A comparative analysis of micrometeorological determinants of evapotranspiration rates within a heterogeneous urban environment

Abstract

Variability in micrometeorological conditions and their influence on estimated reference evapotranspiration (RET) rates were evaluated across a heterogeneous urban environment. Micrometeorological data sets (incoming solar radiation, air temperature, relative humidity and wind speed) were collected over a one-year period at six weather stations in New York City, NY (USA). Weather stations are located at four new urban green space monitoring sites and two airports. Reference evapotranspiration (RET) rates were estimated from the micrometeorological data sets for a short reference surface at a daily time-step using the ASCE Standardized Reference Evapotranspiration Equation, a Penman-Monteith based combination equation. Non-parametric comparative statistical analyses (Kruskal-Wallis) revealed statistically significant differences (at significance level α = 0.05) in micrometeorological conditions and estimated RET rates between the six sites. On a cumulative annual basis, estimated RET varied by up to 40 percent between the sites. A new technique for adjusting weather data collected at one location (e.g. regional airports) for use at another location (e.g. interior engineered urban green spaces) was evaluated. The study highlights the importance, for accurate estimation of ET, of onsite micrometeorological data sets, but concludes that additional research is needed to more thoroughly characterize micrometeorological variability across heterogeneous urban environments, and also to evaluate the influence of non-meteorological determinants, e.g. vegetation type, soil/media type, media moisture conditions and anthropogenic heat fluxes, on urban ET.

1. Introduction

1.1. Background

Micrometeorological conditions are known to vary, due in part to land surface heterogeneity, across urban environments (Oke 1988). Quantification of this variability is important to better manage urban microclimatic conditions (e.g. by developing approaches for mitigating urban heat islands or adapting to other forms of forecasted climate change) and to improve the accuracy of urban hydrologic and energy flux models, themselves used to forecast the effect that different actions (e.g. afforestation projects) could have on urban water and energy budgets.

Hydrologic and energy balances are intimately linked through the evaporative or latent heat flux term. While other factors including vegetation type and media moisture conditions can impact actual rates of evapotranspiration (ET), the influence of micrometeorological conditions alone on ET can be substantial. For example, urban tree transpiration rate studies conducted in Beijing (China) over a two-year consecutive monitoring period found that 80% of the daily variation in tree transpiration rates could be explained by atmospheric and climatic conditions (Wang, Wang et al. 2012). Al-Kofahi, VanLeeuwen et al. (2012) showed that reference evapotranspiration (RET) in Albuquerque, NM varied by zip code, and was based, in part, on temperature differences between locations.

Because of its influence on ET, the spatial variability of micrometeorological conditions in urban environments also carries important implications for the planning, design and management of urban landscapes. For example, differences in urban ET imply different urban landscape irrigation needs (Feldhake, Danielson et al. 1983, Nouri, Beecham et al. 2013), with a direct link to urban water resource management and water conservation planning. Differences in urban ET also imply potential differences in the ecosystem services (e.g. stormwater management, microclimate regulation, and carbon sequestration) that can be extracted from urban landscapes (Jim and Chen 2009, PWD 2009, NYCDEP 2010). Metselaar (2012) suggested that understanding spatial variability in urban ET rates can improve urban design by helping to match vegetation and substrate types to the hydrologic requirements dictated by local micrometeorological conditions. Lemonsu, Masson et al. (2012) assert that to assess the benefits associated with ET, the role of micrometeorological variability and urban ET needs better representation in urban ET modeling.

Table 1 summarizes all of existing studies known to the authors that attempt to measure or model the variation of meteorological conditions and/or evapotranspiration (latent heat fluxes) across heterogeneous urban environments.

Table 1 –

Summary of studies, known to authors, addressing, for heterogeneous urban environments, 1) spatial variability in meteorological and/or evaporative (latent heat) fluxes 2) influence of meteorological variability on variability of ET and/or 3) efforts to represent or account for variability in meteorological conditions and/or ET through modeling

Study	Location	Meteorological Data	Evapotranspiration Method	Key Results
Al-Kofahi, VanLeeuwen et al. (2012)	Albuquerque, NM, USA	Meteorological data acquired from NWS forecast office and Albuquerque COOP station	Stzd Penman-Monteith and Hargreaves	1) spatial and temporal variation in ETo across zip codes 2) --- 3) accounts for spatial variability in ETo by using multiple points in each zip code
Basara, Hall et al. (2008)	Oklahoma City, OK, USA	Air temperature	---	1) diurnal variability in air temp. across urban sites and in comparison to rural sites 2) --- 3) ---
Bueno, Norford et al. (2013)	Basel, Switzerland Toubuse, France	Air temperature and relative humidity	---	1) air temp. variability 2) --- 3) calculates air temp. inside urban canyons using rural weather station
Coutts, Beringer et al. (2007)	Melbourne, Australia	Surface & air temperature, wind speed	Eddy covariance	1) surface temperature differences; air temperature and surface energy balance (including latent heat flux) similar across urban sites 2) --- 3) ---
Czarnecka, Makosza et al. (2011), (Hjort, Suomi et al. 2011)	Szczecin, Poland	Air temperature, relative humidity, wind speed and direction	---	1) reduced relative humidity in city center and two times lower wind speeds (compared to city “outskirts”) 2) --- 3) ---
Hjort, Suomi et al. (2011)	Turku, SW Finland	Air temperature	---	1) variability in air temperature across sites 2) --- 3) predicts air temp. using statistical techniques and explanatory variables on regional scale
Ho, Knudby et al. (2014)	Vancouver, Canada	Air temperature	---	1) variability in air temperature observed across stations and in comparison to reference station 2) --- 3) mapped peak daytime air temp. (relative to reference station) using spatial regression
Jacobs, Elbers et al. (2015)	Arnhem, Netherlands Rotterdam, Netherlands	Air temperature, relative humidity, wind speed and direction, net radiation	Eddy covariance, scintolometer, sap flux FAO Penman-Monteith and modified Makkink	1) strong microweather variability across sites 2) --- 3) use of modified Makkink equation which in given context, “presumably is less sensitive to modifications of microweather conditions by buildings and sealed surfaces”
(Kuang, Liu et al. 2015)	Beijing, China	Latent heat flux and land-surface temperature (LST)		1) latent heat flux was dominant for urban green spaces and croplands (resulting in lower LST) while sensible was dominant for impervious spaces 2) --- 3) ---
(Liu, Hong et al. 2010), Klein and Young (2011)	Oklahoma City, OK, USA	Wind speed and direction	---	1) variability in wind speed and direction across sites 2) --- 3) ---
Liu, Hong et al. (2010)	Oklahoma, USA	Oklahoma Mesonet (Solar radiation, humidity, temperature, wind speed and direction)	Modified surface energy balance (SEB) approach, Mesonet ET (Stzd Penman-Monteith), and AmeriFlux towers	1) variability in ET based on land use and development level 2) --- 3) remote sensing techniques and SEB algorithms to estimate ET at the regional level
Lowry, Ramsey et al. (2011)	Salt Lake City, UT, USA	---	Reference evapotranspiration as reported by Utah Climate Center	1) --- 2) --- 3) predictive model based on plant factors for aerial urban vegetation coverage
Oswald, Rood et al. (2012)	Detroit, MI, USA	Air temperature	---	1) variability in air temperature 2) --- 3) developed regressions based on explanatory variables
Rim (2007), (Rim 2009)	Seoul, South Korea	Sunshine duration, air temperature, relative humidity, wind speed and direction	FAO Penman-Monteith	1) climatological and RET variability 2) relative humidity, solar radiation, and wind speed trends related to urbanization had varying impacts on aerodynamic and energy terms for RET 3) ---
Small (2006)	24 cities worldwide	Surface temperature	---	1) urban thermal field variability 2) --- 3) linear fixture model considering physical components
Stoll and Brazel (1992), (van Hove, Jacobs et al. 2015)	Phoenix, AZ, USA	Air temperature, surface temperature, solar radiation, wind speed and direction	---	1) air and surface temperature variability 2) --- 3) ---
van Hove, Jacobs et al. (2015)	Rotterdam Agglomeration, Netherlands	Air temperature, relative humidity, wind speed and direction	---	1) local climate variability 2) --- 3) evaluates dependencies of intraurban variability on urban land use and geometric characteristics
Zhang, Hou et al. (2005)	Beijing, China	Land surface temperature	Surface evapotranspiration derived from EOSMODIS satellite data	1) LST and surface evapotranspiration variability across urban to suburban areas 2) --- 3) ---
Boegh, Poulsen et al. (2009)	Sjaelland, Denmark		Eddy covariance FAO Penman-Monteith	1) variability of ET across agricultural, forest and urban land surfaces 2) --- 3) ---
DiGiovanni, Montalto et al. (2013)	New York City, NY, USA	Air temperature, relative humidity, wind speed and direction, solar radiation	Weighing Lysimeter Penman-Monteith	1) ET from offsite weather station does not well represent onsite ET 2) --- 3) ---
Lemonsu, Masson et al. (2007), (Lemonsu, Masson et al. 2012)	Nantes, France	Atmospheric pressure, temperature, specific humidity, wind speed incoming shortwave and longwave radiation	Town Energy Balance (TEB) Model	1) --- 3) --- 3) differences in local climate conditions modeled explicitly in TEB model
Chen, Kusaka et al. (2011)	Houston, TX, USA Tokyo, Japan	---	WRF/urban model coupled with EULAG/CFD-urban	1) --- 2) --- 3) downscaling for microscale site specific simulations
Järvi, Grimmond et al. (2011)	Los Angeles, CA, USA Vancouver, Canada	---	Surface urban energy balance scheme (SUEWS)	1) --- 2) --- 3) calculates urban energy and water balances at neighborhood scale

Because spatial differences in micrometeorological conditions are poorly characterized in the urban environment, accurate estimation of actual ET fluxes is difficult. The energy balancebased LUMPS model (Grimmond and Oke 2002) was used to simulate temperature changes under different greening scenarios and water usage rates in Phoenix, AZ (USA). As noted by the author, a limitation of the study was that the LUMPS model used micrometeorological data from a single weather station and did not account for neighborhood level variations (Gober, Brazel et al. 2010). The same limitation was noted by Middel, Brazel et al. (2012) in their attempts to parameterize LUMPS for surface energy balance (SEB) studies in Phoenix, AZ (USA) and Portland, OR (USA). DiGiovanni, Montalto et al. (2013) found that ET estimates from regional weather stations did not perform as well as estimates from onsite micrometeorological data in comparison to actual ET rates measured from a green roof in New York City, NY (USA).

Though some urban energy/water balance models include methods to account for site scale variability in micrometeorological conditions, validation of these approaches is currently limited by the availability of observed data. For example, improvements to the Town Energy Balance (TEB) model (Lemonsu, Masson et al. 2007, Lemonsu, Masson et al. 2012) now allow for the influence of urban green areas and differences in local microclimatic conditions to be modeled explicitly. Without actual urban data sets, the model’s performance cannot be evaluated. Similarly, the Weather Research and Forecasting model (WRF)/urban model, coupled with EULAG/CFD-urban now enables downscaling for microscale (1–10 m) site-specific simulations (Chen, Kusaka et al. 2011). But one of the challenges for executing the WRF/urban modeling system is, “the specification of a potentially vast number of parameters...[which] are rarely available (Chen, Kusaka et al. 2011).” Using a reduced number of inputs in comparison to Grimmond and Oke (1991), the Surface Urban Energy Balance Scheme (SUEWS) (Järvi, Grimmond et al. 2011) calculates urban energy and water balances at the neighborhood scale. Even so, critical site-specific micrometeorological inputs are difficult to parameterize with limited existing data sets.

Other approaches for accounting for spatial variability in the urban microclimate were developed including recent advances, but these too require more urban micrometeorological observations. Microclimate coefficients (K_m) were suggested to adapt estimates of RET computed from Penman-Monteith based combination equations using offsite weather station data (e.g. from airports) to local conditions (Costello and Jones 1994, Eching and Snyder 2005). However, Eching and Snyder (2005) noted that, “…scientifically-based information on these parameters [microclimate, etcetera] is limited.” Bean and Pitt (2012) inventoried the locations of Remote Automated Weather Stations (RAWS) nationwide (US), revealing that readily available micrometeorological data and ET estimates are lacking in urban areas particularly in the eastern USA. At the site scale, Stewart and Oke (2012) presented local climate zones (LCZ) as a means for classifying sites, based on site characteristics, for temperature studies. The LCZ classification system can be used to build spatial databases of urban form and cover for cities worldwide. Once developed, the LCZ system can function, “easily and inexpensively for any city or region,” however, the LCZ classification system cannot be fully elaborated without actual urban microclimatic data.

Because extensive networks of weather stations are not currently found in urban environments, the independent variables driving ET models are often, by necessity, obtained from regional climate stations, typically located at airports and in other open spaces. Due to modifications of urban wind speed and direction as well as incoming solar radiation by the presence of buildings and other above ground structures (Oke 1982, Oke 1988), actual conditions at urban leaf and soil surfaces can differ significantly from those observed at regional weather station sites. Urban air temperatures, in turn, are tempered by the presence of low albedo impervious surfaces (Grimmond and Oke 1999, Takebayashi and Moriyama 2007, Shashua-Bar, Pearlmutter et al. 2009), which may also contribute to differences between values measured at offsite weather stations and at the site level.

Note that throughout this manuscript, we use micrometeorological to refer to our site scale meteorological measurements, based on scale and characteristic time definitions (though our measurements are aggregated to daily values). The definition of microscale in terms of horizontal scale and characteristic time, as presented in Orlanski (1975), are < 2 km and < 1 hr (roughly). Most of the monitored sites fall into the micro γ scale, at <20 m and observations made at hourly or shorter (5 minute) intervals.

1.2. Objectives

Using New York City (USA) as a case study, the objectives of this paper are to:

1. evaluate the spatial variability of micrometeorological conditions, measured at the site scale, and estimated RET rates;

2. determine the relative role of incoming solar radiation, temperature, relative humidity and wind speed in influencing reference evapotranspiration (RET) rates at the site scale; and

3. develop methods for adapting offsite (e.g. airport) micrometeorological and ET data sets to different urban conditions (e.g. interior engineered urban green spaces).

To address the first objective, micrometeorological data gathered at six different NYC weather station sites are used to estimate, and statistically compare RET values across New York City. The micrometeorological data included incoming solar radiation, air temperature, relative humidity and wind speed. The ASCE Standardized Reference Evapotranspiration Equation for short reference surfaces was used to calculate daily RET rates. RET estimates are presented specifically to demonstrate the potential influence that micrometeorological variability (and not other factors) could have on urban ET and thus no correction coefficients to the RET estimates are presented here. The sensitivity of RET estimates to vegetation dependent parameters, are, however, evaluated in this paper and presented in the supplementary materials. The second objective is addressed to determine the relative role of each micrometeorological parameter in influencing RET rates by statistical analyses using correlation coefficients. To address the third objective, site specific microclimate coefficients are applied to RET estimates and new parameter specific microclimate coefficients $(K_{m_p})$ are developed and evaluated.

2. Study Sites

Micrometeorological data sets, including incoming solar radiation (R_sin), air temperature (T), relative humidity (RH) and wind speed (u_z), were acquired from six sites located in NYC. The locations, physical characteristics and local climate zone (LCZ) classification of the monitoring sites are presented in Table 2 and their locations mapped in Figure 1. The sites include one bioinfiltration area, three green roofs and two airport locations. The monitoring setups at the green roof sites and bioinfiltration area were installed by Drexel University and Columbia University as part of ongoing studies. The monitoring setups at the two airport locations are maintained by the National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) and the publicly available data sets were obtained from the Northeast Regional Climate Center (NRCC). Monitoring equipment installed at the sites is listed in Table 3; images of the weather stations are shown in Figure 2. Data presented here was collected between 1 Aug 2010 and 31 July 2013.

Table 2 –

Spatial and physical characteristics of monitoring sites

Site Acronym	Site Type	Site Name	Latitudeb (degrees)	Longitudeb (degrees)	Total Elevation (m)c (Ground Elevation, m)	Vegetated Area of Monitoring Site (m2)	Vegetation Type	Aerial Viewe ━ 15 m	Local Climate Zone (LCZ) Classificationf
Bio-C	Bio-infiltration	Colfax	40.70294	−73.74414	15 (15)	110	Native and non-native trees, grasses and low lying vegetation		LCZ 6 Open low-riseg
GR-C	Green Roof	Columbia (W118)	40.80810	−73.95973	62 (40)	300	Mixed Sedum species		LCZ 2 Compact mid-rise
GR-F	Green Roof	Fieldston	40.88937	−73.90526	70 (55)	520	Mixed Sedum species		LCZ 6 Open low-rise
Air-JFKa	Airport	JFK	40.64673	−73.81732	5 (5)	200	Grass; light colored cobble stoned		LCZ D Low plants
Air-LGa	Airport	La Guardia	40.77945	−73.88027	12 (12)	3,500	Grass; light colored cobble stoned		LCZ D/E Low plants/Bare rock or paved
GR-QBG	Green Roof	Queens Botanical Garden	40.75120	−73.82727	13 (6)	270	Mix of native and non-native grasses and low lying vegetation		LCZ 6 Open low-rise

Caption 1

^a)NOAA/NWS (National Oceanic and Atmospheric Administration National Weather Service) ASOS (Automated Surface Observation Station) monitoring site

^b)Geodetic Datum WGS84 (Google 2016)

^c)Vertical Datum NGVD29 (Microsoft Corporation 2010) NOTE: Total elevation includes building height for green roof sites

^d)personal communication with Tim Morrin, Observation Program Leader at the NWS Forecast Office in Upton, NY NOAA/NWS

^e)Imagery ©2016 Google, Map data ©2016 Google

^f)Stewart and Oke (2012)

^g)as classified in Smalls-Mantey (2017), note that all LCZ classifications are based on LCZ classification at ground level.

Figure 1 –

Map of monitoring site locations (False Color\Near Infrared (432) 1975–2010 - United States Geological Survey (USGS), National Aeronautics and Space Administration (NASA), Esri Inc) NOTE: Vegetation appears in shades of red (generally the brighter the red, the more vigorous the vegetation), urban areas are cyan blue, soils vary from dark to light browns and water appears very dark.

Table 3 –

Micrometeorological monitoring characteristics and equipment

Site	Monitoring Period	Recording Interval	Data Logger	Incoming Solar Radiation (mounting height above surface)	Air Temperature (mounting height above surface)	Relative Humidity (mounting height above surface)	Wind Speed (mounting height above surface)
Bio-C	2011 – present	5 minutes	Campbell Scientific CR1000	Hukesflux NR01 Net Radiometer (4 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (4 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (4 m)	RM Young 05103 Wind Monitor (4 m)
GR-C	2008 – present	5 minutes	Campbell Scientific CR1000	Kipp and Zonen CMP 3 Pyranometer (1.5 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (2 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (2 m)	RM Young 05103 Wind Monitor (4 m)
GR-F	2008 – present	5 minutes	Campbell Scientific CR1000	Kipp and Zonen CMP 3 Pyranometer (1.5 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (2 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (4 m)	RM Young 05103 Wind Monitor (4 m)
Air-JFKa	1948 – present	1 hour	Automated Surface	ASOSb	ASOS (2m)	ASOS (2m)	ASOS (10 m)
Air-LGa	1948 – present	1 hour	Observing System (ASOS)	ASOSb	ASOS (2m)	ASOS (2m)	ASOS (10 m)
GR-QBG	2008 – present	5 minutes	Campbell Scientific CR1000	Kipp and Zonen CMP 3 Pyranometer (1.5 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (2 m)	Campbell Scientific CS215 Temperature and Relative Humidity Sensor (2 m)	RM Young 05103 Wind Monitor (4 m)

Caption 2

^a)NOAA/NWS first order climate station

^b)Daily solar radiation estimates per DeGaetano, Eggleston et al. (1993)

Figure 2 –

Weather stations at monitoring sites a) Bio-C (top left) b) GR-C (top middle) c) GR-F (top right) d) Representative ASOS weather station (All Weather Inc 2014) (bottom left) and e) GR-QBG (bottom right)

3. Methods

3.1. Objective (i) - Evaluate the spatial variability of micrometeorological conditions and estimated RET rates

Reference Evapotranspiration

The ASCE Standardized Reference Evapotranspiration Equation for short reference surfaces (Allen, Walter et al. 2005), as shown in Equation 1, was utilized for the estimation of daily reference evapotranspiration (RET) rates.

$$E{T}_{os}=\frac{0.408\Delta \left(R_n-G\right)+\gamma \left(\frac{C_n}{T+273}\right)u_2\left(e_s-e_a\right)}{\Delta +\gamma \left(1+C_d{u}_2\right)}$$ (1)

ET_os is the standardized reference evapotranspiration for short reference surface (grass) (mm day⁻¹)

R_n is calculated net radiation at the crop surface (MJ m⁻² d⁻¹)

G is soil heat flux density at the soil surface (MJ m⁻² d⁻¹)

T is mean daily air temperature (°C) per calculation procedures for the ASCE Standardized Reference Evapotranspiration Equation

u₂ is mean daily wind speed adjusted to 2-m height (m s⁻¹) per ASCE Standardized Reference Evapotranspiration Equation calculation procedures

e_s is the saturation vapor pressure calculated for daily time steps as the average of saturation vapor pressure at maximum and minimum air temperature (kPa)

e_a is the mean actual vapor pressure (kPa)

Δ is the slope of the saturation vapor pressure-temperature curve (kPa °C⁻¹)

γ is the psychrometric constant (kPa °C⁻¹)

C_n is the numerator constant that changes with reference type and calculation time step, 900 for short (grass) reference surface at daily time step (K mm s³ Mg⁻¹ d⁻¹)

C_d is the denominator constant that changes with reference type and calculation time step, 0.34 for short (grass) reference surface at daily time step (s m⁻¹)

RET rates were estimated at daily time-steps. Incoming solar radiation, air temperature, relative humidity and wind speed measured at five minute or hourly intervals were averaged (between 00:00 and 23:59) to compute daily values, per standard procedures outlined in “The ASCE Standardized Reference Equation” (Allen, Walter et al. 2005), for input into Equation 1. As wind measurements at the monitored sites were taken above two meters height and above surfaces other than clipped grass, the full logarithmic equation as presented in Appendix B of the ASCE-EWRI Standardized Reference Evapotranspiration Equation was applied to adjust wind speed to two meters height (Allen, Walter et al. 2005). Terms not monitored at all sites (e.g. soil heat flux) were estimated using procedures laid out for the ASCE Standardized Reference Evapotranspiration Equation (Allen, Walter et al. 2005). Specifically, soil heat flux was assumed to be zero over the daily time period.

Since RET estimates are presented specifically to demonstrate the potential influence that micrometeorological variability (and not other factors) could have on urban ET estimates, standard methods are followed for all sites, though the limitations of this application are acknowledged. The sensitivity of RET to vegetation dependent parameters, C_n and C_d, are evaluated in this paper and presented in the supplementary materials. According to the guidelines set by the ASCE-EWRI (2005) Task Committee, “Reference evapotranspiration is defined as the ET rate from a uniform surface of dense, actively growing vegetation having specified height and surface resistance, not short of soil water, and representing an expanse of at least 100 m of the same or similar vegetation.” Such conditions often do not exist in urban environments, including in the areas surrounding urban weather stations. Further, according to Allen, Walter et al. (2005), “Many urban weather stations fail both the underlying surface requirement and the recommended separation distance from obstacles…[Weather stations] should be located in sites that closely approximate the reference conditions…” Application of Penman-Monteith based combination equations to estimate ET from heterogeneous urban environments is thus challenging. Some researchers have used crop coefficients (Doorenbos and Pruitt 1977) and non-growing season coefficients (Allen, Pereira et al. 1998) to adjust RET estimates obtained from the ASCE equations to closer approximate actual ET rates. However, ASCE-EWRI (2005) does, “not recommend a methodology for the application of reference evapotranspiration during non-growing seasons (Allen, Walter et al. 2005).” Moreover, because the goal of this study from micrometeorological variability alone, no correction coefficients to the RET estimates are presented here. Further evaluation of the applicability of the ASCE reference evapotranspiration equation to urban green spaces is warranted, though is considered beyond the scope of this study.

RET rates were calculated using MATLAB v. 2012a and 2017b (MathWorks 2012) with a custom-coded program developed by the authors, and validated by hand calculation and through comparison to results obtained by REF-ET software v. 3.1.08 (Allen 2012). Per the developer’s recommendation, REF-ET software was used only as a validation program, and not as the primary means for computing RET.

Statistics

For statistical comparison of micrometeorological and RET data across sites, non-parametric statistical tests of daily data sets were employed. Since the data sets were not normally distributed (especially u₂ and RET) the non-parametric, Kruskal-Wallis test was used to compare R_sin, T, RH and u₂ and RET across the sites. Specifically, the Kruskal-Wallis test was used to test the hypotheses listed in Table 4. Each hypothesis was tested across all sites (e.g. the distribution of reference evapotranspiration (RET) is the same across sites Bio-C, GR-C, GR-F, Air-JFK, Air-LG and GR-QBG) and across all pairs of sites (e.g. the distribution of reference evapotranspiration (RET) is the same across sites Bio-C and GR-F). Kruskal-Wallis tests were evaluated using IBM SPSS Statistics software v. 20.0.0 (IBM Corporation 2011). Statistical analyses were performed on a subset of the data collected for a total of 327 days between 26 Jul 2011 and 5 Aug 2012 for which data was simultaneously available from all of the six monitoring sites.

Table 4 –

Kruskal-Wallis test hypotheses

The distribution of reference evapotranspiration (RET) is the same across sites.

The distribution of incoming solar radiation (Rsin) is the same across sites.

The distribution of air temperature (T) is the same across sites.

The distribution of relative humidity (RH) is the same across sites.

The distribution of wind speed (u2) is the same across sites.

3.2. Objective (ii) - Determine the relative role of micrometeorological conditions in influencing RET rates

The relationship between individual micrometeorological parameters (R_sin, T, RH and u2) and RET were evaluated using Spearman’s rank correlation coefficients. Spearman’s Rho coefficients were determined to rank the relative importance of the influence that each of the various micrometeorological determinants had on estimated RET. Correlation coefficients between ±1.0 and ±0.8 are considered strong, those between ±0.8 and ±0.5 moderate and those less than ±0.5 are considered weak (Devore 2004). Spearman’s rho correlation coefficients were evaluated using IBM SPSS Statistics software v. 20.0.0 (IBM Corporation 2011). Spearman’s rho correlation coefficients were developed based on data collected between 26 Jul 2011 and 5 Aug 2012 for which data was simultaneously available from all of the six monitoring sites.

3.3. Objective (iii) - Develop methods for adapting offsite micrometeorological data sets to different urban conditions

Development of K_m and K_mp

Microclimate coefficients (K_m) and new, parameter specific microclimate coefficients $(K_{m_p})$ were developed from data collected at all sites (Bio-C, GR-C, GR-F, Air-JFK, Air-LG and GR-QBG) between 26 Jul 2011 and 5 Aug 2012. The use of a single microclimate coefficient to adjust RET (estimated by Penman-Monteith based methods) for “local” microclimate differences was proposed by others (Costello and Jones 1994, Eching and Snyder 2005), and applied here, as shown in Equation 2:

$$E{T}_m=K_{m}E{T}_o$$ (2)

where ET_m is the reference evapotranspiration at the local site

K_m is the microclimate coefficient

ET_o is the reference evapotranspiration at the reference site e.g. airport

Here, parameter specific microclimate coefficients $(K_{m_p})$ are proposed to account for differences in local weather conditions given the relationship in Equation 3:

$$p_j=K_{m_{p_{\frac{j}{k}}}}{p}_k$$ (3)

where p is the parameter of interest, in this case R_sin, T, RH, u₂ or RET

j is the site to which the data set is being adjusted to i.e. the local condition, in this case j is Bio-C, GR-C, GR-F, Air-JFK or GR-QBG

$K_{m_{p_{\frac{j}{k}}}}$ is the parameter specific microclimate coefficient for parameter p for site j in relation to site k

k is the site from which the data set is being adjusted from i.e. the offsite measurement, in this case Air-LG

We developed monthly microclimate coefficients for RET parameter specific microclimate coefficients for R_sin, T, RH and u₂ using Equation 4 below. An airport site (Air-LG) was selected as the reference site because operated and maintained weather stations providing publicly available data sets are often located at airports.

$$K_{m_{p_{\frac{j}{k}}}}=\frac{{\sum }_{i=1}^n\frac{x_{p_{j_i}}}{x_{p_{k_i}}}}{n}$$ (4)

$x_{p_{j_i}}$ is the i^th value of parameter p for site j for a designated time-step, in this case one day

$x_{p_{k_i}}$ is the i^th value of parameter p for site k for a designated time-step, in this case one day NOTE: The date and time of $x_{p_{j_i}}$ and $x_{p_{k_i}}$ must be equivalent.

n is the number of values of x, in this case the number of days in a given month

Validation

To evaluate the performance of developed microclimate coefficients, two validation periods were used comparing predicted vs. observed onsite micrometeorological conditions and RET. To determine predicted onsite conditions, the monthly parameter specific microclimate coefficients (developed from data collected 26 Jul 2011 through 5 Aug 2012) were applied to Air-LG data sets for separate validation periods. For Bio-C and GR-F, the validation period was 1 Aug 2012 through 31 July 2013 (the year following the microclimate coefficient development period). Based on data availability, the validation period for GR-C, Air-JFK and GR-QBG was 1 Aug 2010 through 31 July 2011 (the year prior to the microclimate coefficient development period). Though data collection is ongoing at the sites, the validation period was limited to one year to reduce potential temporal impacts. Specifically, shifts in K_m and/or K_mp could occur over time with further urbanization/development and/or climate change and are considered beyond the scope of this paper. Root mean square error (RMSE), mean absolute error (MAE), and mean bias error (MBE) were all used to compare predicted and observed data to represent average errors (with more weight on large errors in the case of RMSE) and bias errors with MBE.

4. Results

4.1. Objective (i) - Evaluate the spatial variability of micrometeorological conditions and estimated RET rates

Micrometeorological and RET Data Sets

Box and whisker plots of micrometeorological data and RET estimates are shown in Figure 3. In the supplementary materials, time-series plots of the observed data are shown in Figure 12 and Table 14 summarizes statistics of the observed data. Also, seasonal box and whisker plots are shown in Figure 13 of the supplementary materials. Cumulative RET for all of the sites is shown in Figure 4. Cumulative RET over the period of analysis at Bio-C, GR-C, GR-F, Air-JFK, and Air-LG, respectively, was 8.5, 17.1, 7.6, 31.7 and 40.2 percent greater than GR-QBG (which had the lowest cumulative RET). Gaps in the curves depict days when data was unavailable at one or more sites. Data was representative of all months and seasons over the roughly year-long observation period. Data was available for all six monitoring sites for between 74 and 100 percent of days for each month (average = 90%; standard deviation = 10%).

Figure 3 –

Box plots for 327-day data sets across all sites of daily (a) RET in mm/day (b) R_sin in W/m² (c) T in °C (d) RH in % (e) u₂ (wind speed adjusted to two meters height) in m/s NOTE: The top of the box represents the 75th percentile, the bottom of the box represents the 25th percentile, and the line in the middle represents the 50th percentile or median. The whiskers (the lines that extend out the top and bottom of the box) represent the highest and lowest values that are not outliers or extreme values. Outliers (values that are between 1.5 and 3 times the interquartile range) and extreme values (values that are more than 3 times the interquartile range) are represented by circles and stars beyond the whiskers, respectively (Elvers 2004).

Figure 4 –

Cumulative RET for 327-day non-consecutive data set NOTE: Bio-C and GR-F cumulative RET are approximately equivalent

Statistical Results

The results of Kruskal-Wallis analyses for the period of analysis across all sites are presented in Table 5. The results indicate that daily data sets of RET, R_sin, T, RH and u₂ were statistically significantly different at the 0.05 significance level when compared across all sites.

Table 5 –

Results of hypothesis testing across all sites (level of significance)

Null Hypothesis	Decision
The distribution of reference evapotranspiration (RET) is the same across sites.	Reject (0.000)
The distribution of incoming solar radiation (Rsin) is the same across sites.	Reject (0.000)
The distribution of air temperature (T) is the same across sites.	Reject (0.000)
The distribution of relative humidity (RH) is the same across sites.	Reject (0.000)
The distribution of wind speed (u2) is the same across sites.	Reject (0.000)

Table 6 through Table 10 present the Kruskal-Wallis test results, also evaluated at the 0.05 significance level, over the period of analysis for each of the paired site to site hypothesis tests. Seasonal results are presented in Table 16 through Table 20 of the supplementary materials.

Table 6 –

Result of test hypothesis: The distribution of daily reference evapotranspiration (RET) rates is the same across sites (level of significance)

	Bio-C	GR-C	GR-F	Air-JFK	Air-LG	GR-QBG
Bio-C	---	Accept (0.343)	Accept (0.530)	Reject (0.000)	Reject (0.000)	Reject (0.043)
GR-C		---	Accept (0.095)	Reject (0.006)	Reject (0.000)	Reject (0.004)
GR-F			---	Reject (0.000)	Reject (0.000)	Accept (0.196)
Air-JFK				---	Accept (0.177)	Reject (0.000)
Air-LG					---	Reject (0.000)
GR-QBG						---

Table 10 –

Result of test hypothesis: The distribution of average daily wind speed adjusted to two meters height (u₂) is the same across sites (level of significance)

	Bio-C	GR-C	GR-F	Air-JFK	Air-LG	GR-QBG
Bio-C	---	Reject (0.000)	Reject (0.000)	Reject (0.000)	Reject (0.000)	Reject (0.000)
GR-C		---	Reject (0.000)	Reject (0.000)	Reject (0.000)	Reject (0.000)
GR-F			---	Reject (0.000)	Reject (0.000)	Reject (0.000)
Air-JFK				---	Reject (0.014)	Reject (0.000)
Air-LG					---	Reject (0.000)
GR-QBG						---

Statistically significant differences were identified for 10 of 15 RET site pairs, seven of 15 R_sin pairs, five of 15 T pairs, 12 of 15 RH pairs, and 15 of 15 u₂ site pairs (Table 6, Table 7, Table 8, Table 9 and Table 10).

Table 7 –

Result of test hypothesis: The distribution of average daily incoming solar radiation (R_Sin) is the same across sites (level of significance)

	Bio-C	GR-C	GR-F	Air-JFK	Air-LG	GR-QBG
Bio-C	---	Accept (0.473)	Reject (0.002)	Accept (0.602)	Accept (0.512)	Accept (0.143)
GR-C		---	Reject (0.001)	Accept (0.624)	Accept (0.649)	Reject (0.029)
GR-F			---	Reject (0.000)	Reject (0.000)	Accept (0.101)
Air-JFK				---	Accept (0.916)	Reject (0.041)
Air-LG					---	Reject (0.034)
GR-QBG						---

Table 8 –

Result of test hypothesis: The distribution of average daily air temperature (T) is the same across sites (level of significance)

	Bio-C	GR-C	GR-F	Air-JFK	Air-LG	GR-QBG
Bio-C	---	Reject (0.000)	Accept (0.859)	Accept (0.881)	Accept (0.312)	Accept (0.239)
GR-C		---	Reject (0.000)	Reject (0.000)	Reject (0.000)	Reject (0.000)
GR-F			---	Accept (0.953)	Accept (0.434)	Accept (0.335)
Air-JFK				---	Accept (0.402)	Accept (0.288)
Air-LG					---	Accept (0.830)
GR-QBG						---

Table 9 –

Result of test hypothesis: The distribution of average daily relative humidity (RH) is the same across sites (level of significance)

	Bio-C	GR-C	GR-F	Air-JFK	Air-LG	GR-QBG
Bio-C	---	Accept (0.367)	Reject (0.001)	Reject (0.009)	Reject (0.000)	Reject (0.016)
GR-C		---	Reject (0.000)	Accept (0.068)	Reject (0.000)	Reject (0.000)
GR-F			---	Reject (0.000)	Reject (0.000)	Accept (0.341)
Air-JFK				---	Reject (0.000)	Reject (0.000)
Air-LG					---	Reject (0.000)
GR-QBG						---

For both the ten site pairs with statistically significant differences in RET and the five site pairs with no statistically significant differences in RET, micrometeorological parameters differed significantly with respect to R_sin, T, RH, and u₂ as seen in Table 11.

Table 11 –

Site pairs with and without statistically significant differences in RET

Site pairs with statistically significant differences in RET	Micrometeorological parameters with statistically significant differences	Site pairs without statistically significant differences in RET	Micrometeorological parameters with statistically significant differences
Bio-C and Air-JFK	RH and u2	Bio-C and GR-C	T and u2
Bio-C and Air-LG	RH and u2	Bio-C and GR-F	Rsin, RH and u2
Bio-C and GR-QBG	RH and u2	GR-C and GR-F	Rsin, T, RH and u2
GR-C and Air-JFK	T and u2	GR-F and GR-QBG	u2; and RH
GR-C and Air-LG	T, RH and u2	Air-JFK and Air-LG	u2
GR-C and GR-QBG	Rsin, T, RH, and u2
GR-F and Air-JFK	Rsin, RH and u2
GR-F and Air-LG	Rsin, RH and u2
Air-JFK and GR-QBG	Rsin, RH and u2
Air-LG and GR-QBG	Rsin, RH and u2

4.2. Objective (ii) - Determine the relative role of micrometeorological conditions in influencing RET rates

The Spearman’s rank correlation coefficients depicting the strength of each of the micrometeorological parameters in estimating RET are presented in Table 12. Incoming solar radiation is strongly correlated to RET (average Spearman’s rho correlation coefficient of 0.93), followed by air temperature with moderate correlation (average coefficient value of 0.74), and relative humidity and wind speed with weak correlations (average correlation coefficients of −0.30 and −0.07, respectively). Seasonal Spearman’s rank correlation coefficients are shown in Table 21 of the supplementary materials. Further, a sensitivity analysis on input parameters for determining RET is included in the supplementary materials.

Table 12 –

Spearman’s rank correlation coefficients between micrometeorological parameters and RET (mm/day), significant at the 0.01 level

	Rsin (W/m2)	T (°C)	RH (%)	u2 (m/s)
Bio-C	0.913	0.705	−0.394	−0.048
GR-C	0.940	0.795	−0.256	0.000
GR-F	0.931	0.753	−0.279	−0.251
Air-JFK	0.921	0.690	−0.342	0.107
Air-LG	0.934	0.743	−0.328	0.018
GR-QBG	0.939	0.774	−0.226	−0.260

4.3. Objective (iii) - Develop methods for adapting offsite micrometeorological data sets to different urban conditions

Development of K_m and ${\text{K}}_{{\text{m}}_{\text{p}}}$

Monthly microclimate coefficients (K_m, here listed as $K_{m_{RET}}$ for distinction from $K_{m_p}$) and parameter specific microclimate coefficients ($k_{m_p}$) are presented in Figure 5. In the supplementary materials, Figure 15 shows plots of each data set, RET, R_sin, T, RH and u₂, for all sites relative to the reference site (Air-LG).

Figure 5 –

Average microclimate coefficients by month relative to reference site (Air-LG) with 5^th and 95^th percentiles

Validation

Charts of predicted vs. observed RET, R_sin, T, RH and u₂ for the microclimate coefficient validation periods are shown in Figure 7 through Figure 11, respectively. Figure 6 presents the root mean square error (RMSE), mean absolute error (MAE) and mean bias error (MBE) between observed and predicted RET, Rsin, T, RH and u_2. Application of microclimate coefficients reduced the RMSE in daily observed vs. predicted RET at the sites from 0.7–1.1 mm/day to 0.3–0.5 mm/day and MBE (mean bias error) from −0.92 through −0.12 to −0.19 through 0.09 mm/day. Further, the error in cumulative annual RET was reduced from a maximum of 40% to a maximum of 9%.

Figure 7 –

Predicted vs. observed RET, Rsin, T, RH and u₂ for Bio-C

Figure 11 –

Predicted vs. observed RET, Rsin, T, RH and u₂ for GR-QBG

Figure 6 –

RMSE, MAE and MBE between observed and predicted RET, Rsin, T, RH and u₂ (grey and black bars indicate before and after application of microclimate coefficients respectively)

5. Discussion

5.1. Objective (i) - Evaluate the spatial variability of micrometeorological conditions and estimated RET rates

Our findings suggest that spatial variability in micrometeorological conditions (specifically $R_{S_{in}}$, T, RH and u₂) across heterogeneous urban environments is significant, and that the variability in micrometeorological conditions impacts spatial variability in site scale reference evapotranspiration. Al-Kofahi, VanLeeuwen et al. (2012) also showed that RET varied across an urban area, specifically Albuquerque, NM (USA). Here, we explore the relationship between RET, $R_{S_{in}}$, T, RH and u₂ for NYC, NY (USA) highlighting the complex relationship between meteorological variability and variability in RET. Notably, for the two thirds of site to site comparisons that showed statistically significant differences in RET, the micrometeorological parameters differed significantly with respect to various sets of parameters (e.g. RH and u₂, T and u₂; R_sin, T, RH, and u₂; etc.).

Wind speed showed the greatest variability across sites with statistically significant differences between all site to site comparisons. We highlight here that, with average ratios of two meter wind speed between Bio-C, GR-C, GR-F, GR-QBG and Air-LG ranging from 0.25 to 0.67 and Air-JFK to Air-LG of 1.08 (Table 12), wind speed at all interior urban green spaces (Bio-C, GR-C, GR-F and GR-QBG) was considerably lower than at the airport sites (Air-JFK and Air-LG). This observation is consistent with findings reported in an analysis of 652 stations across the monsoon regions of China, which found that urban stations generally observed lower wind speeds than rural stations (Guo, Xu et al. 2011). These findings are also consistent with studies which identified decreasing wind speed trends with urbanization in Madrid, Valencia, and Alicante (Spain) (Azorin-Molina, Vicente-Serrano et al. 2014) and Beijing (China) (Li, Yan et al. 2011). Lower wind speeds in urban areas are largely expected based on urban frictional effects (Oke 1988, McVicar, Van Niel et al. 2007). Yet, common practice dictates the use of regional weather stations, commonly located in open areas at airports, to represent interior urban spaces.

The variability of meteorological data sets across sites and particularly between airport and interior urban spaces emphasizes the need for methods to adequately represent actual urban site meteorological conditions (especially for sites without in-situ measurements), and particularly in evaluating ET. The use of regional weather stations, typically located at airports, for the estimation of urban site-scale reference evapotranspiration could introduce substantial errors due to micrometeorological variability. Over the 327-day period we analyzed, cumulative RET (Figure 4) was 40.2% greater at Air-LG (reference airport site) than at GR-QBG, suggesting that, among NYC sites, errors on the magnitude of 40% in cumulative annual RET estimates could be introduced by not considering the local microclimate of individual sites. This finding is significant considering the common practice of using data sets from regional climate stations (usually airports) to estimate ET in a variety of water resource studies. Jacobs, Elbers et al. (2015) also highlighted from their evaluation of micrometeorological and evapotranspiration observations in Dutch cities that, “estimation of urban evaporation from routine weather data using the concept of reference evaporation would be a particularly challenging task…[as] the urban fabric results in strong microweather variability.”

Furthermore, should methods of adapting airport data sets to interior urban spaces not be available or employable, our findings indicate that the use of distributed networks of weather stations in urban areas (as opposed to airport and other generally “well-exposed” sites), like NWS cooperative observers (http://www.nws.noaa.gov/om/coop/recent-obs.htm) or local networks like NYCMetNet (http://nycmetnet.ccny.cuny.edu/), may be more appropriate for evaluations in heterogeneous urban landscapes. It would be of utmost importance, however, to identify weather stations similar, and in close proximity to, desired site conditions and carefully consider the quality and applicability of data sets obtained from alternative stations.

5.2. Objective (ii) - Determine the relative role of micrometeorological conditions in influencing RET rates

Our study underlines the importance of RH and u₂ in influencing evapotranspiration, as the magnitude of variation in RH and u₂ (though both weakly correlated to RET) can impact the overall variability of RET between urban sites. R_sin and T were the strongest drivers in the determination of RET in our study. Sun, Wang et al. (2013) take incoming solar radiation and surface temperature as the “control parameters” of the surface energy balance, of which the latent heat flux (evapotranspiration) is one component. We identified that even sites with no statistically significant differences in R_sin and T could have statistically significant differences in RET due to the magnitude of variation in other determinants of RET, specifically RH and u₂. Interestingly, differences in parameters with strong correlation to RET did not always correspond to differences in RET (Bio-C and GR-C, Bio-C and GR-F, GR-C and GR-F). Micrometeorological parameters that displayed the strongest correlation to RET on an annual basis, namely R_sin and T (Table 12), varied least amongst the sites and those with weak correlation, RH and u₂, varied the most. Though RH and u₂ demonstrated the weakest correlation to RET (with u₂ showing the most variability), the magnitude of the differences between some sites (three (3) of ten (10) site to site comparisons that had differences in RET, specifically Bio-C and Air-JFK; Bio-C and Air-LG; Bio-C and GR-QBG) was enough to account for statistically significant differences in RET data sets. In these instances, the average annual ratios of onsite wind speed at two meters in comparison to Air-LG, were 0.67 and 1.08, 0.67 and 1.00 and 0.67 and 0.25, respectively (Figure 5). The average annual ratios of onsite relative humidity in comparison to Air-LG, were 1.15 and 1.09, 1.15 and 1.00 and 1.15 and 1.22, respectively (Figure 5). Further, Spearman’s rho correlation coefficients, shown in Table 12, indicate a stronger correlation between RH and RET on a seasonal basis than T and RET, which is stronger on an annual basis. This may result from higher variation in RH on a seasonal basis compared to T.

Donohue, McVicar et al. (2010) also highlight the importance of wind speed in determining the dynamics of Penman potential evaporation. Analyzing data across Australia between 1981 and 2006, Donohue, McVicar et al. (2010) showed, through an attribution analysis, that air temperature, wind speed measured at two meters height, net radiation and vapor pressure, respectively, where the most important factors in influencing overall Penman evaporation trends. While air temperature had the strongest attribution and a positive trend, negative trends in other variables, particularly wind speed, were of great enough magnitude to create overall negative trends in Penman evaporation. Additionally, a review of over 30 papers from various regions across the world evaluating the relative contributions of the four primary meteorological determinants of evapotranspiration found that, “wind speed is commonly in the top two most dominate variables influencing evaporative trends,” and that, “in most instances the evaporative demand due to stilling is larger than the evaporative increase due to warming. (McVicar, Roderick et al. 2012)”

Of particular interest from our study is the correlation between u₂ and RET. Based on the relationship between u₂ and RET, it was expected that these two variables would be directly (positively) correlated at all sites. However, while at the airport locations the correlation was indeed direct and positive (Table 12), at the interior urban green spaces the wind speed sometimes had a negative correlation to RET (Table 21). This finding suggests that the interior urban green spaces are influenced by conditions that are not consistent with typical trends, perhaps due to impacts of the surrounding and built environment. For example, the transport of air with higher relative humidity from surrounding vegetated areas to urban green spaces could adversely impact the evaporative capacity of the engineered urban green space. Kuang, Dou et al. (2015) concluded that the ability of urban green spaces to provide cooling benefits decreases with increased green space coverage. Wind direction and urban green space proximity to other “wet” surfaces may be important as vapor may be transported, somewhat analogously to atmospheric rivers (Ralph and Dettinger 2011). As augmentation of urban green spaces is being adopted in cities across the world as a means for climate change adaptation and mitigation, further understanding of evapotranspiration will be required for effective planning. Using the Local-scale Urban Meteorological Parameterization Scheme (LUMPS) to model ET, Middel, Brazel et al. (2012) concluded that under different climates, land cover strategies will have variable impacts on surface energy balances (SEB).

5.3. Objective (iii) - Develop methods for adapting offsite micrometeorological data sets to different urban conditions

The development of microclimate coefficients in our study advances the work of Costello and Jones (1994) by providing quantitatively based values for microclimate coefficients. Further, monthly coefficient values are defined and parameter specific microclimate coefficients proposed, developed and validated.

Applicability of the linear-scaling approach used in our paper, i.e. application of microclimate coefficients, is evaluated for one-year validation periods for each of the five sites and also by analyzing the variability in coefficients during different months. For all interior urban spaces (Bio-C, GR-C, GR-F and GR-QBG) the application of microclimate coefficients to reference site (Air-LG) data improved the prediction of observed local site data (Figure 7, Figure 8, Figure 9, Figure 11) for all parameters. For example, with application of microclimate coefficients, the RMSE of daily RET over the annual basis was reduced to 0.5 mm/day or less for all sites, and, furthermore, MBE also improved for all parameters. Further improvement in the prediction of local site RET may be possible if using adjusted microclimate coefficients to solve for RET, though, given the already very good performance, this was not evaluated in our study.

Figure 8 –

Predicted vs. observed RET, Rsin, T, RH and u₂ for GR-C

Figure 9 –

Predicted vs. observed RET, Rsin, T, RH and u₂ for GR-F

While it is recognized that synoptic vs. mesoscale conditions may impact the applicability of the linear-scaling approach used in our paper, e.g. a passing cloud on the local-scale exerting a “perturbation” on incoming solar radiation (Gentine, Entekhabi et al. 2011), we do not distinguish between the impacts of synoptic vs. mesoscale events, as, with the time-scale analyzed in our study (daily data over a roughly one-year period), the impacts do not seem relevant. Here our data are averaged over a day so perhaps these impacts would be more relevant at shorter time steps e.g. one (1) hr but over daily periods momentary perturbations seem generally masked in daily averages. Were the impacts of synoptic vs. mesoscale conditions to be relevant on the daily time-scale, it would be expected that there would be notably more variability in daily coefficients during months when mesoscale conditions are more likely, but this was not the case. For NYC, synoptic systems are more likely during the months of November through April and mesoscale events more likely from May through October (Bader 2017). However, there appears to be no more variability in coefficient values, by inspection of the 5^th to 95^th percentile range in Figure 5, during May – Oct than during Nov – April for RET, $R_{S_{in}}$, RH or u₂. Temperature has substantially more variability during the months of Dec-Feb than other months. However, this is a result of temperature values being expressed in °C with values near, above and below zero possible. Thus, small differences in temperature could result in large or even negative values of temperature microclimate coefficients. It is suggested that future development of temperature based microclimate coefficients be based on absolute temperature scales e.g. Kelvin or Rankine, to avoid such issues. We do acknowledge areas for future work in the analysis of the applicability of the linear-scaling approach at shorter timescales and also further evaluation of the linearity of wind speed, which at high daily average wind speeds seems to deviate from the microclimate coefficient relationship.

We acknowledge the question of applicability of the microclimate coefficient approach to urban environments without in-situ measurements. In future work, we propose pairing microclimate coefficients with Local Climate Zones (LCZs) such that a site could be classified by LCZ and microclimate coefficients associated with that LCZ applied to the site. Combined application of microclimate coefficients (K_m), parameter specific microclimate coefficients ($K_{m_p}$) and LCZ presents an opportunity for the systematic classification of city structure, micrometeorological and evaporative zones, and presents a clear application for the use of aerial and 3-D imagery (Burian, Brown et al. 2006) as well as GIS. With a larger data set and number of sites than found in this study, it would be possible to evaluate the applicability of standardized parameter specific microclimate coefficients on a regional basis (e.g. for a particular city) dependent on local climate zones (LCZ) defined by Stewart and Oke (2012). Though Stewart and Oke (2012) defined LCZ for temperature and urban heat island studies based on local urban infrastructure and configuration, it is possible that these zones present similarities applicable to other microclimate parameters as well, which is supported by the results of our study. Both airport locations (Air-JFK and Air-LG classified as LCZ D Low plants) showed no statistical differences between RET, $R_{S_{in}}$, or T between sites and ${\text{K}}_{\text{m}}/K_{m_p}$ values close to one for all parameters (range of averages 0.94 to 1.09). Another challenge that exists and should be addressed in future work is the classification of LCZ for building rooftops particularly considering green roof installations. With representative data from LCZ in cities coupled with the development of localized parameter specific microclimate coefficients or other methods, vast advances would be made related to urban climate and urban water resource studies. Furthermore, the proposed parameter specific microclimate coefficients ($K_{m_p}$) provide flexibility in the application of different data sets e.g. downscaling of satellite ET products, transformation of ET estimates determined using various methods from site to site, urban heat island and climate change studies, etc.

6. Conclusion

The objectives of this paper are, using novel urban weather station data sets from a heterogeneous urban environment (New York City), to (i) evaluate the spatial variability of micrometeorological conditions, measured at the site scale, and estimated RET rates; (ii) determine the relative role of incoming solar radiation, temperature, relative humidity and wind speed in influencing reference evapotranspiration (RET) rates at the site scale; and (iii) develop methods for adapting offsite micrometeorological and ET data sets to different urban conditions. Daily data sets of micrometeorological determinants of ET, specifically incoming solar radiation (R_sin), air temperature (T), relative humidity (RH) and wind speed adjusted to two meters height (u₂), as well as RET rates were compared over a one year period collected from six sites located throughout New York City. The six monitoring sites include urban green spaces and airport sites. Micrometeorological data sets acquired for analyses from the six monitoring sites were used as inputs for estimation of daily RET rates by the ASCE Standardized Reference Evapotranspiration Equation (ASCE-EWRI 2005) for short (grass) reference surfaces. Cumulative RET was evaluated over the period of analysis. Statistical tests including non46 parametric Kruskal-Wallis test and Spearman’s Rho correlation coefficients were utilized for comparative and correlative analyses. Non-parametric Kruskal-Wallis analyses were used for statistical comparison of data sets of micrometeorological determinants of ET and RET rates across sites. Non-parametric Spearman’s rho correlation coefficients were evaluated between data sets of micrometeorological parameters and RET rates to assess the relative role of each in influencing RET rates at the sites. The development of parameter specific microclimate coefficients $(K_{m_p})$ for the adjustment of offsite data sets to local conditions for individual micrometeorological parameters was demonstrated. Furthermore, the pairing of $K_{m_p}$ with local climate zones, defined by Stewart and Oke (2012), is proposed.

Our findings suggest that micrometeorological variability across heterogeneous spaces, particularly urban environments, is substantial and needs to be considered in evaluating ET rates, particularly in urban water and energy modelling (Oke 1972; Eching and Snyder 2005; Gobel and Bazel 2012).

Micrometeorological variation across cities is an important factor in consideration of urban evapotranspiration and latent heat fluxes, for example, in evaluating ecosystem good and services offered by urban green spaces (Wadzuk, Schneider et al. 2013) changes in land use over time (Järvi, Grimmond et al. 2011), climate change mitigation/adaption strategies (Masson, Marchadier et al. 2014, Groot, Bosch et al. 2015) and the impact of climate change on engineered urban green space vegetation (Maria Raquel, Montalto et al. 2016).

The findings presented in this paper based on data sets collected at six monitored locations across New York City include:

• Over a 327-day non-consecutive period, cumulative RET was up to 40 percent greater in comparison between sites.

• Micrometeorological conditions (R_sin, T, RH and u₂) and daily RET rates were statistically significantly different across sites when all sites were compared together.

• All site wind speed at two meters were statistically significantly different from other sites based on site by site comparisons.

• Differences in micrometeorological data sets between sites resulted in statistically significant differences in RET rates between the majority, but not all, sites based on site by site comparisons.

• R_sin and T have the strongest correlation to RET (on average 0.93 and 0.74 respectively) and varied least across sites (7 of 15 site to site comparisons and 5 of 15 site to site comparisons showed statistically significant differences) while RH and u₂ had the weakest correlation to RET (on average −0.30 and −0.07 respectively) and showed the greatest variation amongst sites (10 of 15 and 15 of 15 site to site comparisons showed statistically significant differences respectively).

• Microclimate coefficients (K_m) and parameter specific microclimate coefficients $(K_{m_p})$ were proposed, developed and validated from daily-data sets. Use of these coefficients at shorter time-scale should be considered cautiously, as e.g. a passing cloud could greatly impact site conditions, and the exploration of non-linear scaling techniques should be considered for future work.

Building on the recommendations of others (Costello and Jones 1994, Eching and Snyder 2005), new parameter specific microclimate coefficients ($K_{m_p}$), ranging from, an average of, 0.25 to 1.22 for the studied sites over the study period, were developed for the adjustment of offsite data sets to local conditions. There is clear potential for the pairing of these parameter specific microclimate coefficients with local climate zones (LCZ) defined by Stewart and Oke (2012). We acknowledge that such paired coefficients could be an interim for representing variability across urban environments, and adapting data from e.g. local airports to urban sites without meteorological measurements, and would require a large data set over a range of climatic conditions to develop. Evaluation of long-term data sets of urban micrometeorological conditions and urban ET with representation from more sites and site types would lend further insights as is highlighted in the publication by Vicente-Serrano, Azorin-Molina et al. (2014). Data collection from the new urban green space monitoring sites in our study are ongoing.

7. Future Work

Our paper focused on the relationship between micrometeorological conditions and RET in a heterogeneous urban environment and supports that micrometeorological variation across heterogeneous urban environments is an important factor in evaluating urban ET rates. A growing body of work (Kotthaus and Grimmond 2014, Vicente-Serrano, Azorin-Molina et al. 2014, Jacobs, Elbers et al. 2015, van Hove, Jacobs et al. 2015) focuses attention on the variability of micrometeorological conditions across urban areas and recommends further research in this area. Consideration should also be given to the influence of non-micrometeorological determinants, e.g. vegetation type, media/soil type, moisture conditions and anthropogenic heat fluxes (Oke 1982), on urban ET rates. As seen in the supplementary materials, the sensitivity of RET in urban green spaces to vegetation dependent parameters (specifically C_n and C_d in the ASCE standardized reference evapotranspiration equation) can be at least as important as that of meteorological parameters.

Figure 10 –

Predicted vs. observed RET, Rsin, T, RH and u₂ for Air-JFK

Table 13 –

Average microclimate (K_m) and parameter specific microclimate coefficients (K_mp) with airport (Air-LG) reference site

Site	$K_{m_{RET}}$	$K_{m_{R_{sin}}}$	$K_{m_T}$	$K_{m_{RH}}$	$K_{m_{u_2}}$
Bio-C	0.75	1.06	0.94	1.15	0.67
GR-C	0.80	0.96	1.25	1.15	0.41
GR-F	0.72	1.22	0.95	1.24	0.46
Air-JFK	0.94	1.01	0.96	1.09	1.08
GR-QBG	0.67	1.12	1.01	1.22	0.25

Highlights.

• Micrometeorological conditions (R_sin, T, RH and u₂) monitored at six sites in NYC

• Reference evapotranspiration (RET) estimated for airport & urban green space sites

• Spatial variability of micrometeorological conditions and RET evaluated

• R_sin, T, RH, u₂ and RET statistically significantly different across sites

• Methods for adjusting data from collection site to local conditions explored