• urban parametrization schemes;
  • urban energy balance;
  • urban canopy models;
  • model evaluation;
  • sensitivity analysis;
  • parameter optimization


  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

For an increasing number of applications, mesoscale modelling systems now aim to better represent urban areas. The complexity of processes resolved by urban parametrization schemes varies with the application. The concept of fitness-for-purpose is therefore critical for both the choice of parametrizations and the way in which the scheme should be evaluated. A systematic and objective model response analysis procedure (Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm) is used to assess the fitness of the single-layer urban canopy parametrization implemented in the Weather Research and Forecasting (WRF) model. The scheme is evaluated regarding its ability to simulate observed surface energy fluxes and the sensitivity to input parameters. Recent amendments are described, focussing on features which improve its applicability to numerical weather prediction, such as a reduced and physically more meaningful list of input parameters. The study shows a high sensitivity of the scheme to parameters characterizing roof properties in contrast to a low response to road-related ones. Problems in partitioning of energy between turbulent sensible and latent heat fluxes are also emphasized. Some initial guidelines to prioritize efforts to obtain urban land-cover class characteristics in WRF are provided. Copyright © 2010 Royal Meteorological Society and Crown Copyright.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

With the ever-increasing computer resources available, complex mesoscale modelling systems able to simulate both the dynamics of the atmospheric flow and the main physical processes associated with it have flourished. The scale, resolution, and the type of processes they should be able to parametrize are determined by their application. A common feature in recent years, however, has been the realization that a better representation of urbanized areas is required. Given current resolutions, Numerical Weather Prediction (NWP), Air Quality Forecasting (AQF) and even Global Climate Models (GCM) now require an adequate parametrization of urban-atmosphere exchange (of heat, moisture, momentum or pollutants). This concern has been highlighted by recent efforts to include a separate representation of urban surfaces in operational NWP models (e.g. Taha, 1999; Masson, 2000; Chen et al, 2004; Best, 2005) or more recently in GCMs (Oleson et al, 2008a). Modelling systems designed for decision-making purposes (e.g. urban planning or climate-change mitigation strategies) or emergency response (e.g. toxic gas release from industrial leakage or terrorist activities, industrial fires) have further needs in terms of the physical processes to be modelled by an urban parametrization scheme (Baklanov et al, 2009).

The choice of scheme to include in a particular modelling system needs to be based on the targeted application; the methods and criteria to use for its evaluation should also be selected accordingly. The ‘fitness-for-purpose’ guidance presented by Baklanov et al(2009) illustrates such a concern and a number of application-dependent components to consider in model evaluation can be linked to that concept:

  • Firstly, there is consideration of the requirements of the model. The type and amount of input information on which the parametrization is based should enable a representation of the urban canopy features relevant for the application and yet be consistent with the data realistically procurable at the scale resolved. A similar compromise arises between the level of detail with which processes should be modelled (numerical resolution, scale of processes parametrized) and the cost in computing time.

  • Secondly, there is assessment of how the model performs relative to the changes in parameter values. In order to accurately represent the diversity of constraints that urban environments impose on the atmospheric flow, a significant model response to changes in its input is desirable. However, the degree of sensitivity to a particular input should be linked to the level of uncertainty inherent to its estimation at the grid scale: excessive sensitivity is to be avoided when input parameter values are not procurable with a matching accuracy.

  • Thirdly, there is performance of the model as compared to observations. To ensure that the evaluation procedure is relevant to the targeted application, measurement campaigns should be specifically designed to collect observations at a scale similar to the one resolved, while on the other hand model simulations need to be set up to reproduce the conditions during the campaign. Similarly, only an application-dependent set of statistics can provide an objective picture of the model's performance.

In this study, focus is given to the land surface and urban parametrization schemes in the Weather Research and Forecasting (WRF) model designed for NWP purposes. Their primary function is to simulate outgoing energy fluxes which act as lower boundary conditions for a parent atmospheric model. Hence, estimation of the surface energy balance in each grid cell classified as urban arises as a main requirement. The surface energy balance (SEB) as introduced by Oke (1978) and restated more fully by Offerle et al(2005, 2006) provides the adequate framework in which to evaluate the scheme's performance:

  • equation image

Q* is the net all-wave radiation which combines the net short-wave (K*) and net long-wave (L*) contributions both resulting from a balance between their incoming (K[DOWNWARDS ARROW], L[DOWNWARDS ARROW]) and outgoing (K[UPWARDS ARROW], L[UPWARDS ARROW]) components:

  • equation image

QF is the anthropogenic heat flux, QH turbulent sensible heat flux, QE turbulent latent heat flux and ΔQS net storage heat flux. The net horizontal advection flux ΔQA is usually dealt with by three-dimensional (3-D) models rather than land surface schemes which typically represent a single column of atmosphere. When integrated as part of an NWP modelling system, the horizontal dimension of such a column corresponds to a grid cell while its vertical extent is defined by the height of the first atmospheric level. Being explicitly resolved by the parent atmospheric model, advection is therefore only represented above the column. The S term accounts for all other possible sources and sinks of energy, including for instance heat removed by rainfall runoff or photosynthetic heat (Offerle et al, 2006). Currently, these are not usually modelled within urban parametrization schemes designed for NWP purposes and are by definition not measured.

The ability of such schemes to account for the large energy storage in the urban fabric, the trapping of incoming radiation in street canyons and the enhancement of turbulent processes due to an increased urban roughness represents the main challenge. Although no ideal approach has yet been objectively identified (Grimmond et al, 2010), three categories can be listed (Masson, 2006): (1) empirical models reproducing measured features of the urban energy balance using statistical approaches, (2) Land Surface Models (LSM) initially developed for vegetated surfaces and modified to account for the specificities of urban environments, and (3) Urban Canopy Models (UCM) which represent the next level of complexity and take into account the urban morphology. A further subdivision of categories (2) and (3) is introduced with regards to whether the schemes simulate the vertical stress distribution inside the urban canopy to account for a momentum drag on the atmospheric flow (multi-layer schemes, e.g. Martilli et al, 2002).

Designed for mesoscale forecasting purposes, the level of detail which can be modelled by such schemes is by nature restricted: running time and consequently grid resolution have limits dictated by the need to produce a forecast in time. A scheme fit for NWP purpose would hence describe the urban morphology, roughness, radiative and thermal properties with a set of parameters meaningful at the scale of a model grid box. Ideally, the set of understandable inputs should be kept small and procurable from a systematic procedure (e.g. geographic information database, remote sensing or image processing techniques). The response of the scheme to parameter changes needs to be coherent with the accuracy of their estimation, especially when default land-cover classes are used to characterize the urban grid cells in the modelled domain.

Evaluating the performance and sensitivity of urban parametrization schemes as part of a complete NWP modelling system is a complex task due to both the limited control available on the fields directly forcing the scheme and possible error compensation phenomena occurring between the different components of the system. For instance, the NWP model bias in surface radiation fluxes would directly impact our assessment of how well the urban parametrization is able to represent the SEB. As a consequence, thorough studies of model performance and sensitivity are best performed with a decoupled or ‘offline’ version of the scheme where the parent atmospheric model is removed (Masson et al, 2002). This does not permit any assessment of the importance of advection nor of potential interactions occurring between neighbouring cells but ensures that the scheme is evaluated on its own.

Observations of the forcing fields (K[DOWNWARDS ARROW], L[DOWNWARDS ARROW] plus common meteorological fields) at a height above the roughness sub-layer (Roth, 2000) are provided as a substitute to the parent atmospheric model's outputs. Measurements of the surface energy balance fluxes at a scale compatible with that of a grid box (e.g. the local or neighbourhood scale as defined in Grimmond and Oke (2002)) are also needed to enable a direct evaluation of the scheme's outgoing fluxes, along with an extensive survey of input parameter values characterizing the footprint area of the measurements (Grimmond, 2006).

In this paper, we introduce an objective and systematic procedure to evaluate model response using the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm of Vrugt et al(2003). The methodology is applied to the single-layer urban canopy parametrization (Kusaka et al, 2001) implemented in the WRF model (Skamarock et al, 2005), using hourly data from a measurement campaign in Marseille (Grimmond et al, 2004; Lemonsu et al, 2004). The applicability for NWP purposes of the main parametrizations implemented as part of the scheme is assessed, and some modifications are introduced where needed. It is anticipated that these amendments will be suitable for other applications; for example, providing the meteorological conditions for air quality forecasting. The scheme performance is analysed in terms of the quality of the surface energy balance flux simulations, and the utility of the model response analysis method as a tool providing guidelines for the refinement of WRF land-cover classes is underlined.

2. Systematic and objective model response analysis using the MOSCEM algorithm

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

When trying to quantify the sensitivity to input parameter values, offline models are run iteratively usually, perturbing a set of selected parameters at each step (Sellers and Dorman, 1987; Arnfield and Grimmond, 1998; Kawai et al, 2007; Oleson et al, 2008b). The impact on the model's outputs, often illustrated by statistical measures comparing simulated and observed fields, is then seen as an indicator of how the model responds to a particular parameter change. Designed for the automatic calibration of hydrological models, the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm of Vrugt et al(2003) provides a systematic and unbiased tool for such a purpose. Of particular interest is its ability to: (1) objectively sample the entire parameter space rather than a discrete predefined set of values, and (2) optimize with respect to several criteria (multi-objective optimization), thereby providing some insight into the trade-offs which control the modelled SEB (multi-objective optimization identifies situations where improving one criteria is possible only at the expense of another: Gupta et al, 1998; Khu and Madsen, 2005; Confesor and Whittaker, 2007; Shafii and De Smedt, 2009). The trade-off surfaces, composed of all parameter values leading to an optimum compromise in the performance of the modelled fluxes, are referred to as Pareto fronts to highlight the non-uniqueness of the solution (Yapo et al, 1998). They are approximated by MOSCEM using a Markov Chain Monte Carlo sampler, designed to avoid the grouping of the solution in a subspace of the Pareto front, and deal with the strong correlation between parameters which typically occurs in land surface models (Vrugt et al, 2003).

The algorithm iteratively updates a set of model input parameters while minimizing several optimization criteria (objective functions) which here are the Root Mean Square Errors (RMSE) for Q*, QH and QE. The set-up of a MOSCEM run requires each parameter to be given a default value and limits between which it can evolve. To be as objective as possible, wide ranges that are physically meaningful should be specified. This will increase the convergence time of the algorithm, but ensures that the model response to any type of value change is accounted for. Default values should be objectively determined in an attempt to reproduce the conditions in which the evaluation and forcing data were measured.

For a comprehensive analysis of the model response, only one parameter is optimized at a time while all others are kept at their default values. MOSCEM then randomly initializes s samples (s different sets of parameter values spread out in the parameter space) and iteratively updates their values towards s optimized samples minimizing the RMSE of the fluxes (details of the algorithm are provided in Vrugt et al(2003)). For some of the parameters only a Pareto set of solutions emerges, showing that no optimum state can be objectively identified. Others provide an optimum value for which all fluxes reach their minimum RMSE (see Figure 6, panels 1 and 4, for illustration of the two behaviours when only two fluxes are considered). For the latter, a measure of the model response to the parameter optimized can be derived when subtracting the RMSE from a default run of the model (all parameters being set to their default) to the one obtained with the optimized value. Ideally, the resulting ΔRMSE would be negative for all fluxes, indicating an improvement of all objectives. For parameters triggering some trade-offs, at least one of the ΔRMSE will stay positive for any value change along the Pareto front. It is possible to assess the model response for a particular flux by selecting the value leading to the best improvement for this flux (lowest ΔRMSE). The trade-off effects are measurable from the impact a value change along the Pareto front has on the RMSE. Like all sensitivity analyses, the procedure is a function of what is chosen as default. In the unlikely situation of a near-zero RMSE, the responsiveness would appear difficult to analyse.

This procedure is designed to analyse how the model behaves with regards to a change in one of its inputs and does not intend to identify the optimum values of all model parameters leading to the best or minimum RMSE. Calibration of the scheme for a particular site would require an optimization of all parameters simultaneously, hence complicating our understanding of each parameter's influence. The use of MOSCEM to perform such a multi-parameter optimization would however provide an efficient method to derive the default values for urban land-cover classes, and will be considered for future studies.

Repeating the procedure for all parameters, an objective model-sensitivity-ranking can be obtained in terms of the RMSE improvements (ΔRMSE < 0 W m−2) for each of the fluxes considered (Q*, QH and QE). Such a ranking is to be accompanied by a trade-off effect ranking (ΔRMSE > 0 W m−2) for all parameters leading to a Pareto front of solutions. This procedure (Figure 1), presents how the model responds to any parameter change and therefore provides a very powerful tool to: (1) identify the parameters to which the modelling of each flux is most sensitive, (2) sort out the ones which do not significantly affect the model performance, and (3) highlight potential trade-offs in the modelling of the SEB. From such knowledge, urban parametrization schemes can be adapted to better fit NWP requirements. Figure 2 summarizes the procedure applied to the Single-Layer Urban Canopy Model implemented in WRF (SLUCM: Kusaka et al, 2001; Chen et al, 2010).

thumbnail image

Figure 1. Flow chart of the model response analysis using the MOSCEM algorithm.

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Figure 2. Flow chart of the procedure applied to improve the applicability of the Noah/SLUCM.

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3. The single-layer urban canopy model in WRF

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

The single-layer urban canopy parametrization in WRF results from a coupling between the Noah land surface model (Chen and Dudhia, 2001) and the Single Layer Urban Canopy Model (Kusaka et al, 2001; Kusaka and Kimura, 2004) using a tile approach. This prevents any interaction between the two components, since each scheme is run separately and their output fluxes are weighted according to the relative portion of the grid cell considered urbanized (furb):

  • equation image

where QGRID is the grid-averaged value of an outgoing flux (K[UPWARDS ARROW], L[UPWARDS ARROW], Q*, QH or QE), QSLUCM and QNoah refer to the scheme's modelled fluxes.

First introduced in WRF v2.2 (June 2006), the SLUCM was initially implemented with the same set of parametrizations as formulated by Kusaka and Kimura (2004). Table I summarizes the main input requirements of this on-line version of the scheme along with the key terms they impact. Ambiguities arise as to how many of the required site parameters should be specified. For example, a user planning to refine the default WRF parameter values for a particular site would be left to estimate the normalized canyon height (Znorm) and width (Cnorm), the normalized roof width (Rnorm), the drag coefficient by building (CDB), their volumetric parameter (BV) or the roughness lengths (for heat and momentum) of roof surfaces and the canyon space (Z0R, Z0HR, Z0C, Z0HC). In addition, without care it is also possible to change individual parameters values without appropriately changing others (e.g. canyon roughness length independent from its geometry). In an attempt to: (1) clarify the physical meaning of input parameters, (2) add consistency between the various parametrizations involved, and (3) take into account the complexity of parameter estimation at the scale of a model grid box, several modifications were made to this initial version (Table II). Some of these changes have already been implemented in WRF v3.1 (March 2009), all others are planned for next release (v3.2, 2010).

Table I. Key parameters required by the SLUCM in its original online version (WRF v2.2).
SLUCM parameters in WRF v2.2Main parametrization in which they are involvedDefinition of symbols
Normalized roof height: ZnormView factors:Φwall[RIGHTWARDS ARROW]sky, Φroad[RIGHTWARDS ARROW]sky, Φwall[RIGHTWARDS ARROW]road, Φwall[RIGHTWARDS ARROW]wall:
Normalized roof width: Rnorm wall to sky, road to sky, wall to road and wall to wall view factors.
Normalized canyon width: Cnorm N: iteration limit (N = 100)
 equation imagedz = Znorm/(N + 1): integration step when moving down the wall
 equation image 
 equation image 
 equation image 
 equation image 
 Partitioning of SLUCM fluxes: 
 equation imageQSLUCM, Qroof, Qwalls, Qroad: generic notation for any of the outgoing fluxes from the SLUCM, the roof, the walls or the road.
Canyon roughness length for heat and momentum: Z0C, Z0HCDerivation of canyon/air exchange coefficients for heat and moisture:CH, CE: turbulent exchange coefficients for heat and moisture
 equation imageκ: von Kármán's constant.
Canyon zero plane displacement height: ZDequation imageΨm, Ψh: integrated universal functions for momentum and heat
 equation imageφm, φh: non-dimensional gradients for momentum and heat
  ZA: first atmospheric level (forcing level).
 φm, φh: Dyer and Hicks (1970) in unstable conditions (equation image), and Kondo et al(1978) in stable conditions (equation image).L: Obukhov length
Roof roughness length for heat and momentum: Z0R, Z0HRDerivation of roof/air exchange coefficients for heat and moisture:As above
 equation image 
Mean roof height: ZRWind profile:UC: wind velocity at level ZC = 0.7ZR inside the canyon.
Drag coefficient by building: CDBequation imageUA: wind velocity at forcing level (ZA), UR: at roof level (ZR).
Building volumetric capacity: BV a: attenuation coefficient (Inoue, 1963)
 equation imagelm: mixing length
Table II. Changes made to the WRF/SLUCM
Modification/ImplicationDescriptionDefinition of symbols
  • emdash were included in WRF release v3.1.

Canyon height, width and roof width are read as inputInput:ZR, Wroad and Wroof (m)ZR: roof height
  Wroad: road width
Canyon geometry inputs now with a clear physical meaning. Wroof: roof width (Figure 3)
Normalized ratios are derived from canyon geometry equation imageFwalls, Froof and Froad: normalized fraction of canyon surfaces covered by walls, roof and road.
 equation image 
 equation image 
 equation image 
Ratios Znorm, Rnorm, Cnorm are removed from list of inputs.  
Canyon roughness from MacDonald et al(1998)equation imageλP, λF: building's plan area fraction and frontal area index.
 equation image 
Canyon roughness is linked to its geometry. Cd: drag coefficient (Cd = 1.2).
Z0C and ZD are removed from the list of inputs.equation imageκ: von Kármán's constant (κ = 0.4).
  αm, βm: empirical coefficients (αm = 4.43, βm = 1.0).
Roof roughness (Z0R) parameterized using the standard deviation of building height (σZ). σZ: standard deviation of building height
 equation image 
 equation image 
  σZmin: minimum value for σZ (currently set to 1 m)
Z0R is removed from the list of inputs, σZ is introduced instead. λF, σ: modified frontal area index based on σZ.
Attenuation coefficient in wind profile as a function of known quantities only  
CDB and BV are removed from the list of inputs.equation imageSee Table I
Change of non-dimensional functions in the SLUCM for stable conditions: Paulson (1970) formulations are now implemented as in Noah (Chen et al, 1997)equation imageSee Table I
Same turbulence routine now used in both schemes.equation image 
Ratios of roughness length of momentum to heat from Kanda et al(2007)equation imageaK: empirical constant from Kanda et al(2007)
 equation imageReR*, ReC*: roughness Reynolds number for roof and canyon.
Z0HC and Z0HR are removed from the list of inputs. Empirical coefficient aK is introduced.equation imageu*: friction velocity (at level ZA)
  ν: molecular diffusivity of the air.

The fundamental unit of the SLUCM is the 2-D canyon (Figure 3), which is best described with reference to its height and the width of its street and roof before any normalization occurs (i.e. from mean average values of building height and roof/street widths at the local scale). From these dimensions many of the previously required inputs can be calculated internally ensuring that if individual characteristics are changed, all others which should change are also appropriately recalculated (Table II). It allows fundamental Geographic Information System (GIS) data to be directly usable without requiring interpretation as to what parameters might be, although the choice of an adequate technique to derive areally averaged values of ZR, Wroad and Wroof at the selected scale (e.g. 1 km × 1 km model grid box) is still left to the user.

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Figure 3. Schematic of the 2-D canyon structure used in WRF/SLUCM. See text for symbol definitions.

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The portion of canyon surfaces covered by walls, roads and roofs are normalized internally by the total width (Wroof + Wroad) to provide the Fwalls, Froof and Froad fractions (Table II, Eqs 13–15) which determine the contribution each type of surface has on the fluxes from the SLUCM (i.e. as in Table I, Eq. 5):

  • equation image

The building's plan area fraction (λP) and frontal area index (λF) characterizing the building morphometry (Grimmond and Oke, 1999) are linked respectively to Froof and the normalized building height Znorm (Table II, Eq. 16). The original relations for the view factors (Table I, Eqs 1–4) required to represent the trapping of radiation inside an infinitely long canyon (i.e. 2-D canyon) are kept. They now depend on Froad, Fwalls and Znorm which are unambiguously linked to the specified canyon geometry:

  • equation image

Given additional input information on the albedo and emissivities of materials, the net radiative budget at each canyon surface can be computed.

For turbulent fluxes (QH, QE) Monin–Obukhov similarity theory is applied to characterize the turbulent exchange coefficients above the roof and canyon space where turbulent energy transfer is likely to happen due to strong temperature gradients (Masson, 2000). Further inputs are needed to represent the roughness of both the roof and canyon. The canyon roughness length for momentum Z0C and corresponding zero-plane displacement height ZD are now parametrized as a function of the canyon geometry (Table II, Eq. 18: MacDonald et al, 1998), using a value of Cd = 1.2 for the drag coefficient, κ = 0.4 for von Kármán's constant and αm = 4.43, βm = 1.0 for the two empirical parameters required (MacDonald et al, 1998; Grimmond and Oke, 1999; Kastner-Klein and Rotach, 2004). Given the strong sensitivity to the input value of Z0R (Loridan et al, 2009) and the inherent complexity in its estimation at the scale required for NWP, a new approach based on the formulation of MacDonald et al(1998) is proposed for its parametrization in future releases of WRF: it is adapted to take into account the variability in roof height using a modified frontal area index λF, σ based on the standard deviation of building height σZ (Table II, Eqs 19, 20). Consequently Z0R is removed from the list of input and replaced by new parameter σZ which is physically more relevant at the scale of a model grid cell and can be obtained from an urban Digital Elevation Model (DEM) or GIS, satellite imagery or aerial photographs (e.g. Ratti et al, 2002). Variability in roof geometry has been shown to be a predominant factor in turbulence above the urban canopy layer (Rafailidis, 1997; Kastner-Klein and Rotach, 2004; Xie et al, 2008).

Knowledge of the turbulent exchanges from wall and road surfaces is needed to characterize both the temperature and humidity of the air inside the canyon. These are derived from Jurges' formula (Kusaka et al, 2001) that directly links the exchange coefficients to the wind velocity. Being a single-layer model, the SLUCM does not explicitly compute the wind profile down to street level. Instead a logarithmic profile is assumed from the forcing level (ZA) down to the roof (ZR), with an exponential decrease to a height ZC inside the canyon (Table I, Eq. 10). The corresponding wind velocity (UC) is therefore parametrized as a function of its forcing value (UA) and the roof-level value (UR). The attenuation coefficient (a) in the exponential equation uses Inoue's (1963) parametrization developed for vegetation canopies and was originally adapted for application in urban areas using two input parameters: a drag coefficient by building and a building volumetric capacity (Table I, Eq. 11). These two parameters are now removed and the attenuation coefficient is derived from an urban morphology relation (Table II, Eq. 21) using available parameters (Coceal and Belcher, 2004; Di Sabatino et al, 2008).

Bulk transfer equations are used to model the turbulent fluxes of heat (QH) and moisture (QE) in both Noah and the SLUCM:

  • equation image

QH−S and QE−S are generic notations which apply to the turbulent exchanges of energy above natural surfaces, roof surfaces or the canyon space. Subscript S refers to the surface considered, and A to the atmospheric forcing value of either the potential temperature (θ) or the specific humidity (q). ρ is the density of air, cp the specific heat, and LV the latent heat of vaporization. The turbulent exchange coefficients CH and CE are based on Monin–Obukhov similarity theory (Table I, Eqs 6–8) and are assumed identical in both the Noah and SLUCM schemes (Table I, Eq. 6). The non-dimensional functions for momentum and heat in stable cases originally differed from one scheme to another. To improve the coherence between the two formulations the Paulson (1970) equations as implemented in Noah were substituted into the SLUCM (Table II, Eqs 22, 23). However, since the ratio of roughness length for momentum to heat is considerably larger over urbanized surfaces than vegetated ones (Voogt and Grimmond, 2000), a specific approach to the modelling of Z0HR and Z0HC needs to be taken for the SLUCM. The relation derived by Kanda et al(2007) using an outdoor scale model and evaluated against field data is chosen because it was developed specifically for urban conditions and has recently been applied to the Simple Urban Energy Balance Model for Mesoscale Simulations (SUMM), which is very similar to the SLUCM in its approach (Kanda et al, 2005; Kawai et al, 2009). It links the roughness length for heat to that for momentum using the roughness Reynolds number and an empirical constant aK (Table II, Eqs 24, 25). The formula is applied to both the roof surfaces and canyon space using the best-fit value of aK = 1.29 identified by Kanda et al(2007) as well as two distinct values of the roughness Reynolds number (Table II, Eq. 26). In Noah, the Zilitinkevich (1995) approach is used to parametrize this ratio over vegetated surfaces with a default CZIL value of 0.1 (WRF 3.1: Chen et al, 1997):

  • equation image

where Z0, veg and Z0H, veg respectively represent the roughness length for momentum and heat and Reveg* the roughness Reynolds number over vegetated surfaces. The recently formulated CZIL as a function of vegetation canopy height (Chen and Zhang, 2009) is not used here.

Altogether these modifications have resulted in a reduction of seven input parameters. The two main contributions are: (1) a smaller list of more physically meaningful inputs, and (2) more consistency in the main parametrizations involved in the SLUCM as they are now explicitly linked to the canyon geometry. The on-line implementation of the scheme directly benefits from both aspects.

4. Performance compared to observations from Marseille

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

This version of Noah/SLUCM, after modifications (Table II), is evaluated ‘offline’ using hourly data from Marseille (Grimmond et al, 2004; Lemonsu et al, 2004). The evaluation focuses on the ability to simulate Q*, QH, QE (and ΔQS) as these are key to incorporating urban areas for NWP purposes. These results are the base or control simulation used as a reference in the model response analysis presented in section 5.

4.1. The campaign

Both the forcing fields required to drive the model and SEB fluxes are available for a 26-day period in summer (16 June to 12 July 2001—Day of year (DOY) 167 to 193). Instruments were mounted on an adjustable pneumatic tower installed on the roof of a 20 m high building in the city centre of Marseille (43°17′ N, 5°23′ E), leading to measurements at two distinct heights: 34.6 and 43.9 m above street level (Grimmond et al, 2004; Roberts et al, 2006). The measurement system (composed of a sonic anemometer, an open path gas analyser and a net radiometer) allows a direct observation of: Q*, QH and QE.

The anthropogenic contribution to these fluxes is also sensed by the instruments and therefore needs to be taken into account. Using measurements of CO2 fluxes as an indication of human activity in the area, Grimmond et al(2004) estimated QF to vary between a night-time value of 15 W m−2 and a daytime one of 50 W m−2, with two peaks (1000 and 1900, Local Standard Time) to a value of 75 W m−2 during the transition periods (see profile Figure 7(b)).

In a related study using data from the meso-NH mesoscale model and two intensive observation periods (21–23 and 24–26 June), Pigeon et al(2007) have shown that for a particular set of synoptic conditions (e.g. sea breeze or Mistral wind) the contribution of advection to these fluxes can be of considerable importance. However, the lack of adequate measurements over the entire 26-day period of the campaign does not permit the inclusion of ΔQA in the present analysis (Grimmond et al, 2004). The SLUCM simulates the SEB fluxes at a reference level (ZA) corresponding to the measurement height. Turbulent fluxes of heat (QH) and moisture (QE), modelled without any advection component, are evaluated against observed fluxes including such contributions. This presents a limitation to offline analysis but corresponds to what would occur within the WRF modelling system since the SLUCM does not deal with advection below its forcing level. This shortcoming of the urban parametrization would be sensed in the lower boundary fluxes provided to the atmospheric component of WRF at the first vertical level in the same way that it is in the current offline analysis. Following a similar argument, the S term is not modelled by the SLUCM and therefore omitted from the present offline model evaluation.

The ‘observed’ storage heat is then estimated as a residual, closing the energy balance:

  • equation image

Although such a method is only one of several alternatives, its applicability to the current data is confirmed by Roberts et al(2006): using a subset of the same Marseille dataset (from 4 to 11 July—DOY 185 to 192), three additional independent methods to estimate ΔQS were analysed in their study. They demonstrate good agreement with the energy balance residual method selected here. Given the set of assumptions previously described this residual storage heat implicitly takes into account the contributions from the S and ΔQA terms. As for QH and QE, the modelled and observed values of ΔQS will consequently not rigorously represent the same quantities since none of these contributions is modelled by the SLUCM. This however corresponds to its conditions of use in the on-line mode.

All measurements, independent of environment, have errors associated with them (Lee et al, 2004; Grimmond, 2006; Foken, 2008a). These are linked to instrument siting and operation, fetch, or processing of data, and energy balance closure is rarely observed. There is some evidence that the scale of patchiness of the surface may influence the ability to obtain closure (Wilson et al, 2002; Foken 2008b).

4.2. Model parameters and variables

To set up an offline run of the Noah/SLUCM for the site of Marseille, a total of 68 parameters require an input value (30 for the SLUCM, 37 for Noah and one for the coupling: the urban fraction), while 11 state variables need to be initialized (3 for SLUCM, 8 for Noah). Model runs performed at the same location with the Town Energy Balance (TEB) model (Lemonsu et al, 2004; Roberts et al, 2006) and the Soil Model for Sub-Mesoscales, Urbanized version (SM2-U: Dupont and Mestayer, 2006) were used as a reference to gather this information. Both models are very similar to the SLUCM in their approach and most of the urban values required were therefore available in the corresponding publications. For Noah, the default values corresponding to the ‘mixed shrubland/grassland’ vegetation class as implemented in WRF and a ‘clay/loam’ soil as documented in Chen and Dudhia (2001) were used which corresponds to the natural surfaces used by Dupont and Mestayer (2006) in their simulations (i.e. trees and shrub with a clay-loam soil). Most of these default values are listed in Table III.

Table III. Input parameters selected for analysis of model response
 ParameterMin.Max.DefaultParameter DefinitionReference for default
  1. Default values are from: Lemonsu et al., 2004 (LE04), Dupont and Mestayer, 2006 (DM06), Roberts et al., 2006 (RO06), Kanda et al., 2007 (KA07), Chen and Dudhia, 2001 (CD01) and Chen et al., 1997 (CH97).

1ZR12.618.615.6Roof height (m)LE04
2Wroof11.231.221.2Roof width (m)LE04
3Wroad3.615.69.6Road width (m)LE04
4σZ1.015.09.0Standard deviation of roof height (m)
5aK0.52.01.29Empirical coefficient from Kanda et al(2007)KA07
6αroof0.050.40.22Roof albedo (−)LE04 and DM06
7αwall0.050.550.20Wall albedo (−)LE04 and DM06
8αroad0.050.250.08Road albedo (−)LE04 and DM06
9εroof0.850.980.90Roof emissivity (−)LE04 and DM06
10εwall0.850.980.90Wall emissivity (−)LE04 and DM06
11εroad0.850.980.94Road emissivity (−)LE04 and DM06
12kroof0.191.50.90Conductivity of roof materials (W m−1 K−1)RO06
13kwall0.092.30.55Conductivity of wall materials (W m−1 K−1)RO06
14kroad0.032.11.77Conductivity of road materials (W m−1 K−1)RO06
15Croof0.6 × 1062.3 × 1061.77 × 106Heat capacity of roof materials (J m−3 K−1)RO06
16Cwall0.4 × 1062.3 × 1061.67 × 106Heat capacity of wall materials (J m−3 K−1)RO06
17Croad0.3 × 1062.3 × 1061.89 × 106Heat capacity of road materials (J m−3 K−1)RO06
18dz, roof0.050.50.32Total thickness of roof layers (m)RO06
19dz, wall0.11.00.26Total thickness of wall layers (m)RO06
20dz, road0.52.01.24Total thickness of road layers (m)RO06
21dzfrac, roof (1) of dz, roof covered by layer 1RO06
22dzfrac, roof (2)0.10.490.468Fraction of dz, roof covered by layer 2RO06
23dzfrac, roof (3) of dz, roof covered by layer 3RO06
24dzfrac, wall (1) of dz, wall covered by layer 1RO06
25dzfrac, wall (2) of dz, wall covered by layer 2RO06
26dzfrac, wall (3)0.10.590.577Fraction of dz, wall covered by layer 3RO06
27dzfrac, road (1) of dz, road covered by layer 1RO06
28dzfrac, road (2) of dz, road covered by layer 2RO06
29dzfrac, road (3)0.10.490.4Fraction of dz, road covered by layer 3RO06
30furb0.7640.9640.864Urban fraction (−)LE04
31Rcmin40400170Stomatal resistance (s m−1)CD01 (+DM06)
32Rgl30100100Radiation stress parameter (−)CD01 (+DM06)
33hS36.2554.5639.18Vapour pressure deficit parameter (−)CD01 (+DM06)
34αveg0.100.300.23Vegetation albedo (−)CD01 (+DM06)
35εveg0.880.970.93Vegetation emissivity (−)CD01 (+DM06)
36Z0, veg0.031.60.05Roughness length for momentum of vegetation (m)CD01 (+DM06)
37Θs0.3390.4760.465Maximum soil moisture content (m3 m−3)CD01 (+DM06)
38Θref0.2360.4530.382Reference soil moisture content (m3 m−3)CD01 (+DM06)
39Θw0.0100.20.103Wilting point (m3 m−3)CD01 (+DM06)
40Θdry0.0100.20.103Dry soil moisture content (m3 m−3)CD01 (+DM06)
41LAI1.05.03.0Leaf Area Index (m3 m−3)CD01 (+DM06)
42fv0.10.80.7Green vegetation fraction (−)CD01 (+DM06)
43QTZ0.100.920.35Soil quartz content (−)CD01 (+DM06)
44Csoil0.5 × 1064.0 × 1061.26 × 106Soil heat capacity (J m−3 K−1)CD01 (+DM06)
45CZIL0.011.00.1Zilitinkevitch parameterCH97

Hourly data of incoming short- and long-wave radiation (K[DOWNWARDS ARROW] and L[DOWNWARDS ARROW]), air temperature, relative humidity, wind components and pressure are interpolated to a 10-minute time step for forcing. This is the longest time step that ensures there are no numerical instabilities from the turbulence scheme (e.g. oscillations between stability regimes). The hourly profile of anthropogenic heat estimated by Grimmond et al(2004) is added to the sensible heat flux from the SLUCM at each step and the net storage heat is computed as a residual of the total (modelled) energy balance. The grid-averaged output fluxes (Q*, QH, QE and ΔQS) for the first 10 minutes of each hour are used for evaluation against the hourly observed data. With such a setting the model state variables (and in particular the material surface temperatures) are updated every 10 minutes and the fluxes are evaluated as close as possible to the time step when the forcings are provided, to align with the observations.

Figure 4 shows the time series of the modelled and observed SEB fluxes for the entire simulation period and the corresponding diurnal means and standard deviations, plus scatter plots with regression lines. Statistics commonly used in the field (Willmott, 1982; Jacobson, 1999; Grimmond et al, 2010) are reported in Table IV to quantify the model performance for all hours, daytime (from 2 h after K[DOWNWARDS ARROW]> 0 W m−2 to 2 h before K[DOWNWARDS ARROW] = 0 W m−2), night-time (from 2 h after K[DOWNWARDS ARROW] = 0 W m−2 to 2 h before K[DOWNWARDS ARROW]> 0 W m−2) and transition periods (remaining time periods).

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Figure 4. (a)–(d) Time series, (e)–(h) diurnal mean and standard deviation (vertical lines) and (i)-(l) scatter plots of modelled versus observed SEB fluxes for: Q* (a, e, i), QH (b, f, j), QE (c, g, k) and ΔQS (d, h, l). This figure is available in colour online at

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Table IV. Summary statistics of simulated and observed fluxes for the overall, day, night and transition time periods (see text for details): (a) Q*, (b) QH, (c) QE and (d) ΔQS.
(a) Q*UnitsAllDayNightTransition
Number of points62631578233
Mean (Noah/SLUCM)W m−2139.4358.0− 95.9− 77.4
Mean (obs)W m−2165.1393.5− 80.4− 61.4
Standard deviation (Noah/SLUCM)W m−2255.7179.612.341.1
Standard deviation (obs)W m−2266.3185.912.240.3
Coefficient of determination (R2)0.9970.9930.5090.946
Root mean square error (RMSE)W m−230.839.318.118.7
RMSE systematic (RMSES)W m−22836.215.916
RMSE unsystematic (RMSEU)W m−212.915.58.69.6
Mean absolute error (MAE)W m−225.935.815.516.2
Mean bias error (MBE)W m−2− 25.8− 35.5− 15.5− 16.0
Index of agreement (IOA)0.9970.9880.5970.949
(b) QH     
Number of points62131078233
Mean (Noah/SLUCM)W m−2147.9281.310.016.5
Mean (obs)W m−2156.4275.527.041.4
Standard deviation (Noah/SLUCM)W m−2157.2117.55.912.6
Standard deviation (obs)W m−2147.9119.61938.4
Coefficient of determination (R2)0.8350.5660.0710.401
Root mean square error (RMSE)W m−264.683.624.940.4
RMSE systematic (RMSES)W m−29.631.724.339.2
RMSE unsystematic (RMSEU)W m−263.977.35.69.8
Mean absolute error (MAE)W m−247.066.619.930.0
Mean bias error (MBE)W m−2− 8.55.9− 17.0− 24.9
Index of agreement (IOA)0.9530.8630.4790.537
(c) QE     
Number of points61430378233
Mean (Noah/SLUCM)W m−214.328.8− 0.60.5
Mean (obs)W m−
Standard deviation (Noah/SLUCM)W m−216.511.71.11.9
Standard deviation (obs)W m−27490.730.842.2
Coefficient of determination (R2)0.1330.0280.0060.008
Root mean square error (RMSE)W m−274.396.531.845.6
RMSE systematic (RMSES)W m−272.795.931.845.6
RMSE unsystematic (RMSEU)W m−215.411.51.11.9
Mean absolute error (MAE)W m−241.559.421.225.1
Mean bias error (MBE)W m−2− 25.9− 36.5− 8.4− 18.0
Index of agreement (IOA)0.3440.320.2360.275
(d) ΔQS     
Number of points61430378233
Mean (Noah/SLUCM)W m−25.595.4− 90.4− 79.4
Mean (obs)W m−2− 3.899.9− 100.2− 106.3
Standard deviation (Noah/SLUCM)W m−2106.175.89.536.4
Standard deviation (obs)W m−2157.4162.433.955.4
Coefficient of determination (R2)0.7270.570.1570.518
Root mean square error (RMSE)W m−287.3116.132.746.9
RMSE systematic (RMSES)W m−267.510531.539.6
RMSE unsystematic (RMSEU)W m−255.449.68.725.2
Mean absolute error (MAE)W m−259.388.623.933.0
Mean bias error (MBE)W m−29.2− 4.59.926.8
Index of agreement (IOA)0.8840.7430.4530.747

For Q*, a systematic underestimation of the observed fluxes for all time periods is easily identified from the mean diurnal evolution (Figure 4(e)), as well as the relative position of the linear regression and 1:1 lines (Figure 4(i)). The high negative Mean Bias Errors (MBE) reported in Table IVa also confirm this trend. As the systematic portion of the root-mean-square error (RMSES) is larger than the unsystematic (RMSEU), this suggests underestimation is likely attributable to the model itself or the choice of default parameter values, and could potentially be improved. For QH on the other hand, overall and daytime RMSEU are considerably larger than the RMSES, meaning that the majority of the error is linked to the spread of the observed data. Yet night-time and transition values of the RMSES are dominant, hinting at some issues with the modelling of QH under weak turbulent forcing. A daytime timing issue can also be identified in the mean diurnal evolution (Figure 4(f)) with a morning value larger than the observation and an evening one smaller. The simulated values of QE are underestimated for all time periods, and the large RMSES values again suggest some fundamental problems in the modelling approach or a bad choice of default parameter values (e.g. vegetation and soil classes). The magnitudes of the MBEs (Table IVc) are similar to those for Q* (section 5 investigates the extent to which both processes are linked). All previously mentioned biases accumulate in the SEB residual ΔQS which therefore has the poorest RMSE statistics (Table IVd). As noted in section 4.1, the lack of representation of S and ΔQA in the SLUCM and measurement errors also are incorporated in these results.

To enable a comparison with TEB and SM2-U the RMSE values are recalculated for the same period as the one analysed in the corresponding studies (i.e. 18–30 June and 5–11 July: Lemonsu et al, 2004; Dupont and Mestayer, 2006) (Figure 5). Q* is better modelled by SM2-U, while TEB has the lowest RMSE for QH and ΔQS. The performance attained by the Noah/SLUCM is similar to TEB for both Q* and QH, but is considerably poorer than the two other schemes for QE, and consequently ΔQS. The analysis in section 5 enables determination of whether this bias in the modelling of the turbulent latent heat flux can be solved by a change in the default parameter values or a consequence of a more fundamental problem.

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Figure 5. Comparison of RMSE obtained by TEB, SM2-U and Noah / SLUCM using Marseille data for Q*, QH, QE and ΔQS (see text for details).

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5. Analysis of model response

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

5.1. Set-up

Having modified the type of input information needed by the Noah/SLUCM, an assessment of the model response to its updated list of input parameters is required. The systematic and objective procedure introduced in section 2 is applied here to the Table II version of the scheme. The forcing and observation data from Marseille and the section 4 run are used as the reference to provide both default parameters values and RMSE.

After preliminary tests of their influence on the RMSE statistics, 45 out of 68 parameters were selected to be optimized. The remaining 23 were left out of the optimization procedure since they did not influence the model performance (mainly soil- and vegetation-related coefficients involved in the parametrization of processes of little impact in the case of Marseille). Each is given a default value and limits between which it can evolve (Table III). Ranges for each parameter were determined using typical properties of building materials as listed in the ASHRAE tables (ASHRAE, 2005; Anderson, 2009) as well as the Chen and Dudhia (2001) default values for different vegetation and soil classes.

The algorithm is set to initialize 100 samples (s = 100), and two sets of MOSCEM runs are performed here:

  • (1).
    Using only the RMSE for Q* and QH as objective functions, the key parameters in modelling Q* are identified while providing some insight on the processes transferring the energy towards QH. Discarding the RMSE for QE from the procedure, this first set of runs focuses on the two largest fluxes of the urban energy balance. It also enables a graphical representation of trade-offs illustrating many of the concepts introduced in section 2.
  • (2).
    Adding the RMSE for QE as a third objective forces MOSCEM to search for the best overall compromise (in terms of RMSE).

5.2. Optimization with regard to Q* and QH

Results from the multi-objective runs optimizing the RMSE for Q* and QH are presented in scatter plots (Figure 6) also known as ‘objective spaces’, which clearly illustrate the two distinct behaviours discussed in section 2:

  • For some parameters an optimum value emerges: the 100 solutions are clustered in a very compact area of the objective space, and at least one of the RMSE is improved from the performance obtained with the default run of section 4 (ΔRMSE ≤ 0 W m−2) (e.g. Figure 6, panel 1: ZR).

  • For the remaining parameters only a Pareto front of solution is identified: their optimization results in some ‘trade-offs’ in the modelling of the two fluxes (e.g. Figure 6, panel 6: αroof)

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Figure 6. RMSE for the 100 samples identified as optimum by MOSCEM when optimized for both the RMSE for Q* and QH. The results from control single-objective runs are also plotted (solid lines). Parameters 1 to 29 (SLUCM-related) and the urban fraction (furb) are shown. See Table III for definitions. This figure is available in colour online at

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Additionally, results from a set of control single-objective runs (using only one of the RMSE as objective) are reported on the plots (solid lines) to underline the ability of MOSCEM to cover the entire range of trade-offs and reach the same performances as when optimization is done for only one flux. Interestingly, in some cases the multi-objective runs outperform the single-objective ones suggesting that the algorithm is more efficient in its multi-objective mode.

The extent of RMSE improvement relates to the sensitivity of the model to a specific parameter. The 20 parameters with largest impact on the default RMSE for Q* (Table Va) and QH (Table Vb) are ranked, and corresponding changes in RMSE for the other two fluxes directly simulated by the model are reported as an indication of possible trade-offs. To further illustrate the importance of such trade-offs the 20 parameters leading to a Pareto front of solution are presented (Table VI). The ranking in terms of biggest improvement in RMSE of one flux (Q* in Table VIa, QH in Table VIb) can be obtained from a change of value along the front (i.e. by moving from the value giving the lowest RMSE to the one giving the highest). The impact of the same value change on the other fluxes is also listed to show the trade-offs (i.e. when ΔRMSE > 0 W m−2). Among the parameters selected to be optimized, two categories can be distinguished: parameters defining the urban morphology, radiative properties, heat capacities, conductivities or depth of materials for instance can to a certain extent be assigned objective values based on observation at a given site. They represent the first category of inputs which can be related to a measurable physical quantity. On the other hand, parameters such as aK or CZIL must be seen as ‘tunable’ quantities since they arise from empirical models which are by nature only a simplification of physical phenomena too complex to be explicitly resolved (e.g. momentum, heat and moisture exchange by turbulent transport). In that sense they do not relate to any objectively measurable quantity and can only be determined with regard to a given experiment (e.g. Kanda et al(2007) found aK varied (1.24–1.41) depending on dataset in their study). Although not an input, coefficients αm and βm from MacDonald et al(1998) are in the same category (Table II, Eqs 17, 18). Other examples include soil- and vegetation-related coefficients such as the minimum stomatal resistance (Rcmin) or the radiation stress parameter (Rgl). As far as this second category is concerned, departures between default and MOSCEM-selected optimum values can be (partly) attributed to conditions differing from either the theoretical framework in which they were developed or the dataset used to determine their initial estimates. For the first category, any departure from the default measured values needs to be interpreted as an attempt of MOSCEM to compensate for model deficiencies and for uncertainties in estimating parameters.

Table V. Sensitivity of (a) the net all-wave radiation (Q*) and (b) the turbulent sensible heat flux (QH) simulated by Noah / SLUCM. The 20 input parameters with the largest influence on RMSE performance, ranked based on best improvement made by a change in their default value (ΔRMSE ≤ 0 W m−2) are shown. Impact on the RMSE of the other two modelled fluxes is also given as an indication of trade-offs.
(a)ParameterDefaultOptimumGain in Q* (ΔRMSE)Impact on QH (ΔRMSE)Impact on QE (ΔRMSE)
1αroof0.220.135− 12.396.350
2aK1.290.529− 7.606.170
3αwall0.20.052− 6.620.560
4αveg0.230.102− 6.361.17− 0.74
5Wroof21.211.2− 3.54− 2.890
6Wroad9.615.6− 3.21− 1.030
7εroof0.90.851− 2.810.200
8furb0.8640.764− 1.660.64− 3.73
9σZ914.946− 1.621.060
10εwall0.90.98− 1.07− 0.090
11kwall0.552.299− 0.97− 2.220
12εveg0.930.880− 0.610.04− 0.08
13dz, wall0.260.894− 0.570.410
14kroof0.90.363− 0.535.810
15Croof1769000604674− 0.392.910
16αroad0.080.05− 0.37− 0.010
17εroad0.940.98− 0.30− 0.030
18Cwall16760002299510− 0.29− 0.830
19dz, roof0.320.496− 0.261.690
20ZR15.618.599− 0.24− 0.150
(b)   Gain in QH (ΔRMSE)Impact on Q* (ΔRMSE) 
1kroof0.91.495− 3.380.780
2dz, roof0.320.16− 2.930.490
3Wroof21.211.2− 2.89− 3.540
4kwall0.552.3− 2.22− 0.960
5aK1.291.999− 1.907.120
6σZ93.168− 1.807.550
7dzfrac, roof(2)0.4680.228− 1.620.170
8dz, wall0.260.1− 1.53− 0.180
9Rcmin17040.234− 1.220− 2.25
10Wroad9.615.6− 1.03− 3.210
11CZIL0.10.999− 0.9100.70
12Cwall16760002299910− 0.84− 0.290
13αroof0.220.248− 0.795.950
14dzfrac, wall(3)0.570.146− 0.69− 0.140
15Croof17690002283860− 0.690.130
16αveg0.230.298− 0.473.700.47
17LAI34.995− 0.460− 0.76
18dzfrac, road(2)0.160.1− 0.42− 0.060
19dzfrac, wall(1)0.0380.1− 0.38− 0.070
20dz, road1.240.663− 0.290.230
Table VI. Trade-off effects in the modelling of Q* and QH. Parameters are ranked in terms of the biggest improvement in RMSE for (a) Q* and (b) QH which can be obtained from a change of value along the Pareto front (ΔRMSE ≤ 0 W m−2). The corresponding impact on the RMSE for the other fluxes is reported as a measure of the trade-off effects.
(a)ParameterChange in valueGain in Q* (ΔRMSE)Impact on QH (ΔRMSE)Impact on QE (ΔRMSE)
1αroof0.248 to 0.135− 18.347.140
2aK1.999 to 0.529− 14.728.070
3αveg0.298 to 0.102− 10.051.65− 1.21
4αwall0.255 to 0.052− 9.430.590
5σZ3.168 to 14.946− 9.362.860
6εroof0.938 to 0.851− 4.950.240
7kroof1.495 to 0.363− 1.319.200
8εveg0.970 to 0.880− 1.10.07− 0.14
9furb0.822 to 0.764− 0.950.78− 1.75
10dzroof0.16 to 0.496− 0.754.620
11Croof2283860 to 604674− 0.523.590
12dz, wall0.1 to 0.894− 0.391.930
13dz, road0.663 to 1.942− 0.260.410
14dzfrac, roof(2)0.228 to 0.490− 0.191.850
15dzfrac, wall(2)0.220 to 0.297− 0.040.180
16dzfrac, wall (3)0.147 to 0.211− 0.030.090
17dzfrac, road(1)0.068 to 0.097− 0.030.110
18dzfrac, roof(3)0.100 to 0.378− 0.010.030
19dzfrac, roof(1)0.099 to 0.078− 0.010.140
20dzfrac, road(2)0.1 to 0.101− 0.010.010
(b)  Gain in QH (ΔRMSE)Impact on Q* (ΔRMSE) 
1kroof0.363 to 1.495− 9.201.310
2aK0.529 to 1.999− 8.0714.720
3αroof0.135 to 0.248− 7.1418.340
4dzroof0.496 to 0.16− 4.620.750
5Croof604674 to 2283860− 3.590.520
6σZ14.946 to 3.168− 2.869.360
7dz, wall0.894 to 0.1− 1.930.390
8dzfrac, roof(2)0.49 to 0.228− 1.850.190
9αveg0.102 to 0.298− 1.6510.051.21
10furb0.764 to 0.822− 0.780.951.75
11αwall0.052 to 0.255− 0.599.430
12dz, road1.942 to 0.663− 0.410.260
13εroof0.851 to 0.934− 0.244.960
14dzfrac, wall(2)0.297 to 0.22− 0.180.040
15dzfrac, roof(1)0.078 to 0.1− 0.140.010
16dzfrac, road(1)0.098 to 0.0676− 0.110.030
17dzfrac, wall(3)0.223 to 0.147− 0.090.030
18εveg0.880 to 0.969−
19dzfrac, roof(3)0.378 to 0.1− 0.030.010
20dzfrac, road(2)0.102 to 0.1− 0.010.010

Table V highlights a strong sensitivity of the model to all roof-related parameters. This relates to the direct impact roof surfaces have on the simulation of Q* and QH (no canyon interference) and the dominant role they play in a dense city with narrow streets such as Marseille (plan area fraction λp = 0.69, frontal area index λF = 0.5). The values identified as optimum, based on the RMSE for Q*, can be interpreted as an attempt to provide more radiative energy (reduction of αroof, εroof) while reducing heat storage (reduction of Croof, kroof), thus increasing the available energy for the turbulent fluxes. This tends to decrease both the day and night-time biases for the default case (Figure 4, Table IVa) since a larger proportion of the incoming solar energy would be made available during the day when it can be dissipated via turbulent processes hence limiting the long-wave emissions. It would also reduce the large negative values of night-time Q* by keeping the roof temperature lower when turbulent activity is typically weak and energy is mostly lost as L[UPWARDS ARROW]. Yet it also triggers an increase in the RMSE of QH (i.e. a trade-off); with a limited storage capacity, solar radiation warms roof surfaces with almost no time lag, hence strengthening the daytime temperature gradient between the roof and the air at forcing level. As a result, exchanges of heat via turbulent processes are enhanced and the model reaches a state where it overestimates the sensible heat fluxes. The observed peak turbulent sensible heat fluxes may also be underestimated (Foken, 2008b). This suggests roof characteristics must be determined with great care due to their large impact on the RMSE of Q* and QH and potential trade-offs.

The optimization of canyon parameters (walls, road) is the source of fewer trade-off effects than roof-related ones, and in many cases an optimum state is identified (e.g. for αroad, εroad, εwall, kroad, kwall, Croad or Cwall). As argued by Harman and Belcher (2006) this shows heterogeneities between the energy balance of the roof and canyon, and underlines the importance of an accurate estimate of the relative space they occupy. Parameters characterising road properties do not show significant impact on any of the RMSE values suggesting that, if left with the choice, more effort should be put to determining appropriate values for roof or wall characteristics than road ones (e.g. when refining urban land-cover data for a particular site). Among the different properties considered, albedo values are most critical for Q* while conductivities as well as the roof thickness particularly influence QH. These conclusions are valid for particularly dense cities, like the one investigated (λp = 0.69, λF = 0.5) on the upper end of the range indicated by Grimmond and Oke (1999).

Wroad and Wroof are ranked highly but do not trigger any trade-offs. This underlines the key role they play in normalizing all morphological parameters (Table II, Eqs 12–15, 19) and therefore in defining the relative importance of roof and canyon exchange processes. The impact on the mean diurnal fluxes of the components involved in modelling Q* (Figure 7(a)) and QH (Figure 7(b)) at the forcing level, with the walls and road contributions combined into the canyon component, can be analysed. This comparison prior to their weighting helps to explain the clear tendency towards an increase of the canyon space which results from the optimum values selected by MOSCEM (decrease of Wroof, increase of Wroad). Assigning more weight to the canyon space allows more trapping of the incoming radiation (Figure 7(a)) while minimizing the relative importance of turbulent exchange above roof surfaces (Figure 7(b)) which can be attributed to higher wind speed values at roof level than inside the canyon (inset Figure 7(b)). However, as both Wroof and Wroad are involved in the parametrization of the roughness length above the canyon and roof surfaces (Table II, Eqs 16–20) the impact on QH is not limited to the relative weight each surface is assigned.

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Figure 7. Based on Marseille forcing and observations the contribution of each surface represented in Noah/SLUCM for (a) Q*, and (b) QH. Inset to (b): diurnal mean wind speeds at forcing level (ZA), roof level (ZR) and inside canyon (ZC). The anthropogenic heat flux QF (Grimmond et al, 2004) is plotted in (b). This figure is available in colour online at

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There are two main ways canyon structure impacts modelling of QH (Figure 8). The relative space occupied by roof surfaces can be reduced (by a direct reduction of the roof width or a wider road) (Figure 8(a) and (d)). Such a change limits the weight assigned to the roof contribution (Froof(= λP)< 0.6), but this enhances its magnitude via an increased roughness (Table II, Eqs 19, 20). The resulting impact on modelled QH at the forcing level is therefore limited. The opposite case is an increased roof contribution (Figure 8(b)–(c)) (roof is widened or road narrowed). Although the roof roughness is now reduced, its increased weight compensates, keeping the overall impact on QH low. Note that in the most extreme case (Figure 8(c), Froof = 0.85) the roof contribution is almost sufficient to represent the overall QH value (skimming flow regime).

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Figure 8. Impact on QH of (a) a 10 m reduction in roof width (λp = 0.54), (b) a 10 m increase in roof width (λp = 0.76), (c) a 5 m reduction in road width (λp = 0.85) and (d) a 5 m increase in road width (λp = 0.58) from the default values (λp = 0.69). This figure is available in colour online at

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Wroof and Wroad form the basis of the homogenized input list (section 3) and can be estimated with good confidence from GIS data. The high responsiveness of the model to their values is therefore acceptable. Yet the extreme values selected during the optimization procedure (Wroof = 11.2 m and Wroad = 15.6 m) highlight some deficiencies of the scheme with regard to the modelling of Q* and QH (first category of inputs).

The scheme is far less sensitive to the σZ parameter than it was to the previously required value of Z0R (Loridan et al, 2009). As noted, its estimation is relatively straightforward and therefore the sensitivity to its value does not appear excessive. The value selected by MOSCEM when optimizing for QH did not reach the lower limit indicating that reducing σZ to a value of 3.16 m was sufficient to reach an optimum RMSE in the case of Marseille. The size is also physically reasonable as it is the order of one storey. This again represents a compensation for other shortcomings of the scheme (first category of inputs) but suggests that the model responds effectively to a change in σZ.

The sensitivity of the scheme to aK, and the significant trade-offs associated with any change demonstrates the importance of adequate characterization of the ratio of roughness length for heat and momentum in urban areas. It also confirms the results of the sensitivity analysis performed with the SUMM model using the same parametrization (Kawai et al, 2007, 2009). Previously introduced in this section as a ‘tunable’ quantity (second category of inputs), the choice of an appropriate value for the Marseille dataset would depend on the relative importance given to each of the two optimized fluxes: any reduction of aK greatly improves the modelling of Q* but has a negative impact on QH (Figure 6, panel 5, Table VIa); the opposite is true for any increase of aK (Table VIb).

To assess the extent to which this second category of ‘tunable’ parameters can impact the performance of the scheme (in terms of the RMSE for Q* and QH), a multi-parameter run is performed optimizing the main empirical coefficients involved in the turbulence parametrization equations (aK, CZIL, αm and βm). This allows all possible ‘tuning’ combinations to be accounted for through multi-parameter optimization. Figure 9 shows the objective plots of the 100 samples used in this multi-parameter run, along with the corresponding combinations of values selected by MOSCEM (inset). The minimum and maximum values that are the basis for each normalization are given in Figure 9. The combinations which perform best (for Q* and QH respectively) lie in different areas of the ranges. This suggests, once again, that no optimum values exist for the modelling of the two fluxes (ideally all samples (grey lines) would follow the same unique line indicating the values to be assigned to each coefficient). For Q* the combined impact of the four parameters results in a minimum RMSE of 16 W m−2. However, a careful inspection of the combined values suggest αm and aK reach their minimum which shows the danger of this kind of model optimization: when trying to compensate for other model deficiencies (here a negative bias in Q*), MOSCEM can yield physically unrealistic values (e.g. a higher roughness length for heat than momentum if aK = 0.1 and the roughness Reynolds number is very small). It should be remembered that MOSCEM does not consider the physical meaning of a parameter, so analysis of the role of each parameter in the processes parametrized is required before changing their default values. In this particular case, tuning the coefficients to minimize the RMSE for Q* is not advisable as it would result in considerable deterioration of the modelling of the turbulent processes. For QH, the best combination leads to a minimum RMSE of 62 W m−2, with all four coefficients being assigned values consistent with the parametrization they impact (CZIL = 0.92, αm = 5.7, βm = 1.83 and aK = 1.9). Consequently it can be argued that for this site a physically plausible optimum setting to model QH has been identified within the parameter space. This highlights the added complexity of a model response analysis using MOSCEM in a multi-parameter mode: parameter value changes tend to compensate for each other leaving any detailed analysis of model sensitivity to a particular input almost impossible.

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Figure 9. Multi-parameter optimization of empirical coefficients CZIL, αm, βm and aK. Inset shows the 100 combinations of parameter values (normalized) selected by MOSCEM. This figure is available in colour online at

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The inability of all SLUCM-related parameters to influence the RMSE for QE shows some limitation to modelling QE within the urban tile. As no water reservoir is included in the SLUCM, urban evaporation is limited to rain episodes. In addition no transfer of energy from Q* to QE is directly represented by Noah/SLUCM: all incoming radiative energy retained in the urban tile is either dissipated as sensible heat or stored in the urban fabric; and QE is entirely dealt with by Noah. Section 5.3, where the RMSE for QE is included as an objective function in the optimization procedure, is designed to identify the key parameters to which its modelling is sensitive.

5.3. Optimization with regards to Q*, QH and QE

Results from sensitivity rankings for modelling Q* and QH do not provide any additional information to what is presented in Table V and are therefore not shown. Table VII has the 16 parameters, with some influence on QE, ranked based on their impact on the RMSE for QE. After the urban fraction (furb), the parameters the scheme is the most sensitive to are stomatal resistance (Rcmin), followed by Leaf Area Index (LAI). In Noah, both these parameters are involved in the parametrization of the canopy resistance which is required in canopy evapotranspiration. Both the decrease of Rcmin and increase of LAI suggested by MOSCEM lead to a reduction of the canopy resistance (Eq. 16 from Chen and Dudhia, 2001), and therefore an enhancement of the transpiration from the vegetation. The other parameters effectively acting on QE are the soil characteristics (Θref, Θdry, Θw, Θs) which determine the direct evaporation from the ground, and are used to determine plant transpiration through available soil moisture in root zone and water stress response function for the canopy resistance. In particular, the reduction of the reference soil moisture content Θref (field capacity) arising from the optimization is directly linked to an increase in the direct evaporation from the soil. However, since it is the green vegetation fraction fv which partitions the total evaporation between soil direct and canopy evaporation, the increase in its value resulting from the optimization indicates that canopy evaporation is the dominant factor. The choice of a vegetation class with a low Rcmin, combined with high LAI and fv is therefore recommended for urban applications. Only eight parameters lead to some trade-offs and the corresponding ranking is presented in Table VIII.

Table VII. Sensitivity of turbulent latent heat flux simulated by Noah/SLUCM
 ParameterDefaultOptimum valueGain in QE (ΔRMSE)Impact on Q* (ΔRMSE)Impact on QH (ΔRMSE)
  1. The 16 parameters with the largest influence on RMSE performance, ranked based on best improvement made by a change in their default value )ΔRMSE ≤ 0 W m−2). Impact on the RMSE of the other two modelled fluxes is also given as an indication of trade-offs.

1furb0.8640.764− 3.73− 1.660.64
2Rcmin17040.234− 2.250− 1.22
3LAI34.999− 0.760− 0.46
4αveg0.230.102− 0.74− 6.361.17
5Θref0.3820.284− 0.460− 0.21
6Rgl10030.046− 0.430− 0.21
7Θdry0.1030.010− 0.350− 0.21
8fv0.70.800− 0.2900
9Θw0.1030.010− 0.130− 0.06
10Θs0.4650.436− 0.090− 0.09
11εveg0.930.880− 0.08− 0.610.04
12Z0, veg0.050.415− 0.0600.20
13hs39.1836.262− 0.050− 0.04
14CZIL0.10.029− 0.0400.10
15Csoil1260000519855− 0.0200.02
16QTZ0.350.101− 0.0200.11
Table VIII. Trade-off effects in the modelling of QE, Q* and QH.
 ParameterChange in valueGain in QE (ΔRMSE)Impact on Q* (ΔRMSE)Impact on QH (ΔRMSE)
  1. Parameters are ranked in terms of the biggest improvement in the RMSE for QE which can be obtained from a change of value along the Pareto front (ΔRMSE ≤ 0 W m−2. The corresponding impact on the RMSE for the other fluxes is reported as a measure of the trade-off effects.

1furb0.822 to 0.764− 1.75− 0.950.78
2αveg0.298 to 0.102− 1.21− 10.051.65
3CZIL0.987 to 0.029− 0.7301.01
4εveg0.970 to 0.880−
5Z0, veg0.031 to 0.415− 0.0900.27
6Csoil3929810 to 519855− 0.0700.03
7Θref0.323 to 0.284− 0.0500
8QTZ0.904 to 0.101− 0.0400.39

For all parameters characterizing evaporative properties of soil and vegetation (Rcmin, LAI, Rgl, hs, fv, Θref, Θdry, Θw, Θs), the improvement in RMSE for QE provided by their optimization is associated with an improvement in QH. In the vegetated tile, Q* is shared between QH and QE. Any enhancement of QE which does not modify the radiative balance directly leads to a decrease in QH. Given the daytime positive bias of QH in the default simulation, this translates into a decrease of its RMSE. This is particularly interesting since it represents the way in which energy can be transferred indirectly from one scheme to another in a tile approach model such as Noah/SLUCM: with its canyon structure and building materials allowing high energy storage, the SLUCM has the ability to retain incoming radiation. The poor representation of evaporative processes in the absence of a water reservoir inside the urban tile only permits the dissipation of energy via turbulent sensible heat or its storage. To compensate for this underestimation of the urban contribution to QE, evaporative processes within the vegetated tile need to be enhanced. This in turn helps with reducing the overestimated turbulent heat flux as it reduces its vegetated value. Physically this can be seen as a way to account for processes not represented by the urban scheme such as the evaporation of water from street cleaning, fountains or any other urban sources. This approach however relies heavily on the value of the urban fraction (see ranking in Table VII), and for highly urbanized sites the vegetated tile might not have enough impact on the grid-averaged fluxes to balance the limitations of the urban scheme.

Figure 10 shows the diurnal mean evolution of Q*, QH, QE and ΔQS from a new run of Noah/SLUCM where the results from Tables V and VII were used as an indication of how to: (1) provide more radiative energy in the system (αroof = 0.15, αwall = 0.15, αveg = 0.19) and, (2) enhance evaporative processes from the vegetated tile (Rcmin = 40.0, LAI = 4.0, fv = 0.8). Note that in terms of the vegetation classification used in WRF this would represent a switch to the ‘cropland/grassland mosaic’ category which currently is the standard urban vegetation class in WRFv3.1. In this run we assume that the ‘mixed shrub/grass’ vegetation type used in the default run was restricting evaporation due to an excessive canopy resistance. A second simulation is also performed with the same settings and a value of 0.813 for the urban fraction, which represents a reduction of one standard deviation relative to its mean estimated value (Lemonsu et al, 2004). The performance of this later run is plotted (Figure 5) along with the default run to show improvements.

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Figure 10. Diurnal mean for (a) Q*, (b) QH, (c) QE and (d) ΔQS from two different runs of the Noah/SLUCM (αroof = 0.15, αwall = 0.15, αveg = 0.19, Rcmin = 40.0, LAI = 4.0, fv = 0.8) plus furb = 0.864 (dashed) and furb = 0.813 (solid). See text for notation. This figure is available in colour online at

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The critical role played by the urban fraction in the partitioning of the energy between turbulent sensible and latent heat fluxes is clearly highlighted by the diurnal evolution of QE (Figure 10(c)). Large deviations between observed and simulated QE occur during night-time, even after changing the vegetation class and urban fraction. This shows the limitations of compensating with Noah for deficits in the urban scheme. During much of the night, positive QE were measured. Plant transpiration is negligible during the night, and even if soil evaporation could be possible, it is unlikely that soil moisture at the surface is consistently so high as to allow significant night-time fluxes (unless irrigation occurs). The fluxes could however be anthropogenic. In particular the proximity of the site to a flower market and regular street cleaning (Grimmond et al, 2004) support this. This presents a fundamental problem since it cannot be fixed with parameter choices in the Noah LSM or urban fraction. It also explains the large systematic night-time errors in QE, even though the model appeared to well reproduce the observed night-time Q*, QH, and ΔQS.

In order to reduce such biases, a better representation of the water balance inside the urban tile is needed (e.g. Mitchell et al, 2007; Oleson et al, 2008a) and should be a priority in future developments of urban energy balance schemes.

6. Conclusion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

A systematic and objective model response analysis method using the MOSCEM algorithm of Vrugt et al(2003) is used to assess fitness of an urban parametrization scheme. An updated version of the parametrization implemented in WRF (Noah/SLUCM) is presented, focussing on features which improve its applicability. In particular, input parameter values with ambiguous meaning at the scale of a grid cell (e.g. Z0C, Z0R) have been linked to urban morphology. Using observations from Marseille the updated version of Noah/SLUCM was tested offline and compared to other similar urban canopy models. The need for an analysis of the scheme's response to its updated list of input parameters was used as a case-study to apply the procedure, and led to the ranking of all parameters in terms of their impact on the modelling of the surface energy balance fluxes.

Results with Marseille data suggest that the Noah/SLUCM scheme is most sensitive to roof-related parameters, and the associated default values to be implemented for the urban land use in WRF should therefore be derived with particular care. Albedo values represent the most critical characteristic in the modelling of Q* while QH is mainly sensitive to roof (wall) conductivities and the thickness of roof materials. Given the unifying role they now play in the set of parametrization implemented in the SLUCM, canyon geometry parameters are also of particular importance for the modelling of both fluxes. Road characteristics on the other hand do not significantly impact the model performance and a higher degree of uncertainty in their estimation can therefore be accepted.

The difficulty the scheme has in correctly partitioning turbulent energy between latent and sensible heat is highlighted. The choice of a vegetation class with a low stomatal resistance (e.g. ‘cropland/grassland mosaic’ or ‘grassland’) is recommended for urban applications in order to balance the insufficient representation of urban evaporation in the SLUCM. Further research is needed to represent the anthropogenic source of moisture, because the current approach appears limited for highly urbanized sites where the anthropogenic contribution is likely to be more important than that from natural vegetation. These results have implications for application of this type of model to consider different countermeasures to urban heat islands; such as green roofs.

This study provides some first insights into the critical parameters in the estimation of the surface energy balance for a dense European city centre such as Marseille, and suggests an approach for urban parameter optimization using field observations. The analysis however needs to be repeated with additional sites offering contrasting levels of urbanization and various climatic conditions before drawing general conclusions on the most influential parameters. That the scheme appears mostly sensitive to ‘objectively determined’ parameters (first category of inputs) highlights the difficulties in its implementation for NWP applications: since it is close to impossible to derive all needed inputs for every single urban grid cell in a particular domain, some generic urban classes are needed (e.g. urban climate zones: Oke, 2004) and the choice of model input values to best characterise each class will once again result from a trade-off. As noted (section 2), only a multi-parameter optimization of these inputs would enable identification of optimum values to be assigned for urban land-cover classes in WRF. Finally, a real-time assessment of how much the resulting flux improvements impact forecasting is needed to determine the overall fitness of the scheme for NWP. The added complexity induced by forcing the scheme from WRF rather than observations might however considerably alter its response. This offline evaluation of the Noah/SLUCM provides an objective assessment and is highly complementary to the evaluation of the coupled WRF/Noah/SLUCM modelling system (e.g. Lin et al, 2008; Miao et al, 2009).


  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References

Thanks to all those who were involved in the Marseille/ESCOMPTE field campaign, and to both Jasper A. Vrugt and Luis A. Bastidas for the development and sharing of the MOSCEM optimization software. The authors would also like to thank the reviewers for the careful review. Financial support for this project was provided by the US National Science Foundation ATM-0710631. The work conducted at NCAR was supported by the US Air Force Weather Agency (AFWA), NCAR FY07 Director Opportunity Fund, and the Defense Threat Reduction Agency (DTRA) Coastal-urban project.


  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Systematic and objective model response analysis using the MOSCEM algorithm
  5. 3. The single-layer urban canopy model in WRF
  6. 4. Performance compared to observations from Marseille
  7. 5. Analysis of model response
  8. 6. Conclusion
  9. Acknowledgements
  10. References
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