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  • View in gallery

    Locations of streamflow gauges used in this study.

  • View in gallery

    5-yr (1998 to 2002) observed and simulated annual streamflow at nine basins in the northeastern U.S. for (a) default simulation, (b) VF experiment, (c) VM experiment, and (d) VFM experiment.

  • View in gallery

    RMSEs and bias between observed and simulated annual runoff ratios at nine basins in the northeastern U.S. for the period from 1998 to 2002.

  • View in gallery

    Simulated annual evaporations for (a) VF and default, (b) VM and default, (c) VFM and default, and (d) estimated precipitation for nine basins in northeastern U.S. for the period from 1998 to 2002.

  • View in gallery

    Normalized optimal and default RSMIN for four different experiments.

  • View in gallery

    Daily correction factors derived from Eq. (1) for (a) snow, (b) rain, and (c) mixed precipitation when different optimal WMO model parameters are used.

  • View in gallery

    Mean annual correction factors for nine basins in the northeastern U.S. for three experiments [basin number is shown in Table 1. Daily precipitation is adjusted by daily correction factors as shown in Fig. 5, and is accumulated to annual precipitation. 5-yr (1998 to 2002) averaged annual precipitation is calculated, and then is divided by default mean annual precipitation to get this figure.].

  • View in gallery

    (a) RMSE and bias between observed and simulated runoff ratios and (b) normalized optimal minimum stomatal resistance RSmin for VF1, VF, and VF2 experiments.

  • View in gallery

    Optimal estimates for (a) mean annual precipitation, (b) mean annual evapotranspiration, and (c) mean annual streamflow at nine basins in the northeastern United States for the period from 1998 to 2002.

  • View in gallery

    A simple schematic diagram about error sources for the LaD land surface model (errors represented in solid line are studied in this paper, and errors represented in dashed line are not studied in this paper).

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Calibration of LaD Model in the Northeast United States Using Observed Annual Streamflow

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  • 1 Atmospheric and Oceanic Science Program, Princeton University, Princeton, New Jersey
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Abstract

Calibration of land surface models improves simulations of surface water and energy fluxes and provides important information for water resources management. However, most calibration studies focus on local sites and/or small catchments because of computational limitations, lack of atmospheric forcing data, and lack of observed water and energy fluxes. Even though a well-established streamflow gauge network exists, its data are not well suited to the calibration of land surface models in cold regions because of large systematic precipitation biases. This study provides a newly developed method to adjust systematic precipitation biases arising from gauge undercatch (e.g., wind blowing, wetting loss, and evaporation loss). The new method estimates model parameter and precipitation errors simultaneously through the use of observed annual streamflow in the northeastern United States. The results show that this method improves streamflow simulations and gives a reasonable estimate for systematic precipitation bias. In addition, the impacts of model parameter errors on the calibration of the Land Dynamics (LaD) model and on the estimation of systematic precipitation biases are investigated in the northeastern United States.

* Current affiliation: Environmental Modeling Center, NOAA/National Centers for Environmental Prediction, Camp Springs, Maryland

Corresponding author address: Youlong Xia, NOAA/Geophysical Fluid Dynamics Laboratory, Princeton University, Forrestal Campus, Princeton, NJ 08542. Email: youlong.xia@noaa.gov

Abstract

Calibration of land surface models improves simulations of surface water and energy fluxes and provides important information for water resources management. However, most calibration studies focus on local sites and/or small catchments because of computational limitations, lack of atmospheric forcing data, and lack of observed water and energy fluxes. Even though a well-established streamflow gauge network exists, its data are not well suited to the calibration of land surface models in cold regions because of large systematic precipitation biases. This study provides a newly developed method to adjust systematic precipitation biases arising from gauge undercatch (e.g., wind blowing, wetting loss, and evaporation loss). The new method estimates model parameter and precipitation errors simultaneously through the use of observed annual streamflow in the northeastern United States. The results show that this method improves streamflow simulations and gives a reasonable estimate for systematic precipitation bias. In addition, the impacts of model parameter errors on the calibration of the Land Dynamics (LaD) model and on the estimation of systematic precipitation biases are investigated in the northeastern United States.

* Current affiliation: Environmental Modeling Center, NOAA/National Centers for Environmental Prediction, Camp Springs, Maryland

Corresponding author address: Youlong Xia, NOAA/Geophysical Fluid Dynamics Laboratory, Princeton University, Forrestal Campus, Princeton, NJ 08542. Email: youlong.xia@noaa.gov

1. Introduction

The error in a variable simulated by a land surface model is determined by the error in model formulations, the error in model parameters, and the error in atmospheric forcing data. The purpose of calibrating land surface models is to reduce errors of model output by matching simulations with observations through adjusting the model parameters, the model formulations, and the atmospheric forcing data. Xia et al. (2002) indicated that complex land surface models have a better performance than simple land surface models if they are calibrated. This is because a complex model is closer to the “real world” than a simple model if the model physical formulations are reasonable. For a given land surface model, model output errors are reduced only by adjusting model parameters and the forcing data errors because model formulations are predetermined. In general, forcing data errors are not considered in the calibration of land surface models. Some investigators assume that the forcing data are accurate, or contain small errors, and use different calibration algorithms to optimize model parameters to reduce the associated model output errors (Sellers et al. 1989; Gupta et al. 1999; Leplastrier et al. 2002; Jackson et al. 2003; Xia et al. 2004a, b). Others do not use forcing data with large errors and use only forcing data with small errors to calibrate land surface models (Milly and Shmakin 2002b). Neither method addresses how to use forcing data with large errors to calibrate land surface models. Indeed, it is well known that large forcing errors will affect the calibration of land surface models. In particular, large forcing errors in cold regions cannot be avoided because a significant proportion of the precipitation falls as snow, which is largely underestimated in these regions (Goodison et al. 1998; Yang et al. 1998a, b; Ungersboeck et al. 2002). Precipitation accuracy is a key to accurate simulation of the land surface water and energy balance. Therefore, the issue of how to use forcing data with large errors to calibrate land surface models is not a trivial one. As indicated by Milly and Dunne (2002a), most observed streamflow has a 5% error and some has up to 10%–15% error in mountainous regions. However, precipitation errors are usually 30% or higher in cold regions. Therefore in these regions, optimization algorithms, observed streamflow, and available land surface models can be used to inversely estimate precipitation errors. Recently, this procedure was employed for Valdai, Russia (Xia et al. 2005). The results show that an optimization algorithm can be inversely used to estimate optimal precipitation errors that are consistent with the observed values.

This method has not yet been explored at the regional or global scale because the adjustment methods for precipitation were unknown and the computational demands are large. Recently, the World Meteorological Organization (WMO) Solid Precipitation Measurement Intercomparison (Goodison et al. 1998) evaluated the relative biases of standard precipitation gauges using a rigorous method (Yang et al. 1998a). The WMO organizing committee for the intercomparison designed the octagonal vertical double fence, surrounding a shielded Tretyakov gauge, to measure “true” precipitation data in a range of climatic conditions. These true precipitation data were used to compare the original data measured by regular gauges. Altershielded and unshielded U.S. 8″ nonrecording gauges were compared and evaluated within the United States. Based on this comparison, Goodison et al. (1998) and Yang et al. (1998a, b) developed different regression models for different types of precipitation (i.e., snow, mixed precipitation, and rainfall) and gauges (i.e., altershielded, unshielded). Adam and Lettenmaier (2003) used the regression models developed by Goodison et al. (1998) to calculate correction factors for precipitation undercatch using observed air temperature and wind speed at selected observation sites and then interpolated correction factors to global grid boxes with a 1° × 1° resolution. Bowling et al. (2003) used the regression models developed by the Sweden Meteorological Institute to correct the precipitation undercatch at the Torne-Kalix river basin for the Project for Intercomparison of Land Surface Parameterization Scheme (PILPS) phase 2e.

However, these methods are site-specific, and therefore they cannot directly be used to adjust the North American Land Data Assimilation System (NLDAS; Mitchell et al. 2004) gauge-based precipitation because 1) it is derived from many diverse types of recording gauges within the U.S. network (i.e., Weighing Gauge, tipping bucket, Fischer and Porter, etc.) and 2) daily wind speed and air temperature are reanalysis products rather than observed values at a given grid box. The different types of recording gauges have different WMO regression models; thus it is not clear which regression model should be used for a given grid box. To use WMO regression models to adjust NLDAS precipitation forcing, only their functional forms are assumed and regression coefficients (parameters) are varied, and the parameters are determined through a calibration process. In this process, model parameter errors and precipitation errors determined by unspecific WMO regression models are adjusted simultaneously so as to minimize the departures between simulated and observed annual streamflow in the northeastern United States.

It should be noted that the precipitation error estimate using the procedures described in this paper may be model-dependent, although the results show that estimated correction factors are comparable to those of Legates and Willmott (1990, hereafter LW). This issue needs further investigation by comparing multiple land surface models, as in the PILPS phase 2e (Bowling et al. 2003). Such comparisons should not focus on different model outputs but rather should focus on comparison of inversed precipitation error estimation derived from the use of the different models.

2. Model, data, method, and experimental design

a. LaD model

The details of the Land Dynamics (LaD) model are described by Milly and Shmakin (2002a), and land-characteristic contributions to spatial variability and interannual variability of global water and energy balances are discussed in Milly and Shmakin (2002b) and Shmakin et al. (2002). Here, we give only a brief summary of the model. The LaD model was developed from Manabe’s (1969) model of land water and energy balances at large scales by adding several features to the original version, including non-water-stressed stomatal resistance to control evaporation processes, a ground heat storage process, a groundwater storage process, and varying land characteristics, such as vegetation root depth, vegetation roughness length, and soil and vegetation albedo. Like other land surface models, the LaD model partitions precipitation into evapotranspiration, runoff, and soil storage, and partitions net radiation into sensible heat flux, latent heat flux, and ground heat storage. Water is stored in snow, glacier ice, root-zone soil water moisture, and groundwater storage. Heat is stored as latent heat of fusion of snow and glacier ice and as sensible heat in the ground. Runoff is generated when root-zone soil water storage exceeds a water holding capacity, which depends on the soil and vegetation type. All runoff passes through a groundwater reservoir of specified residence time, and a river discharge is calculated by summing all grid cells of a basin according to a river routing network (Oki et al. 1999). A bulk stomatal resistance and an aerodynamic resistance control the land surface evapotranspiration process. It should be noted that there is no precipitation interception process in the LaD model.

b. WMO regression model

1) Regression equations

Following Goodison et al. (1998) and Yang et al. (1998a, b), the WMO regression equation for snow, mixed precipitation, and rain is given as follows:
i1525-7541-8-5-1098-e1a
i1525-7541-8-5-1098-e1b
i1525-7541-8-5-1098-e1c
where a, b, c, d, and e are adjustable parameters when altershielded and unshielded gauge types are considered (see Table 2); V(h) is daily averaged wind speed at gauge height h (h = 2 m); and CFs, CFm, and CFr are daily correction factors for snow, mixed precipitation, and rain, respectively.
Wind speed at gauge height h was calculated from 10-m NLDAS grid wind speed using similarity theory (logarithmic profile):
i1525-7541-8-5-1098-e2
where V(H) is NLDAS daily wind speed at 10 m and Z0 is the roughness length (m). According to Sevruk (1982) and Golubev et al. (1992), Z0 = 0.01 m for a winter snow surface and Z0 = 0.03 m for a short grass site in the summer are appropriate values for most sites. In this study, roughness lengths of 0.01 and 0.03 m were used for the colder (November–April) and warmer (May–October) halves of the year, respectively.
Following Forland et al. (1996) and Rubel and Hantel (1999), precipitation type is distinguished between rain, mixed precipitation, and snow as follows:
i1525-7541-8-5-1098-e3a
i1525-7541-8-5-1098-e3b
i1525-7541-8-5-1098-e3c
where T is the NLDAS mean daily air temperature at 2 m.

2) Calculation of monthly mean correction factors

Following Yang et al. (1998b), the bias adjustment precipitation for each day and at each grid point can be expressed as
i1525-7541-8-5-1098-e4a
i1525-7541-8-5-1098-e4b
i1525-7541-8-5-1098-e4c
where Pa is the adjusted daily precipitation, Pg is the NLDAS daily precipitation, ΔPw is wetting loss, ΔPe is evaporation loss, and CF is a daily correction factor calculated using the WMO regression equations described above. The subscripts r, m, and s denote rain, mixed precipitation, and snow, respectively. Wetting loss is 0.15 mm day−1 for rain (Adam and Lettenmaier 2003) and 0.075 mm day−1 for mixed precipitation and snow. Evaporation loss is 0.05 mm day−1 for all types of precipitation (see Forland et al. 1996).

c. Data

The LaD model parameters are effective depth of the root zone, available water capacity, bulk heat capacity of the ground, thermal conductivity of the ground, surface roughness length, non-water-stressed bulk stomatal resistance, groundwater residence time, snow-free surface albedo, and snow-masking depth. All parameter values are taken from a lookup table (Milly and Shmakin 2002a). These model parameters depend on soil and vegetation types, which are taken from the Global Soil Wetness Project phase 2 (GSWP2; see http://www.iges.org/gswp/) and Matthews (1983), respectively.

Six years (1997–2002) of NLDAS retrospective data for the northeastern United States are used as atmospheric forcing (Cosgrove et al. 2003). This dataset features a 0.125° spatial resolution. It includes surface air temperature at 2-m height, surface specific humidity at 2-m height, meridional and zonal wind speed at 10-m height, downward shortwave radiation, downward longwave radiation, and precipitation, which is a combination of gauges, satellite precipitation, and radar products. For the northeastern United States, satellite and radar precipitation data are used only to replace missing gauge measurement (less than 10%). Therefore, for this region, NLDAS precipitation is based largely on rain gauge measurements. However, there is no bias correction applied (i.e., undercatch adjustment) for NLDAS precipitation (B. Cosgrove 2005, personal communication). As expected, there is large precipitation undercatch for the NLDAS precipitation dataset.

Five years (1998–2002) discharge data at 9 U.S. Geological Survery (USGS) sites (Table 1; Fig. 1) in the northeastern United States are used to evaluate the performance of the LaD model for streamflow simulations. The daily discharge data are available online (see http://water.usgs.gov/waterwatch/). Annual-mean values are calculated for this study. The quality of the streamflow data is high for these basins because they were carefully selected and used in Milly and Shmakin (2002b). The estimated errors are 5% for annual streamflow (P. C. D. Milly 2004, personal communication). The basic assumption of this current study is that errors in observed streamflow are much smaller than those in observed precipitation. This assumption has important implications for the calibration method presented here. It presumes that the streamflow data are of higher quality than the precipitation forcing (mainly due to undercatch of gauge for snowfalls).

d. Very Fast Simulated Annealing (VFSA)

The VFSA is an optimization algorithm. One may use the temperature construct within the Metropolis algorithm (Metropolis et al. 1953) to locate the global minimum of the error function by very slowly lowering the temperature parameter within
i1525-7541-8-5-1098-e5
where P is the probability of acceptance of a new parameter set with positive change of error function values, ΔE is the change of the error functions as calculated by the new and previous parameter sets (see section 2e), and T is a control parameter analogous to temperature. If the change is negative, this new parameter set is accepted. If the change is positive, and if and only if P is less than a randomly generated number between 0 and 1, the new parameter set is rejected. This iterative process is analogous to the annealing process within a physical system where the lowest energy state between atoms or molecules is reached by the gradual cooling of the substance within a heat bath. Because of this physical analogy, the algorithm is called simulated annealing. To enhance the ability of simulated annealing to converge to the global minimum of the error function, Ingber (1989) introduced a new procedure for selecting parameter sets according to a temperature-dependent Cauchy distribution. This modified simulated annealing algorithm is called very fast simulated annealing. Ingber’s algorithm can be described as follows.
Let us assume that a model parameter mi at kth iteration (annealing step k) is represented by m(k)i such that
i1525-7541-8-5-1098-e6
where mmini and mmaxi are the minimum and maximum values of the model parameter mi. This model parameter value is perturbed at iteration (k + 1) using m(k+1)i = m(k)i + yi(mmaximmini), mminim(k+1)immaxi and yi ∈ [−1, 1]. The Yi is generated from the distribution gT(y) = ΠNMi=1{1/2(|yi| + Ti)ln[1 + (1/Ti)]} = ΠNMi=1gTi(yi) and has a cumulative probability GTi = (1/2) + [sgn(yi)/2]〈ln{1 + [(yi)/Ti]}/ln[1 + (1/Ti)]〉. Here NM is the number of model parameter sets. Ingber (1989) showed that for such a distribution, the global minimum can be statistically obtained by using the following cooling schedule
i1525-7541-8-5-1098-e7
where T0i is the initial temperature for model parameter i, and ci is a parameter to be used to control the temperature. The acceptance rule of the very fast simulated annealing algorithm is the same as that used in the Metropolis rule. However, very fast simulated annealing is more efficient when compared with simulated annealing.

e. Experimental design

As discussed above for a given model, errors in simulations of mean annual streamflow are mostly due to errors in model parameters and errors in forcing data (e.g., precipitation). As indicated by Milly and Shmakin (2002b), for the LaD model, the major streamflow simulation errors are associated with the specification of minimum stomatal resistance and rooting density for a given vegetation type. Errors in forcing data come mainly from undercatch of precipitation, particularly for solid precipitation (Yang et al. 1998a, b). Five parameters related to snow, mixed precipitation, and rain adjustments are used to control precipitation errors (see Table 2).

In this study, a calibrated model parameter [mp; e.g., minimum stomatal resistance, (RSMIN), rooting density, and ZR] is expressed as Fm × mpij, where mpij is a spatially variable model parameter and Fm is the calibration factor for model parameter mpij, where i and j denote longitude and latitude, respectively. For this study, Fm is taken as 10L1 for minimum stomatal resistance and 10L2 for rooting density, respectively. Ranges of L1, L2, and five parameters related to precipitation errors are given in Table 2. The model performance E (error function or cost function) is measured by using the root-mean-square deviation between the simulated and observed annual runoff ratios during 1998 and 2002. E is calculated as
i1525-7541-8-5-1098-e8
where N is the number of basins with suitable observational data in the northeastern United States, M is the number of years, and Onm, Snm, and Pnm are observed and simulated runoff and observed precipitation, respectively.

The six experiments undertaken in this study are listed in Table 3. These include a default simulation, which uses original NLDAS data without any adjustment and the model parameter values calibrated by Milly and Shmakin (2002b); a varied forcing (VF) experiment, wherein NLDAS precipitation is adjusted when model parameters are fixed; a varied model parameters (VM) experiment, wherein model parameters are adjusted when NLDAS precipitation is fixed; a varied forcing and model parameters (VFM) experiment, wherein both NLDAS precipitation and model parameters are adjusted; a VF1 experiment, wherein NLDAS precipitation is adjusted when L1 = 0.35 and L2 = 0.60, respectively; and a VF2 experiment, wherein NLDAS precipitation is adjusted when L1 = L2=-0.6, respectively. Model parameter values for the VF1 experiment are the original values used by Milly and Shmakin (2002a) without calibration. Those parameter values for VF2 are similar (minimum stomatal resistance is reduced by a factor of 4 in this study, and it is reduced by a factor of 5 for a coupled case) to those used in the GFDL global atmosphere and land model (Anderson et al. 2004). The purpose of the experiments VF1 and VF2 is to investigate the impact of model parameter errors on adjusting NLDAS precipitation and calibration of the LaD model.

Milly and Shmakin (2002b) used a manual method to optimize the LaD model. This study uses very fast simulated annealing, an automated optimization algorithm, to search for optimal model parameter values and an optimal precipitation adjustment. The LaD model was run from 1997 to 2002, and the simulated annual runoff from the year 1998–2002 is used to calculate E. This means that 1997 is used as a spinup period. As indicated by Milly and Shmakin (2002a), one year spinup time is sufficient for the LaD model. Very fast simulated annealing usually takes 30–40 experiments to find optimal parameter values for each experiment.

3. Results

a. Comparison of default run with observed streamflow

Figure 2a shows observed and simulated annual streamflow at 9 basins in the northeastern United States for the 5-yr period from 1998 to 2002. The results show that almost all simulated streamflow is smaller than observed streamflow. Large negative biases between simulated and observed runoff ratios indicate that annual runoff ratios are also underestimated (Fig. 3) when compared with observed annual runoff ratios.

Generally, the results suggest that the LaD model underestimates observed streamflow in the northeastern United States. This underestimation results from precipitation forcing errors, LaD model parameter errors, LaD model errors, and/or a combination of the three errors. Milly and Shmakin (2002b) carefully calibrated the LaD model using high-quality precipitation data by excluding all basins with large precipitation errors (Milly and Dunne 2002a). Their results show that the LaD model is able to simulate annual streamflow without large bias. Therefore, we can expect a low possibility that this underestimation results from the LaD model and/or model parameters. Furthermore, Lohmann et al. (2004) show that all four models in the NLDAS project also underestimate observed streamflow in the northeastern United States. Therefore, this underestimation is thought to be caused by systematic precipitation bias. Because topographic effects on precipitation in the northeastern United States are small (Adam et al. 2006), the main bias is thought to result from undercatch of precipitation due to wind effects at gauges.

b. Calibration of LaD model

Figures 2b–d show the observed and simulated streamflow at 9 basins in the northeastern United States for the period from 1998 to 2002 when NLDAS precipitation and/or model parameters are adjusted by calibrating observed annual streamflow. The results indicate that all calibrations (e.g., VF, VM, and VFM) significantly improve streamflow simulations. The RMSE is reduced from 186.8 mm yr−1 to 124.3 mm yr−1, 126.0 mm yr−1, and 124.0 mm yr−1 for the VF, VM, and VFM experiments, respectively. Furthermore, biases are reduced from −151 mm yr−1 to −11.6 mm yr−1, 4.9 mm yr−1, and 6.3 mm yr−1 for the three calibration experiments. This decrease is also significant for annual runoff ratios (Fig. 3). Therefore, calibrations indeed improve streamflow simulations for the LaD model in the northeastern United States. However, the improvement of the streamflow simulation in the VM experiment depends on a more consistent decrease in the evaporation (Fig. 4b) as compared to the VF and VFM experiments (Figs. 4a,c). This is a result of the impacts of a systematic precipitation bias on the calibration of the LaD model. To match the observed streamflow, minimum stomatal resistance is increased 70% from its default value (Fig. 5). This large minimum stomatal resistance hinders evapotranspiration processes, and thus more precipitation is partitioned into runoff and the errors between observed and simulated streamflow are minimized. Therefore, the LaD model generates smaller evapotranspiration than the default simulations because the NLDAS precipitation is smaller than the bias-adjusted precipitation.

Evapotranspiration from the VF experiment is similar to that from the default simulation (Fig. 4a) because they have similar minimum stomatal resistance values (Fig. 5). The increase in simulated streamflow results from increasing the precipitation. VFM has slightly larger evapotranspiration than VF because VFM has smaller minimum stomatal resistance than VF, although they have similar precipitation (Fig. 4d). Therefore, when land surface models are carefully calibrated (i.e., LaD), one can only adjust precipitation errors as in the VF experiment. However, for land surface models that are not carefully calibrated, it is suggested that any calibration should simultaneously incorporate both model parameter errors and precipitation errors simultaneously.

c. Comparison of optimal adjustment factors with LW results

Optimal parameter values for six experiments are listed in Table 4. Optimal adjustment factors for VF, VFM, VF1, and VF2 are shown in Fig. 6. For snow adjustment, VF, VFM, and VF2 have similar correction factors, especially when wind speed is smaller than 3 m s−1. For rain adjustment, VF and VF1 have similar correction factors, and VFM and VF2 have similar correction factors. For mixed precipitation, VF and VF2 have similar correction factors, and VF1 has the smallest correction factors similar to the snow adjustment case. The effects of VF1 and VF2 will be discussed in detail in the following section. Figure 7 shows the optimal annual correction factors for the VF and VFM experiments and the LW annual correction factors for 9 basins in the northeastern United States. The results show that magnitudes of optimal correction factors are comparable with the LW results for 9 basins (Fig. 7), although VFM and VF show larger correction factors, in particular for snow adjustment in winter. The reason may be 1) differences between observed and reanalysis wind speeds in this region and 2) the inconsistency between the exact periods for this study and the LW study (this study covers 1998–2002, whereas the LW results are 1920–80). Although this comparison is for a different period, it still yields some insight into how our correction factors behave with respect to each other.

d. Effect of model parameter errors on estimation of precipitation

To investigate the impact of model parameter errors on the estimation of uncertainty in the NLDAS precipitation, the VF1 and VF2 experiments were conducted. The VF1 and VF2 experiments are compared with the VF experiment. The increasing (decreasing) minimum stomatal resistance experiments show that there are larger RMSE and biases between observed and simulated annual runoff ratio (Fig. 8a). VF1 (VF2) yields less (more) estimated precipitation (Figs. 9a,b) owing to smaller (larger) wind correction factors (Fig. 6). This unreasonable estimation of precipitation results in less (more) evapotranspiration than in the default simulations (Figs. 9c,d). Furthermore, VF1 shows large streamflow simulation errors (Figs. 8a,9e), and VF2 cannot improve streamflow simulation even when observed streamflow is calibrated (Fig. 9f).

The physical explanations of VF1 and VF2 experiments are as follows. For the VF1 experiment, large minimum stomatal resistance greatly hinders evapotranspiration, resulting in much smaller evapotranspiration than in the default simulation (Fig. 8b). More water is partitioned into streamflow from precipitation. Therefore, simulated streamflow can easily match observed streamflow even though precipitation itself does not increase (Fig. 6). For the VF2 experiment, the smaller minimum stomatal resistance (Fig. 8b) hinders less, resulting in smaller streamflow than in the default simulations (Fig. 9). To match observed streamflow with simulated streamflow, precipitation must be significantly increased (Fig. 6). However, most of the additional increased precipitation is partitioned into evapotranspiration, thus the LaD model still exhibits large biases between simulated and observed streamflow (Fig. 9e).

Generally, the model parameter errors significantly affect estimation of the optimal precipitation in the northeast United States. Unreasonable model parameters may generate erroneous estimates for snow, rain, and mixed precipitation. Therefore, the most reliable method to calibrate a land surface model is to simultaneously optimize both model parameters and precipitation errors (e.g., VFM).

e. Discussion

A simple schematic diagram illustrating effects of the model parameter errors, model errors, and forcing errors on the calibration of land surface models is provided in Fig. 10. As discussed above, land surface models divide precipitation into evapotranspiration and runoff. This partitioning is controlled by the minimum stomatal resistance in the LaD model. Because the LaD model lacks evapotranspiration from an interception store and from wet ground, errors in the specification of minimum stomatal resistance will result in runoff and evapotranspiration simulation errors. As Milly and Shmakin (2002b) argued, the absence of these additional pathways for evaporation in the LaD model would be compensated, in the calibrated model, by an artificial reduction in the resistance to vapor flux through foliage. However, forcing errors cannot be compensated for by any calibration process. Forcing errors arise mostly from the errors in the precipitation and radiation forcing. This issue has been discussed by Xia et al. (2005) for a local water flux study and by Milly and Dunne (2002b) for a macroscale water flux study. In this study, neither precipitation errors from topographic effects nor radiation errors are considered. Only precipitation error associated with gauge undercatch due to wind blowing, wetting loss, and evaporation loss is considered.

This study provides an example of using annual streamflow observations to adjust the systematic bias of precipitation forcing (coming from gauge undercatch) for a land surface model applied over a midlatitude cold region. It is also an exploration of a previous study using catchment site research datasets (Xia et al. 2005). It is acknowledged that application of WMO regression models, reanalysis wind speed, and reanalysis air temperature may introduce additional errors. However, the effect of these errors on this study is assumed to be small because the study from Xia (2006) has shown that uncertain reanalysis wind speed and air temperature lead to small errors when compared with the precipitation adjustment itself. Furthermore, model simplification and model parameters may also lead to runoff simulation errors although they have been carefully calibrated using observed annual streamflow. Because WMO regression models are derived from daily data, for this study only, daily averaged air temperature is used to determine the phase of precipitation (rain or snow), although hourly air temperature exists. This is another potential source of inconsistency in the adjustment scheme. Given the region considered, the precipitation phase may not necessarily reflect the daily averaged temperature.

It should also be noted that some basins (e.g., basin 1 and 2, and basin 3, 4, and 6 in Table 1) have nested parts and then they are not independent. These nested river basins may affect the calibration results. However, the sensitivity test applied to six independent basins shows little impact on the research results after the three nested river basins are removed from 9 river basins. In future studies, additional independent river basins, longer forcing and calibration data (e.g., 10 yr), and more representative investigation regions (e.g., the Rocky Mountains, Canada, and North Europe) should be explored. For the Rocky Mountains, determining how to combine the adjustment of systematic biases in precipitation due to wind blowing with adjustments due to topography effects is also a critical issue.

In addition, it is assumed that the default model values for evaporation are the right ones in this study. The LaD model was not calibrated for energy partition because of a lack of observed energy fluxes (i.e., sensible heat fluxes and latent heat fluxes) and observed water fluxes (i.e., evaporation), and therefore the assumption of correctness for evaporation needs to be justified in the future when observed energy and water fluxes are available for these basins.

4. Conclusions

In this paper, the LaD model is calibrated using very fast simulated annealing and observed annual streamflow at nine basins in the northeastern United States. This calibration is quite different from previous works (Gupta et al. 1999; Milly and Shmakin 2002b; Xia et al. 2002, 2004a) in which it is assumed that the forcing data are accurate or only forcing data with small errors are used (forcing data with large errors are removed). Neither method adequately addresses the forcing data error issue, because calibrating land surface models is still needed for cold regions, where forcing data errors are large. The important assumption of the approach presented in this study is that the evaluation data (observed annual streamflow) are unquestionably of higher quality (i.e., less uncertainty/error) than the forcing data (i.e., precipitation) to be adjusted. This assumption is quite reasonable because undercatch of rain gauge results in larger errors than errors in observed streamflow.

This study uses forcing data with large errors to calibrate the LaD model by use of observed annual streamflow. The WMO regression relationships are used to adjust the NLDAS precipitation. This work is an exploration of the previous work (Xia et al. 2005) from a catchment site to a regional area but using an update method for precipitation adjustment. The results show that all three calibrations (e.g., VF, VM, and VFM) improve streamflow simulations at nine basins in the northeastern United States. However, improvement of the VM experiments is at the expense of a degradation in simulated evapotranspiration. A by-product of calibrating the LaD model is the optimal estimate of systematic precipitation bias due to wind, wetting loss, and evaporation loss. This optimal estimate is completed by relating optimal WMO regression models to daily reanalysis wind speed and air temperature. The bias correction process for the NLDAS precipitation is very convenient and is easily applicable to an operational analysis. In addition, the impacts of model parameter errors on the calibration of the LaD model and the estimation of the optimal systematic precipitation bias are analyzed. The results show that model parameter errors result in large streamflow simulation errors even though the LaD model is calibrated only for errors in precipitation. This result shows again that simultaneous calibration of both model parameters and forcing data (e.g., precipitation) is important for cold regions. However, it should be noted that the calibration process may generate incorrect optimal estimates of systematic precipitation bias when errors of model parameters are large. Therefore, model parameter errors significantly affect the calibration of a land surface model and optimal systematic bias estimates.

Acknowledgments

Y. Xia wishes to acknowledge financial support from NOAA Grant NA17RJ2612 and technical support from K. A. Dunne, Fanrong Zeng, and Sergey Malyshev at GFDL. Y. Xia also appreciates Dr. C. J. Jackson at the Institute for Geophysics at University of Texas at Austin for providing VFSA code, Dr. Stephen Dery at GFDL for his editorial recommendations for the original draft, Dr. Curtis Marshall at NCEP/EMC for his editorial help for the draft revised, and beneficial discussions with Dr. P. C. D. Milly.

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Fig. 1.
Fig. 1.

Locations of streamflow gauges used in this study.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 2.
Fig. 2.

5-yr (1998 to 2002) observed and simulated annual streamflow at nine basins in the northeastern U.S. for (a) default simulation, (b) VF experiment, (c) VM experiment, and (d) VFM experiment.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 3.
Fig. 3.

RMSEs and bias between observed and simulated annual runoff ratios at nine basins in the northeastern U.S. for the period from 1998 to 2002.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 4.
Fig. 4.

Simulated annual evaporations for (a) VF and default, (b) VM and default, (c) VFM and default, and (d) estimated precipitation for nine basins in northeastern U.S. for the period from 1998 to 2002.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 5.
Fig. 5.

Normalized optimal and default RSMIN for four different experiments.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 6.
Fig. 6.

Daily correction factors derived from Eq. (1) for (a) snow, (b) rain, and (c) mixed precipitation when different optimal WMO model parameters are used.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 7.
Fig. 7.

Mean annual correction factors for nine basins in the northeastern U.S. for three experiments [basin number is shown in Table 1. Daily precipitation is adjusted by daily correction factors as shown in Fig. 5, and is accumulated to annual precipitation. 5-yr (1998 to 2002) averaged annual precipitation is calculated, and then is divided by default mean annual precipitation to get this figure.].

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 8.
Fig. 8.

(a) RMSE and bias between observed and simulated runoff ratios and (b) normalized optimal minimum stomatal resistance RSmin for VF1, VF, and VF2 experiments.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 9.
Fig. 9.

Optimal estimates for (a) mean annual precipitation, (b) mean annual evapotranspiration, and (c) mean annual streamflow at nine basins in the northeastern United States for the period from 1998 to 2002.

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Fig. 10.
Fig. 10.

A simple schematic diagram about error sources for the LaD land surface model (errors represented in solid line are studied in this paper, and errors represented in dashed line are not studied in this paper).

Citation: Journal of Hydrometeorology 8, 5; 10.1175/JHM618.1

Table 1.

Nine calibrated basins in this study.

Table 1.
Table 2.

Calibration parameters, and their descriptions and ranges.

Table 2.
Table 3.

Summary of the experiment design. Parameter assignments (V = Variable, C = Fixed) are explained in Table 1. Here M indicates model parameters, and F indicates forcing data (i.e., precipitation).

Table 3.
Table 4.

Optimal parameter values for 6 experiments.

Table 4.
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