, J. Fry, N. Hossain, and J. Wickham, 2011: Change of impervious surface area between 2001 and 2006 in the conterminous United States. Photogramm. Eng. Remote Sens., 77, 758762.

    • Search Google Scholar
    • Export Citation
  • Zhang, P., M. L. Imhoff, L. Bounoua, and R. E. Wolfe, 2012: Exploring the influence of impervious surface density and shape on urban heat islands in the northeast United States using MODIS and Landsat. Can. J. Remote Sens., 38, 441451, doi:10.5589/m12-036.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Analysis of NLCD 2006 data of a 9 km × 9 km subset of the PMA (containing the West Phoenix Flux Tower at 33.484°N, 112.143°W, labeled WPHX FT Subset and denoted by a solid black circle), for maps of the (a) categorical C and (b) continuous Ψ and for (c) the distribution of cumulative count of Ψ colored by C, with count per C and total count indicated, and (d) PDFs p(Ψ | Curb) for Curb = DOS, DLI, DMI, and DHI. The same C color scheme is used for (a),(c), and (d). Conditional PDFs are constructed by partitioning Ψ with C. Assessing distributions of Ψ for each C reveals bias of methods that use just one of these data products to derive furb and reveals furb parameterization bias for each C.

  • Fig. 2.

    Multiscale evaluation with fixed Γ0 at WPHX-FT with Curb and Ψ from NLCD 2006 data products for (a) h for p(Ψ) with Eq. (2) (black) and for p(Ψ | Curb) with Eq. (3) (colored by Curb; bottom legend) and for (b) furb (top legend) from using just Curb with Eq. (5) with w(Curb) = (0.50, 0.50, 0.90, 0.95) (labeled NUDAPT), and following thresholds of Ψ as in Eq. (1), with w(Curb) = (0.20, 0.50, 0.80, 1.0) (labeled Max Ψ) and for w(Curb) = (0.20, 0.50, 0.80, 0.95) (labeled w/DOS). (c) The furb estimated by mean, median, and mode with Eq. (6), for just using p(Ψ) (labeled All Ψ) and p(Ψ | Curb) (bottom legend). Thresholds of Ψ per Eq. (1) are indicated by the dash–dotted horizontal lines (colored by Curb) in (b) and (c). The Curb color scheme in (a) and (c) is the same as in Figs. 1a, 1c, and 1d. The exhibits limiting values (ΔΓ > ~3 km), which are reduced for categorical partitioning, indicating improved parameterization of furb, which varies with ΔΓ, along with skewness of p(Ψ | Curb).

  • Fig. 3.

    Maps of derived (%) aggregated to ΔΓ = 990 m for the PMA by (a) mode of p(Ψ) and by Eq. (5) for (c) w(Curb) = (0.50, 0.50, 0.90, 0.95) NUDAPT method and (d) w(Curb) = (0.20, 0.50, 0.80, 0.95) NUDAPT method following Eq. (1). (b) The h (dimensionless) for p(Ψ) corresponding to the in (a). Just μ for p(Ψ) alone as in (a) underestimates the extent of the urban C and has large h for much of the urban area as in (b). The NUDAPT approach overestimates the urban area and furb when combining DOS with DLI [(c) vs (d)].

  • Fig. 4.

    Similar to Fig. 3, but showing a map of [Eq. (6)] for a mosaic approach [Eq. (7)] with Curb being (a) DOS, (b) DLI, (c) DMI, and (d) DHI. The spatial pattern of most probable Ψ for each Curb shows where each class contributes to the aggregated model output [Eq. (7)]. Note that α(Γ | Curb) can be similarly displayed, with the product giving the weight of each Curb in Eq. (7).

  • Fig. 5.

    As in Fig. 4, but following Eq. (3) for with Curb being (a) DOS, (b) DLI, (c) DMI, and (d) DHI. Spatial guidance for categorical partition [Eq. (1)] and parameterization of furb [Eq. (6)] indicates that DOS and DHI have lower than do DLI and DMI, where urban-core areas and roadway corridors have increased , indicating locations of increased heterogeneity within p(Ψ | Curb) and where the parameterization [Eq. (6)] may be less representative of the subgrid development density distribution or an alternate partitioning scheme to Eq. (1) may be needed.

  • Fig. 6.

    Maps of WPHX-FT and ALERT station locations (black circles; yellow circles are within grid cells with furb > 0 and are used for analysis, with station ID string as in Table 2) within the Phoenix metropolitan study area, along with (a) dominant land-cover class (described in text) and (b) terrain elevation (color bar). Also shown in (b) is the boundary of grid cells with = 0.01 (red contour).

  • Fig. 7.

    Diurnal 30-min T2m during 17–20 Jun 2012 for from Eq. (5) with w = μ and α from Ψ > 0 (green squares), with and α from max αc (red times signs), and for from Eq. (7) (orange circles), along with observed values (Obs) at (a) WPHX-FT, (b) DGO, (c) DMS, (d) FHF, (e) GCC, and (f) GLN. See Fig. 6 for ALERT locations.

  • Fig. 8.

    As in Fig. 7, but for ALERT stations (a) MKN, (b) O64, (c) P2B, (d) PJX, (e) WBG, and (f) XRD.

  • Fig. 9.

    Diurnal plots of statistical measures (Willmott 1981; Willmott et al. 1985) for each simulation case (Table 1) over all 12 stations (Table 2) for near-ground air temperature: (a) MAE, (b) index of agreement for RMSE d2, (c) MBE, (d) RMSE, (e) systematic error RMSEs, and (f) unsystematic error RMSEu. See Table 3 for daily totals. The d1 statistic showed a ranking of models that was similar to that for d2 (but with lower values) and so is not shown.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 283 81 11
PDF Downloads 103 18 0