Air temperature and humidity are important descriptors of terrestrial environmental condition [Prihodko and Goward, 1997] and they are two of the most critical meteorological variables in relation to biological and hydrological processes, human thermal comfort, ecosystems, and energy consumption on heating and cooling [Shulman, 1984; Stahl et al., 2006]. Many studies show that land surface heterogeneity, such as local land cover and topography, has a significant effect on microscale air temperature and humidity [Pielke, 2001; Weaver and Avissar, 2001; Lookingbill and Urban, 2003; Chun and Tamura, 2005; Solecki et al., 2005; Robitu et al., 2006; McCarthy et al., 2010; Loridan and Grimmond, 2012; Yao and Steemers, 2013]. The urban heat island, where urban area has higher temperature than surrounding rural areas [Oke, 1973; Akbari et al., 1992; Kim, 1992; Abramowitz et al., 2008; Georgescu et al., 2012], exemplifies how land cover triggers spatial heterogeneity in air temperature; however, within-city variation of air temperature is ignored by most urban heat island conceptual models. Diurnal estimates of microclimate, particularly air temperature and humidity, are important for cities, which are home to 82.4% of the US population and upward of 77.7% of the population in many developing countries [DESA, 2012]. However, spatially detailed microscale maps (<500 m) of diurnal air temperature and humidity cannot be produced with standard diurnal weather station records because they are generally limited to single observations at meteorological stations.
 To obtain the microscale maps of air temperature and humidity, researchers have applied either observational measurement [Takahashi et al., 2004; Georgakis and Santamouris, 2006] or numerical modeling [Elnahas and Williamson, 1997; de La Flor and Dom��́nguez, 2004; Bozonnet et al., 2005; Robitu et al., 2006; Yao et al., 2011]. The observational methods, including direct point measurement with high spatial density and indirect remote sensing measurement, place a significant demand on labor and instrumentation for measurements across large areas. Although remote sensing and infrared thermography can measure the spatially distributed surface skin temperature over large areas, studies show that there is no simple and general relationship between the patterns of surface skin temperature and air temperature [Roth et al., 1989; Stoll and Brazel, 1992; Eliasson, 1996; Jin et al., 2005]. Voogt and Oke  concluded that regression techniques fail to predict air temperature based on remotely sensed skin surface temperature due to spatially variable and complex linkages between the two properties in urban areas. Moreover, due to the coarse temporal measurement interval of satellites, the temporal resolution of remote sensed maps would not satisfy hourly or daily time series needs of environmental applications. Numerical modeling has demonstrated great potential to map spatial air temperature and humidity fields. Computational Fluid Dynamics (CFD) simulations [Dimoudi and Nikolopoulou, 2003; Mortensen et al., 2007; Yao and Steemers, 2013] or microclimate models, such as ENVI-met (http://www.envi-met.com/), use fluid dynamic equations to simulate heat and moisture fluxes, and can predict very detailed microclimate. However, due to the high computing time demand and intense data requirement for the CFD model domain, these models typically are applied to small spatial and temporal scale simulations. Regression models [Chuanyan et al., 2005] and geostatistical models [Ishida and Kawashima, 1993; Eliasson and Svensson, 2003; Lookingbill and Urban, 2003] are also used to spatially distribute meteorological data, but these models are site specific and require extensive observed data for development.
 Land surface models overcome the limitations of observational and CFD or statistical numerical modeling methods in simulation of microscale spatially distributed air temperature and humidity. Land surface models were developed to better estimate the partitioning of energy into sensible heat flux and latent heat flux, but are generally applied in global or mesoscale climate models as the boundary layer representation. Land surface models are built on principles of energy balance and fluxes networks. The heat fluxes are determined by the temperature and humidity differences between vertical layers and are regulated by flux resistances. In the evolution of land surface models, representation of land surface morphology has incrementally improved from the bucket model [Manabe, 1969], big leaf model [Monteith, 1965; Deardorff, 1978], single layer model [e.g., Dickinson et al., 1993; Masson, 2000; Walko et al., 2000; Chen and Dudhia, 2001; Kusaka et al., 2001], and multilayer model [e.g., Ca et al., 1999; Gu et al., 1999; Wilson et al., 2003; Krayenhoff et al., 2013]. The sophistication of land surface model flux balances has also evolved and includes hydrological, biophysical, biochemical, and ecological processes, such as the BATS (Biosphere-Atmosphere Transfer Scheme) [Dickinson et al., 1993], SiB (Simple Biosphere Model) [Sellers et al., 1986; Sellers et al., 1996], NCAR LSM (The National Center for Atmospheric Research Land Surface Model) [Bonan, 1996], LEAF (Land Ecosystem-Atmosphere Feedback model) [Lee, 1992] and LEAF-2 [Walko et al., 2000; Fan et al., 2007; Miguez-Macho et al., 2007; Anyah et al., 2008], TEB (Town Energy Balance model) [Masson, 2000; Hamdi and Masson, 2008], and the ISAM (Integrated Science Assessment Model) [Jain et al., 1996]. With the representation of various physical processes, land surface models not only improved the representation of the climate model boundary layer but were used in independent applications. For example, the LEAF-2 model was applied to estimate the global patterns of groundwater table depth [Fan et al., 2013] and ISAM was used to study carbon storage and flux dynamics in the Amazon basin [El-Masri et al., 2013]. Other land surface models use the canopy layer to explicitly represent the living environment of human beings [Masson, 2000; Kusaka et al., 2001; Lee and Park, 2008] to simulate the temperature and humidity important to population centers. In the evolution of land surface models, they have arrived at a point where they can simulate the urban microclimate.
 The single layer Urban Canopy Model (UCM) coupled with Weather Research and Forecast (WRF) model has been applied to study the urban heat island in many major metropolitan regions [Chen et al., 2011], such as Beijing, Hong Kong, Houston, New York City, Salt Lake City, Taipei, and Tokyo. Chen et al.  found that formidable challenges limit application of this model, including initialization of the detailed spatial distribution of urban canopy state variables, such as temperature profiles within walls, roofs, and roads, and specification of a large number of parameters related to building characteristics, thermal properties, emissivity, and albedo. Moreover, land surface models such as UCM need spatially distributed meteorological forcing data that are not generally available for most urban areas, such as downward direct shortwave radiation, downward diffuse shortwave radiation, and downward longwave radiation. To satisfy these data needs, mesoscale climate models are generally used to provide time-series inputs for urban land surface models.
 Alternative methods to estimate spatial patterns of urban air temperature and humidity are needed to facilitate the growing interest in urban microclimatic response to land cover change. One method advanced by Erell and Williamson  created the urban Canyon Air Temperature (CAT) model. The CAT model uses meteorological parameters monitored at one reference weather station to calculate the air temperature in another urban canyon by cross-comparing land cover. The CAT model assumes that the two sites are under the same mesoscale climatic conditions and the microclimate of the two sites is primarily modified by local land cover. Based on CAT model tests in Adelaide, Australia, it has achieved good simulations of the urban canyon air temperature in a range of weather conditions. However, the CAT model cannot simulate urban canyon humidity, a term important for human comfort and heat index calculations, and it requires detailed 3D description of the urban canyon to account for parameters such as the sky view factor, shading, and total urban surface area. The requirement for a 3D description of the urban canyon limited its application to small spatial scales.
 Our research builds on the CAT model and other urban land surface models (e.g., UCM and TEB) by combining their advantages of the single point weather measurement as input and a simplified urban canopy representation. In this research, we created the Physically based Analytical Spatial Air Temperature and Humidity (PASATH) model to simulate urban microclimate terms of air temperature and humidity at a subdaily time step. In section 2, we introduce the physics of the model; in section 3, we present an example application; in section 4, we discuss the advantages and limitations of the model; and in section 5, we summarize our research findings.