Improving Snow Process Modeling with Satellite ...

Improving Snow Process Modeling with Satellite-Based Estimation of Near-Surface-Air-Temperature Lapse Rate Lei Wang1,2,3*, Litao Sun1,3, Maheswor Shrestha4, Xiuping Li1, Wenbin Liu5, Jing Zhou1, Kun Yang1,2, Hui Lu6, Deliang Chen7

1

Key Laboratory of Tibetan Environmental Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China 2

CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, China 3 4

5

University of Chinese Academy of Sciences, Beijing, China

Water and Energy Commission Secretariat, Kathmandu, Nepal

Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China 6

Center for Earth System Science, Tsinghua University and Key Laboratory of Numerical Simulation for Earth System, Ministry of Education, Beijing, China 7

Regional Climate Group, Department of Earth Sciences, University of Gothenburg, Gothenburg, Sweden

Corresponding author: Lei Wang, Dr., Prof. Key Lab. of Tibetan Environmental Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences No. 16 Lincui Road, Chaoyang District, Beijing 100101, China Tel.: +86-10-8409-7107

Fax: +86-10-8409-7079

Email: [email protected] This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/2016JD025506 © 2016 American Geophysical Union. All rights reserved.

Key points: (1) Distributed snow modeling at a large, cold river basin (upper Yellow River Basin). (2) Lapse rate has a great impact on the snow and streamflow simulations. (3) Satellite-based estimates of lapse rate lead to improved snow process modeling.

Abstract: In distributed hydrological modeling, surface air temperature (Tair) is of great importance in simulating cold region processes, while the near-surface-air-temperature lapse rate (NLR) is crucial to prepare Tair (when interpolating Tair from site observations to model grids). In this study, a distributed biosphere hydrological model with improved snow physics (WEB-DHM-S) was rigorously evaluated in a typical cold, large river basin (e.g., the upper Yellow River basin), given a mean monthly NLRs. Based on the validated model, we have examined the influence of the NLR on the simulated snow processes and streamflows. We found that the NLR has a large effect on the simulated streamflows, with a maximum difference of greater than 24 % among the various scenarios for NLRs considered. To supplement the insufficient number of monitoring sites for near-surface-air-temperature at developing/undeveloped mountain regions, the nighttime MODIS LST is used as an alternative to derive the approximate NLR at a finer spatial scale (e.g., at different elevation bands, different land covers, different aspects, and different snow conditions). Using satellite-based estimation of NLR, the modeling of snow processes has been greatly refined. Results show that both the determination of rainfall/snowfall and the snow pack process were significantly improved, contributing to a reduced summer evapotranspiration and thus an improved streamflow simulation.

Keywords: lapse rate; distributed hydrological model; water and energy cycle; snow process; MODIS land surface temperature.

© 2016 American Geophysical Union. All rights reserved.

1.

Introduction Hydrological processes are sensitive to air temperature ( Tair ), particularly in cold

regions where Tair affects the melting of snow, glaciers, and permafrost, and determines the land-atmosphere exchanges of water and energy (De Scally, 1997; Richard and Gratton, 2001; Zuzel and Cox, 1975). As a result, accurate modeling of spatially-distributed Tair is crucial to hydrological models when applying them to cryosphere studies (Ferguson, 1999; Minder et al., 2010; Petersen and Pellicciotti, 2011). As an important input for hydrological models, surface Tair is usually interpolated from meteorological station observations using near-surface-air-temperature lapse rate (NLR). Lapse rate is commonly defined as the rate at which atmospheric temperature decreases with increasing altitude at a specific location. A steep lapse rate implies a rapid decrease in temperature with altitude (a sign of instability). In distributed land surface hydrological modeling, a NLR is always needed to bridge the surface Tair (usually 2 m) at different locations with different altitudes (e.g., a meteorological station and its adjacent model grids). By using the statistical NLRs obtained from Tair observations (see Section 3.2 for details), we can interpolate the Tair from station data to gridded cells that cover a river basin (e.g., Li et al., 2011). NLR is a key parameter when preparing distributed model inputs of Tair , and thus, it can have significant influence on the simulations of cryosphere components and thereby streamflows. This has highlighted the importance of using a realistic NLR when Tair is interpolated from point measurements to the grids. The most popular method is to use a fixed NLR ranging from 6.0 to 6.5 K/km to generate gridded Tair inputs for distributed hydrological models (Gao et al., 2012, 2014; Immerzeel, 2012; Singh et al., 2006). However, fixed NLR may not reflect real conditions (Minder et al., 2010; Shea and Moore, 2010). In fact, NLR varies on diurnal and seasonal time scales due to changes in © 2016 American Geophysical Union. All rights reserved.

sensible heat flux between the free atmosphere and underlying surface (Gardner et al., 2009); and it also changes spatially depending on macro topography (Yoshino, 1975; Lundquist and Flint, 2006). Given the importance of NLR, a number of studies have investigated the spatiotemporal variability of NLR over various regions (Bolstad et al., 1998; Shea et al., 2004; Marshall et al., 2007; Gardner et al., 2009; Li et al., 2013; Li Y et al., 2015; Gao et al., 2015). However, very little has been done toward improving quantitative understanding of the influence of the spatiotemporally-variable NLR on hydrological simulations in cold regions. This could largely be attributed to insufficient ground-based observation stations for Tair , in particular over the mountainous regions. Since observations of Tair are often sparse and unevenly distributed, satellite-based estimation of Tair and its related variables (e.g., diurnal temperature range) from Land surface temperature (LST) is a promising alternative (e.g., Sun et al., 2006a, 2006b). LST is a key parameter in climatic and environmental studies and can be obtained by satellite remote sensing (Liang, 2001; Pinheiro et al., 2004; Wan and Dozier, 1996). At present, the MODIS LST products (Wan et al., 2002; Wan, 2008) are widely used to retrieve Tair at fine spatial resolutions (Vogt et al., 1997; Zakšek and Schroedter-Homscheidt, 2009; Vancutsem et al., 2010; Zhu et al., 2013; Sun et al., 2014; Shamir and Georgakakos, 2014), due to its reasonable accuracy and strong dependence on Tair . It is found that the MODIS LST agrees well with the observed Tair during the nighttime (Wang et al., 2008), but tends to overestimate the Tair during the daytime, particularly during summer and in non-forested regions (Wang et al., 2009b; Zhang et al., 2014). Therefore, to supplement the insufficient number of Tair monitoring sites over developing mountain regions (e.g., the Tibetan Plateau), nighttime MODIS LST may be used as an alternative to estimate NLRs for Tair © 2016 American Geophysical Union. All rights reserved.

at a finer spatial scale (e.g., at different elevation bands). It can be helpful to refine the spatially-distributed air temperature inputs for hydrological modeling, since the MODIS LSTs have plenty of grid points (“virtual observation sites”) that cover the studied river basins. This study aims to provide more accurate surface Tair by applying satellite-based estimation of NLR; and this has great implications for improving the modeling of snow processes in a typical cold river basin. This paper is organized as follows. Section 2 describes a distributed biosphere hydrological model with snow physics. The methodology and datasets are introduced in Sections 3 and 4. Section 5 depicts the evaluations of the hydrological model. Section 6 demonstrates the model’s sensitivity to the NLR, and the use of MODIS nighttime LST to improve modeling of snow processes. Section 7 summarizes conclusions.

2. Distributed Biosphere Hydrological Model The distributed biosphere hydrological model used for this study is the water and energy budget-based distributed hydrological model, the so-called WEB-DHM (Wang et al., 2009a, b, c). The model was developed by fully coupling a land surface scheme (Sellers et al., 1996a) with a geomorphology-based hydrological model (Yang et al., 2004). The model (see Figure 1) enables consistent descriptions of water, energy, and CO2 fluxes at a basin scale. First, the hydrologically-improved SiB2 (Wang et al., 2009c) describes the transfer of turbulent fluxes (energy, water, and carbon) between the atmosphere and land surface for each grid independently. Second, the hydrological sub-model redistributes water moisture


laterally through simulating both surface and subsurface runoffs using grid-hillslope discretization and then flow routing in the river network (Wang et al., 2009a). In order to physically describe the internal energy exchanges within snow packs, the single-layer snow physics of WEB-DHM has been enhanced significantly with a three-layer snow module (Figure 2). The snow-improved version (hereafter WEB-DHM-S; Shrestha et al., 2010) was developed by incorporating the three-layer energy balance snow scheme of the Simplified Simple Biosphere 3 model (Xue et al., 2003) and the prognostic albedo scheme of the Biosphere Atmosphere Transfer Scheme (Yang et al., 1997) into the WEB-DHM model. This study uses WEB-DHM-S for simulation. In WEB-DHM-S, the Tair (air temperature in canopy air space, K) is directly used for calculating the sensible heat fluxes following the method of Sellers et al. (1996a). H c  c p Tc  Tair  / rb

(1)

H g  c p Tg  Tair  / rd

(2)

where H c is the sensible heat flux from the vegetation canopy to the canopy air space (W m-2); H g is the sensible heat flux from the ground to the canopy air space (W m-2);  is the air density; c p is the specific heat of the air; Tc is the canopy temperature (K); Tg is the soil surface temperature (K); rb is the bulk canopy boundary layer resistance (s m-1); and rd is the aerodynamic resistance between the ground and the canopy air space (s m-1).

Equations (3), (4), and (5) were used to solve 3 prognostic physical state variables: Tc ,

Tg , and deep soil temperature ( Td ) (see Shrestha et al., 2010). Canopy

Cc

Soil surface

Cg

Tc  Rnc  H c  Ec   cs t

Tg t

  K ( Z1 )

Tsn ( Z1 ) 2C g Tg  Td   Z d

(3) (4)


Cd

Deep soil where

Rnc

Td 2C g (Tg  Td )  t  d (365 )1 2

is the absorbed net radiation of the canopy (W m-2);

(5) Ec

is the

evapotranspiration rate of the canopy (kg m-2 s-1); C c , C g , and C d are the effective heat capacities (J m-2 K-1);  is the latent heat of vaporization (J kg-1);  d is the day length (s);

K ( Z1 ) is the effective thermal conductivity at the snow/soil interface; Tsn ( Z1 ) is the snow temperature at the snow/soil interface; and  cs is the energy transfer due to phase changes in the canopy interceptions (W m-2). Meanwhile, the total evapotranspiration comprises four components: evaporation (Sellers et al., 1996a; Wang and Koike, 2009) from the canopy interception ( E ci ), transpiration of soil water extracted by the root system and lost from the dry fraction of the canopy ( E ct ), loss from soil surface interception ( Egi ), and evaporation of soil moisture from within the surface soil layer ( Egs ).

(

)

(6)

λEci = [(e* (Tc ) - ea ) / rb ] ρc p / γ Wc Ktc

)

(7)

Egi  e* Tx  - ea / rd c p /  Wg Ktg

(8)

Egs  hsoil e* Tg - ea /rsoil  rd c p /  1- Wg 

(9)

λEct = [(e* (Tc ) - ea )/ (1/gc + 2rb )] ρc p /γ (1 - Wc )

(

where

e* T  is the saturation vapor pressure at temperature T ; ea is the vapor pressure

in the canopy air space; Tx  Tsnow if M gs  0 , Tx  Tg if M gw  0 ; Tsnow is the temperature of the snowpack and its underlying surface soil layer;  is the psychrometric constant; Wc is the canopy wetness-snow cover fraction; W g is the soil wetness-snow © 2016 American Geophysical Union. All rights reserved.

cover fraction; KTc ,g = 1 when M c , gw  0 , KTc,g = λ (λ + λs ) , when M c , gs  0 ; s is the heat of sublimation; g c is the canopy conductance; hsoil is the relative humidity of the  1g RTg

soil pore space, hsoil  e

when

e* Tg   ea , hsoil  1 when

e* Tg   ea ,  1 is the

soil moisture potential of the surface layer, and g is the acceleration due to gravity; R is the gas constant; and rsoil is the soil resistance. It is expected that more accurate Tair inputs, with help of realistic NLR, would contribute to more reliable estimates of temperatures (Tc, Tg, and Td) and improve the simulations of sensible heat fluxes and latent heat fluxes (evapotranspiration and its four components Eci, Ect, Egi, and Egs). This will further contribute to improved estimates of water interception stores (liquid water and snow at canopy and ground, M c and M g ), soil moisture profiles as well as groundwater levels, and finally, result in better discharge simulations. This is because the physically-based hydrological model (WEB-DHM) calculates the discharges comprising three components (surface, subsurface, and groundwater flows; Wang et al., 2009a). Surface flow is described by the Manning equation, and it largely depends on the ground water interceptions. Subsurface flow is calculated by Darcy’s law and is mainly determined by the soil moisture conditions. Groundwater flow is also simulated with Darcy’s law and is largely controlled by the groundwater level.


3. Methodology 3.1. Study area and experiment design To investigate the influence of NLR on hydrological simulations involving cryosphere, we selected a typical, large cold region, the upper Yellow River basin, as our study area. The basin has an area of over 124,000 km2, and thus is expected to have some spatial variability in terms of NLR. Yellow River, as the major river in China, is considered the cradle of Chinese civilization. For thousands of years, it has always been a key water source for the millions of people who live in northern China (Xu et al., 2005). The upper Yellow River basin (see Figure 3) is the primary region providing surface water resources, contributing more than 35 % of the total streamflows in the whole Yellow River Basin (Chen and Liu, 2007; Xu et al., 2009). The basin is covered by snow in the cold seasons and at high elevations; and therefore, the modeling of snow processes is vital for simulating/predicting the streamflows. As shown in Table 1, a control run (CTRL) and 9 additional experimental runs (EXP1EXP9) have been designed for investigating the influence of NLRs on cryosphere hydrological simulations. The control run refers to the hydrological (WEB-DHM-S) simulation using mean monthly NLRs over a 10-year period (see Figure 4b), which were estimated from the monthly mean Tair observations averaged over 1996-2005 using a linear regression method (see Section 3.3 for details). The runs of EXP1-EXP8 are the same as the control run, but using different NLRs (see Table 1) for interpolating the Tair (spatiotemporally variable) from point station data to grid cells that covers the whole river basin; while EXP9 is the same as EXP8, but keeping the same snowfall as EXP2. Taking EXP2, EXP8, and EXP9 into consideration, the different results of EXP8 and EXP9 can help quantify the impact of the NLR on the increased/reduced snowfall and thereby the snow hydrological simulations (since the new NLR derived Tair influences the rainfall/snowfall determination). On the other


hand, keeping the snowfall constant (as in EXP2 and EXP9) will assist in determining how much of the changes in the simulated results are due to snow pack processes. It should be noted that compared to EXP1, the NLRs in EXP2 are more site-specific, and thus more reasonable. Meanwhile, compared to EXP2, the NLRs in the CTRL, EXP3, and EXP4 can better depict the temporal variability of the NLRs on different time scales. Furthermore, in contrast to the runs of the CTRL and EXP1-EXP4, the NLRs in EXP5-EXP8 were derived using a gridded satellite-based LST product, and thus may better represent the spatial variability of the NLRs.

3.2. Estimating NLRs from ground-based Tair observations A simple linear regression method is adopted in our study, which refers to only the influence of elevation (longitude and latitude are not included here due to the small size of the region covered) on the NLR, since other factors (except elevation) such as latitude and the distance inland would not unduly influence the NLR calculations for a river basin. Y  a0  a1 X

(10)

where Y is the Tair at each station; X is the elevation of each station; a0 and a1 are the regression coefficients; and a1 designates the estimated NLRs for the time period corresponding to Y. For the control run (CTRL), using Equation (10), the NLRs can be estimated for the study basin, based on the monthly mean Tair averaged over 1996-2005. For EXP2, EXP3, and EXP4, the NLR estimates were based on the long-term (1996-2005) mean Tair, the monthly mean Tair from 1996 to 2005, and the monthly-mean hourly Tair averaged over 1996-2005, respectively. © 2016 American Geophysical Union. All rights reserved.

3.3. Estimating NLRs from gridded MODIS nighttime LSTs For EXP5-EXP7, using Equation (11), the NLRs were estimated for any specific part (e.g., an elevation band) of the study basin using linear regression, based on the mean MODIS nighttime LSTs averaged over 2001-2004. Here, the MODIS nighttime LST data in 2005 were excluded due to missing data in November.

Y *  a0  a1 X * *

*

(11)

where Y* is the nighttime LST of each MODIS grid; X* is the elevation of each MODIS grid; a0

*

*

*

and a1 are the regression coefficients; and a1 designates the estimated

approximate NLRs for the time period corresponding to the averaged LST.

4. Datasets 4.1 Model inputs The datasets used for WEB-DHM-S simulations are given below. Time-invariant data input for WEB-DHM-S includes topography, land cover, and soil. The digital elevation model (DEM; Figure 3, top) used was from the SRTM 90-m Digital Elevation Data (Jarvis et al., 2008; URL: http://srtm.csi.cgiar.org/). To reduce computational cost, the 90-m DEM was aggregated into a 5-km grid size for model simulation, while the sub-grid topography was described by the 90-m DEM. The elevation of this basin varies from about 2571 to 6289 m. Grid slopes vary from 0° to 30° with a mean value of 10.5° for all the model grids. A digital map of a 1-km resolution SiB2 land use map (Figure 3, middle) was available from the US Geological Survey (URL: http://edc2.usgs.gov/glcc/) and resampled to 5-km resolution for this study. Agriculture/C3 grassland was the dominant vegetation type (more than 88.5 %). The soil type for the basin (Figure 3, bottom) was obtained from the


Food and Agriculture Organization (2003) together with soil hydraulic parameters, including saturated soil moisture content, residual soil moisture content, saturated hydrologic conductivity for the soil surface, and the van Genuchten (1980) parameters (α and n). The static vegetation parameters including morphological, optical, and physiological properties were defined following Sellers et al. (1996b). The dynamic vegetation parameters are Leaf Area Index (LAI) and the Fraction of Photosynthetically Active Radiation (FPAR) absorbed by the green vegetation canopy, which can be obtained from satellite data. Global LAI and FPAR (MOD15) 0.05 degree datasets (Myneni et al., 1997) were used in this study. Surface meteorological inputs for the model were precipitation, wind speed, Tair , relative humidity, air pressure, and downward shortwave and longwave radiation. The precipitation, wind speed, Tair , relative humidity, air pressure, and sunshine duration were obtained from 22 CMA (China Meteorological Administration) standard stations (Figure 3, top); whereas, the downward shortwave and longwave radiation (SWD and LWD) data were obtained from Yang et al. (2010). In this study, the CMA data were used to estimate SWD and LWD by simple models and these estimates were then compared with satellite estimates, and evaluated against in situ data (see Yang et al., 2010). For simplicity, precipitation was divided into liquid and solid components (rainfall and snowfall) with a threshold Tair (2 oC in this study). All the meteorological variables were interpolated from the observational sites to the 4965 5-km model grids through the Inverse Distance Weight method, where Tair at a specified model grid was further corrected (with a NLR) by considering the elevation difference between the grid and its control meteorological station. Winter precipitation was modified to correct errors from wind-induced undercatching following Ye et al. (2004).


4.2 Datasets for model evaluation Besides the gauge observations of daily river discharge at Tangnaihai hydrological station, a satellite-based product of daily snow depth (SD) over China (Che and Dai, 2011) was used for model evaluation as well. The SD simulations are evaluated against the dataset derived from passive microwave satellite remote sensing (Che and Dai, 2011). The Chinese SD datasets, with a 0.25o spatial resolution, include the microwave SD retrievals from SSMR (1978–1987), SSM/I (1987–2008), and AMSR-E (2002–2012) (see Che et al., 2008). The SD distribution was validated indirectly by MODIS snow cover products by comparing the area of snow extent.

4.3 Satellite datasets for deriving NLRs at a finer spatial scale To supplement the insufficient number of Tair monitoring sites, we use the nighttime MODIS LST (with cloud-contaminated values removed) to derive the approximate NLRs at a finer spatial scale (e.g., at different elevation bands). This is because the MODIS LSTs closely follow the air temperatures during the night (see Wang et al., 2009b; Zhang et al., 2014) and have plenty of grid points that cover the study region. In this study, the MOD11C3 V005 (1 March 2000~now; Wan, 2008), which provided monthly composited and averaged temperature values at 0.05-degree (5600 m at the Equator), is used to calculate approximate NLRs for air temperatures.

5. Model Evaluation By using WEB-DHM-S forced with various NLRs (Table 1 and Figure 4), we have performed 10 runs for the study basin (one control run and 9 experimental runs). For the control model simulation, the 10-year (1996-2005) mean monthly NLRs (Figure 4b) derived from the observed Tair are adopted to correct the spatial Tair inputs based on the elevation © 2016 American Geophysical Union. All rights reserved.

differences between model grids and their adjacent meteorological sites. The Nash-Sutcliffe model efficiency coefficient (Nash) (Nash and Sutcliffe, 1970) and the bias error (BIAS) were used to assess the accuracy of the WEB-DHM model, and they are defined as follows. n

n

i 1

i 1

Nash  1   ( X oi  X si ) 2 /  ( X oi  X 0 ) 2 n

n

n

i 1

i 1

i 1

BIAS  ( X si   X oi ) /( X si )  100%

(12)

(13)

where X oi is the observed discharge; X si is the simulated discharge; n is the total number of time-series for comparison; and X 0 is the mean value of the observed discharges over the simulation period. The higher the Nash value is, the better the model performs; a perfect fit should have a Nash value equal to one (Nash & Sutcliffe, 1970). The lower the BIAS is, the better the model performs; a perfect performance should have a BIAS value equal to zero.

5.1. Calibration and validation with observed discharges The control run was conducted with a 5-km grid size and hourly time step from 1996 to 2005. The model was first calibrated with the data of 2001 and then validated over the other years. Here, we attempt to obtain a more reasonable initial condition for the calibration run for 2001, by running the model from 1996 to 2000. On the other hand, we had initially planned to use MODIS satellite data (starting from March 2000) for model evaluation purposes, in addition to the calibration with ground-based streamflows. All the soil hydraulic parameters were kept the same, as from Food and Agriculture Organization (2003), whereas the static vegetation parameters for Agriculture/C3 grassland were revised from Sellers et al.


(1996b), which is thought to be more suitable for the plateau environment. Table 2 lists the basin averages for the optimized land surface parameters. Figures 5a and 5b show the daily and monthly hydrographs at Tangnaihai with the Nash and BIAS. Results show that the model reproduces the 1996–2005 daily discharges with an acceptable accuracy (Nash = 0.656 and BIAS = -8.3 %), after the calibration with 2001 data (Nash = 0.703 and BIAS = -4.8 %), given the 10-year (1996-2005) mean monthly NLRs. The monthly hydrograph generally confirms that the model reliably represents the seasonal runoff variations (Nash = 0.794), although the summer runoff was slightly underestimated in 1999. This has contributed to an underestimation in the annual runoff for 1999 (Figure 5c), although the model could generally reproduce the inter-annual changes in discharge (Nash = 0.577). Figure 6 plots the mean seasonal changes of the simulated water budget components and ET components averaged over the upper area of Tangnaihai. The simulated mean-monthly discharges are, in general, comparable to the observed discharges (Nash = 0.834), but they slightly underestimate the summer (JJA) discharges, which may be attributed to the overestimation of summer ET. The total snowmelt that contributes to soil and overland runoff, shows a bimodal pattern (peaking in May and October), which is consistent with the snowfall distribution. This has resulted in a high Egs (evaporation from the moisture within the surface soil layer) in May, while the Ect (transpiration) generally follows the distribution of vegetation (LAI). The evaporation from interception stores (Egi and Eci) are constrained by both the intercepted water (from both rainfall and snowfall) and the available energy for evaporation.


5.2. Evaluation of snow depth The simulated daily SD was compared to the SSM/I-derived estimates from 01 July 1996 to 30 June 2005 (Figure 7). In general, the SD simulated by our model (with a mean of 0.91 cm) is comparable to the SSM/I-derived values (with a mean of 1.09 cm), but with obvious underestimates in the winters of 1998 and 2000. The mean spatial distributions of the SSM/I-derived and the simulated SD (in annual mean values) are comparable to each other, with large SD values over high mountainous areas.

6. Impact of NLR on the simulation of snow and streamflows The hydrological model is demonstrated to perform well at various time scales after calibration, and is further used to conduct experiments (EXP1 to EXP9) to investigate the impact of NLR on snow and streamflow simulations.6.1.Sensitivity

of

the

simulated

streamflows to NLRs Table 1 shows the sensitivity of simulated streamflows to the calculated NLRs with different time scales (also Figure 4) and different spatial patterns (also see Tables 3-5). Results show that the simulated discharges (Qsim) could have a maximum difference greater than 24 % by using the different NLRs considered here. This has motivated us to carefully estimate the NLR for improved streamflow simulations. One way to refine the model is to use a NLR with a finer time scale (e.g., the monthly NLRs or the monthly-mean hourly NLRs). However, we found the improvements of the simulated discharges are limited (< 2.60 %), when changing the NLRs from a long-term mean (EXP2) to a monthly mean (EXP3) or to a monthly-mean hourly (EXP4) NLRs. This can be confirmed with the similar ETs obtained from EXP2, EXP3 and EXP4 (Figure 12).


Another way to refine the model is to use a NLR with a finer spatial scale (e.g., use different NLRs over a few elevation bands, or different land covers). To overcome the limited number of observational stations (for Tair) within the basin, alternatively the satellite-based LSTs were used.

6.2. Use of MODIS LST to obtain spatially-variable NLRs This section introduces how we used MODIS nighttime LSTs to derive NLRs at a finer spatial scale, and demonstrates the improved model performance in simulating snow, ground surface temperature, evapotranspiration, and streamflows. Monthly-mean nighttime LSTs from MODIS are highly correlated with the corresponding Tair, with a general 1:1 slope between them (Figure 8). This indicates that substituting MODIS nighttime LST for nighttime Tair is reasonable. Furthermore, it is also necessary to obtain a daily-mean NLR (from the nighttime NLR) that can be used for preparing air temperature inputs at different time. In order to achieve this purpose, we compared the ground-based NLRs between the monthly-mean hourly values and the nighttime (22:00) values calculated from the observed Tair (Figure 9). It was found that the annual mean nighttime NLR (-4.88 K/km) is very close to the annual mean daily NLR (-4.98 K/km), although they differ over time frames of several months. We also observed that the daily NLR tends to be greater than the nighttime NLR in the warm months (April-October) and smaller in the cold months (November-March). The annual mean daytime (10:00) NLR (-5.11 K/km) is also close to the annual mean daily NLR (-4.98 K/km), although they differ over time frames of several months (Figures 9a and 9c). This indicates that substituting the mean nighttime NLR for the mean daily NLR over all the months (that is the long-term mean NLR) is also reasonable in the basin (Figure 9b).


Therefore, the long-term mean NLR for Tair can be approximately estimated from the nighttime LST from MODIS. In Figure 10, the MODIS nighttime LST (here only 2001-2004 LSTs were analyzed) was used to estimate the time-invariant NLRs over different elevation bands. The NLRs at 3 elevation bands have been obtained, which are -8.08 K/km for the area lower than 3400 m, -3.93 K/km for the area during 3400-4000 m, and -5.86 K/km for the area above 4000 m, indicating complex variations in NLR. Furthermore, the NLRs derived for different land covers, different terrain (flat, northward, and southward), and different snow conditions were also examined and tabulated (see Tables 3-5 and Figure 3(middle) and Figure 11), in order to check the influence of the spatial variability of NLRs on the hydrological simulations. With the new NLRs considered in the hydrological model’s spatial variability (at individual elevation bands, land covers, aspects, and snow conditions; EXP5-EXP8), the hydrological model did a better job at reproducing the streamflows than EXP2, which only used a single (both time-invariant and spatially-invariant) NLR for the whole basin (-4.98 K/km). This is not surprising, since the spatially-variable NLRs would refine the spatial heterogeneity of Tair inputs, which directly influence the rainfall/snowfall determination and all the related land surface hydrological processes at each model grid (Figures 12-15). To check the snow process-based variables that led to the various performances in streamflow simulations, the basin-averaged values of the interpolated Tair and the simulated ET were calculated for all the scenarios (Figure 12). Compared to the CTRL, EXP2-EXP4 gave similar basin-averaged values in Tair inputs (mostly within ±0.2 K) and the simulated ET (mostly within ±1 mm/month), while as expected, EXP1 with the global constant NLR (-6.5 K/km) showed the largest errors in the interpolated Tair inputs (among -1.0 ~ -0.4 K) and the simulated ET (among -6.0 ~ 0.5 mm/month).


Meanwhile, simulations in EXP5-EXP8 were carefully examined for the interpolated Tair inputs and the simulated ET (Figure 12), by comparing them with EXP2, which used the long-term mean NLR for the whole basin. It was determined that all the experiments that considered the spatial variability of the NLR (EXP5-EXP8) give quite similar results for the basin-mean Tair and ET. However, the four scenarios obtained very different Tair in their spatial distributions as they adopted very different spatial NLRs (Figure 13). The Tair difference between each scenario (EXP5-EXP8) and EXP2 generally followed the spatial patterns of DEM (EXP5; see Figure 3), land use (EXP6; see Figure 3), aspect (EXP7; see Figure 11), and snow conditions (EXP8; see Figure 11). In addition, the different Tair inputs directly influenced the rainfall/snowfall determination in the hydrological modeling (see Figure 14). Figure 15 shows the improved streamflow simulations of EXP5-EXP8 compared to EXP2, due to the consideration of the spatial variability of the NLR. The daily streamflow simulation was improved by 6-7 % compared to EXP2, which

underestimates the

observations by 15.3 %. As seen in Table 1, the seasonal cycle of the streamflows at Tangnaihai was also better reproduced by using the new NLRs (with a Nash of 0.835 and a BIAS of -4.43 % for EXP5, a Nash of 0.861 and a BIAS of -4.41 % for EXP6, a Nash of 0.856 and a BIAS of -5.06 % for EXP7, and a Nash of 0.869 and a BIAS of -3.41 % for EXP8), comparing to EXP2, which uses a single NLR for the whole basin (with a Nash of 0.790 and a BIAS of -10.79 %). This is largely attributed to an improved ET estimation, that is, a reduced summer ET leads to an increased summer runoff (see Figure 12 (bottom)). Finally, we took EXP2, EXP8, and EXP9 (see Table 1 for details) into consideration, in order to discriminate between the impacts of NLR on the snow pack processes and on the rainfall/snowfall determination (through newly interpolated spatial inputs of Tair). The results of EXP8 and EXP9 can help quantify the impact of the NLR on the increased/reduced


snowfall and thereby on the snow hydrological simulations. Keeping the snowfall constant (as in EXP2 and EXP9), on the other hand, will assist in figuring out how much of the changes in the simulated results are due to snow pack processes. As illustrated in Figures 13 and 14, EXP8 obtained a higher Tair and less snowfall in the east and northwest part of the basin, while it had a lower Tair and more snowfall in the southwest and middle part of the basin. These results were all consistent with the spatial distributions of mean snow depth derived from the SSMI (Figure 11(lower)). Figures 16 and 17 demonstrate the spatial distributions of EXP2, the difference between EXP9 and EXP2, and the difference between EXP8 and EXP9, in terms of snowfall, sensible heat flux (H), evapotranspiration (ET), ground surface temperature (Tg), snow depth (SD), snow water equivalent (SWE), and wetness at surface and root zone (Wsfc and Wrt). As expected, EXP9 has the same snowfall as EXP2, while EXP9 has the same Tair as EXP8. Figure 16 shows that regarding the influence of the NLR on snow modeling, it is the snow pack process rather than the determination of rainfall/snowfall that controls the simulations of land surface energy and water cycles. In Figure 17, root zone depths for different vegetation types are defined following Sellers et al. (1996b), and the depth of surface layer is defined as 2 cm over the whole basin. The root zone wetness is defined by the volumetric water content divided by the saturated water content in the root zone. As given in Figures 16b and 17b, a lower Tair results in a lower Tg and ET but a higher H, leading to wetter soil (surface and root zone) and a greater amount of snow. On the other hand, a higher Tair results in a higher Tg and ET but a lower H, leading to drier soil (surface and root zone) and a lower amount of snow on the ground. As plotted in Figures 16c and 17c, with only the difference in the determination of snowfall/rainfall (given the same total precipitation), EXP8 and EXP9 gave much smaller differences in the simulated energy and water cycles than the ones in Figures 16b and 17b. It is found that a larger snowfall input has resulted in a greater


amount of snow on the ground, a lower Tg, and thus a lower H, leading to wetter soil (surface and root zone). In summary, through the evaluations of simulated streamflows at different time scales (daily, monthly, mean-monthly, and yearly) using ground based discharge observations, the EXP8 (NLRs estimated at different snow conditions) was approved as the best NLRs in the study, which also produced most realistic snow flows.

7. Summary and conclusions In this study, an improved simulation of snow processes has been achieved by using satellite-based estimation of NLR (from MODIS nighttime LST) in a distributed biosphere hydrological model, followed by the evaluation of the model’s performance in the upper Yellow River basin from 1996 to 2005. The model was first calibrated and validated for 10-years of discharge at a stream gauge, and it generally demonstrated good performance in reproducing the observed streamflows on daily, monthly, and yearly time scales. The model was further evaluated with the SSM/I derived estimates of snow depth, and demonstrated a reasonable performance in simulating the basin-wide snow presence and amount. Experiments are designed to explore how NLR varies temporally may influence model's performance on snow and streamflow estimates. We found that streamflow is highly sensitive to NLR, motivating a refinement of the NLR for the hydrological modeling. We have demonstrated that the use of NLRs estimated by fine resolution MODIS nighttime LSTs improved the model’s simulations of the amount of snow (snow depth, and snow water equivalent), and streamflows. Due to the global coverage of MODIS nighttime LST data, the methodology developed in this study can be applied to various river basins around the world.


This work is partly limited by the sparse Tair observational sites in the studied basin. If the existing ground based Tair stations are dense enough and cover the target basin in a reasonable way, the satellite-based NLR estimates in various experiments (exploring the spatial variation of NLRs in the basin) can be rigorously validated with ground-based NLRs in a direct way. This will help us clarify the spatial heterogeneity of NLRs in a basin scale. In addition, it is recommended that diurnal variations of NLR should be further explored within each month (other than using the monthly-mean diurnal cycle, EXP4 in this paper) in future studies, as a NLR often changes in time during a day and also fluctuates from day to day (see Figure 18). Furthermore, regarding the use of MODIS nighttime LSTs, more attention should be paid to the missing data caused by clouds, since the NLRs in sunny days and cloudy days can be quite different (e.g., Figure 19).

Acknowledgements This

study

was

financially

Basic Research Program of China

supported

(2013CBA01800),

the

by

the

National

National Key

Natural

Science

Foundation of China (Grant 41322001, 41190083, and 41571033), the “Strategic Priority Research Program” of the Chinese Academy of Sciences (XDB03030302), the Key Technologies R&D Program of China (2013BAB05B03), and the hundred talents program of Chinese Academy of Sciences and Top-Notch Young Talents Program of China. Deliang Chen is supported by Swedish VR, BECC and MERGE. The microwave snow depth data in China were provided by the Environmental and Ecological Science Data Center for West China, National Natural Science Foundation of China (http://westdc.westgis.ac.cn). The MODIS

data

were

obtained

from

the

NASA

Reverb

website

(http://reverb.echo.nasa.gov/reverb/).


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Table 1.

Impact of NLRs (that were used for interpolating Tair from station data to gridded

cells) on the simulated streamflows at Tangnaihai hydrological station. Here, the observed steamflow at Tangnaihai is 140.0 mm/year averaged over 1996-2005.

Run

NLR (K/km)

Descriptio n

Number of NLR Qsim values (mm/ye BIAS used for ar) interpolat ion

Nash coefficient

QYear ly

QMeanMo nthly

QMont QDa hly

ily

NLRs estimated from monthly mean Tair averaged over 1996-2005

12

128.2

-8.3 %

0.57 7

0.834

0.79 4

0.6 56

EXP constant 1 (-6.50)

-6.50 K/km

1

159.0

13.7 %

0.41 4

0.758

0.72 9

0.5 46

long-term EXP mean 2 (-4.98; Figure 4a)

NLR estimated from long-term (1996-200 5) mean Tair

1

124.8

-10.8 %

0.51 5

0.790

0.76 7

0.6 35

monthly EXP (Figure 3 4c)

NLRs estimated from monthly mean Tair from 1996 to 2005

120

128.3

-8.3 %

0.61 8

0.834

0.79 5

0.6 59

EXP monthlymean 4 diurnal

NLRs estimated from

288

125.26

-10.4 %

0.53 4

0.816

0.78 6

0.6 54

CT RL

mean monthly (Figure 4b)


cycle (Figure 4d)

No

NLR (K/km)

monthly-m ean hourly Tair averaged over19962005

Descriptio n

Number of NLR values Qsim used for (mm/ye BIAS hydrolog ar) ical modeling

Nash coefficient

QYear ly

QMeanMo nthly

QMont QDa hly

ily

Long-term mean at 3 EXP elevation 5 bands (Figure 10)

NLRs estimated at each elevation band with MODIS LSTs

3

133.7

-4.4 %

0.67 0

0.835

0.79 2

0.6 48

Long-term mean at EXP different 6 land covers (Table 4)

NLRs estimated for each land cover with MODIS LSTs

8

133.7

-4.4 %

0.66 9

0.861

0.81 5

0.6 57

Long-term mean at EXP different 7 aspects (Table 5)

NLRs estimated at 3 aspects (flat, southward, northward) with MODIS LSTs

3

132.8

-5.1 %

0.66 2

0.856

0.81 2

0.6 55

NLRs estimated

4

135.1

-3.4

0.69

0.869

0.82

0.6

EXP

Long-term mean at


8

various snow conditions (Table 6)

EXP Same as 9 EXP8

at different SSMI-base d snow depths with MODIS LSTs Same as EXP8, but keeping 4 snowfall as EXP2

N/A

%

6

N/A

N/A

N/A

1

59

N/A

N/ A

Note: (1) The NLRs in EXP5-EXP9 were derived at the sub-regions of the basin by using the 2001-2004 MODIS nighttime LSTs, to represent the spatial heterogeneity of NLRs. Differently, the other NLRs except those for EXP1 were calculated from the 2-m Tair observations at the 22 CMA stations in the basin during 1996-2005. (2) Totally 10 runs were performed at the study basin by using WEB-DHM-S using different NLRs. Here, “CTRL” refers to the control run, and “EXP1- EXP9” are additional 9 experimental runs. (3) QMeanMonthly refers to the 10-year (1996-2005) mean monthly discharges. It represents the mean seasonal variation over the years. (4) The best model performance is indicated in bold.


Table 2. Land surface parameters used in the upper Yellow River Basin. These values are basin averages based on areal percentages of each land use type.

Symbol

Parameters

Value

Source

z2 (m)

Height of canopy top

0.40

Optimization

z1 (m)

Height of canopy bottom

0.11

Optimization

Zs (m)

Ground roughness length

0.001

Optimization

D1 (m)

Depth of surface layer

0.02

Optimization

Dr (m)

Root depth (D1+D2)

0.28

Optimization


Table 3. The derived NLRs at different land covers from MODIS nighttime LSTs.

Standard NLR

deviation

(K/km)

of NLR

Correlation coefficient

Elevation Area

between

Land Cover

range (%)

LSTs and (K/km)

(m)

elevations

Broadlead-deciduous trees

-4.23

-0.92

0.2

1217

Broadleaf and Needleleaf trees

1.57*

0.20

0.3

334

Needleleaf-deciduous trees

-2.57

-0.61

0.3

523

Short vegetation/C4 grass

-3.38

-0.78

1.0

1090

Broadleaf shrubs with bare

2.93

-0.92

-5.87

2605 4.9

soil Drawf trees and shrubs

-6.11

-0.72

2.9

2386

Agriculture/C3 grassland

-5.08

-0.89

88.9

2134

Water body

0.91*

0.09

1.3

1093

Note: The NLRs with the star superscript (*) were derived with a narrow elevation range (for the samples used for linear regression), or obtained with a low Pearson’s correlation coefficient (< 0.5). The information of dominant land cover (Agriculture/C3 grassland) is given in bold.


Table 4. Same as Table 3, but for different aspects (flat, northward, and southward).

NLR aspect (K/km)

Standard

Correlation

deviation

coefficient

Area

elevation

between LSTs

(%)

range (m)

-0.97

3.0

1008

-0.87

55.0

2617

-0.87

42.0

2429

of NLR (K/km)

Flat

-6.31

Northward

-5.01

Southward

-5.18

0.71

and elevations


Table 5. Same as Table 3, but for different snow conditions. Here, the mean (1996-2005) SSMI-based snow depths (Che et al., 2008; Che and Dai, 2011) were used in describing snow conditions.

Mean snow

NLR

depth (cm)

(K/km)

Standard

Correlation

deviation

coefficient

Area

elevation

between LSTs

(%)

range (m)

of NLR (K/km)

and elevations

> 2.5

-5.48

-0.73

8.9

1668

1.5 ~ 2.5

-5.51

-0.79

21.7

1092

0.86 0.5 ~ 1.5

-6.21

-0.91

32.3

1948

< 0.5

-4.14

-0.75

37.1

2152


Figure 1. Overall structure of WEB-DHM: (a) division from basin to sub-basins, (b) subdivision from sub-basin to flow intervals comprising several model grids, (c) discretization from a model grid to a number of geometrically symmetrical hillslopes, and (d) description of the water moisture transfer from atmosphere to river. Here, the land surface submodel is used to describe the transfer of the turbulent fluxes (energy, water, and carbon) between atmosphere and ground surface for each model grid, where Rsw and Rlw are downward solar radiation and longwave radiation, respectively, H is the sensible heat flux, and λ is the latent heat of vaporization; the hydrological submodel simulates both surface and subsurface runoff using grid-hillslope discretization, and then simulates flow routing in the river network.


Figure 2. The soil model coupled with a 3-layered snow model used in WEB-DHM-S (Shrestha et al., 2010).


Figure 3. The upper Yellow River basin: DEM, meteorological and discharge sites (top); land use (middle) and FAO soil type (bottom).


Figure 4. The long-term mean (a), mean monthly (b), monthly (c), and monthly-mean diurnal cycle (d) of the lapse rate and its correlation coefficient with elevation. The values were derived from the hourly observed 2-m air temperatures at the 22 stations in the basin. The error bar is indicated in (b), (c) and (d), with the standard deviation.


Figure 5. The observed and simulated daily (a), monthly (b), and yearly (c) streamflows at Tangnaihai gauge from 1996 to 2005. Here, we use the 10-year (1996-2005) mean monthly NLRs (derived from 2-m air temperature observations at the 22 CMA meteorological stations in the upper Yellow River basin during 1996-2005) when interpolating air temperature from station data to gridded cells.


Figure 6. Mean monthly input LAI and Tair (a), as well as the simulated water budget components (b) and four ET components (c) averaged over the upper area of Tangnaihai gauge from 1996 to 2005. The total snow melt that goes to soil and overland runoff is given in (b) for reference.


Figure 7. The simulated snow depth comparing to the SSM/I derived estimates (Che and Dai, 2011) averaged over the basin: (a) is daily time-series, (b) and (c) illustrate the mean (from 1 July 1996 to 30 June 2005) spatial patterns of the SSM/I derived and the simulated snow depth.


Figure 8. Comparisons between the monthly-mean nighttime (at 22:00) 2-m Tair over the 22 CMA stations with their corresponding 0.05-degree monthly MODIS nighttime LSTs in the basin during 2001-2004. Here, the data in 2005 were not included due to the missing MODIS data in November. Comparison of the elevations between CMA sites with the corresponding 5-km model grids is also given for reference. © 2016 American Geophysical Union. All rights reserved.

Figure 9. Comparison of ground-based NLRs (K/km) between the monthly-mean hourly values and the nighttime (22:00) as well as daytime (10:00) values, calculated from the Tair observations at the 22 CMA stations during 1996-2005. The composite time-series averaged over 1996-2005 is given at the top (a), while the scatterplots for the 120 monthly values in the lower (b, and c).


Figure 10. Satellite-based lapse rates derived at different elevation bands (a, lower than 3000 m; b, 3400~4000 m; c, above 4000 m) by using the four-year (2001-2004) averaged MODIS nighttime LSTs in the while basin (totally 4965 grids at a 5-km resolution). Here, the MODIS LST data in 2005 were excluded due to the missing data in November.


Figure 11. Distributions of aspects in the study area (upper), and the snow conditions classified according to the SSMI-based snow depths (lower).


Figure 12. Monthly differences between EXP1-EXP4 and CTRL (upper) as well as between EXP5-EXP8 and EXP2 (lower), for the basin-averaged values of the interpolated gridded model inputs of Tair and the simulated ET. © 2016 American Geophysical Union. All rights reserved.

Figure 13. Spatial distributions of the interpolated air temperature (an important input for snow modeling) averaged over 1996-2005: the actual values in EXP2, and their differences from EXP5, EXP6, EXP7, EXP8, respectively.


Figure 14. Spatial distributions of the snowfall (determined by a temperature threshold of 2 o

C) averaged over 1996-2005: the actual values in EXP2, and their differences from EXP5,

EXP6, EXP7, EXP8, respectively.


Figure 15. Scatterplots of the observed and simulated daily streamflows during 1996-2005 when using the NLRs at different elevation bands (EXP5), different land covers (EXP6), different aspects (EXP7), and different snow conditions (EXP8), comparing to the one that using the same NLR for the whole basin (EXP2).


(b) EXP9 – EXP2

(a) EXP2

(c) EXP8–EXP9

Figure 16. Spatial distributions of the difference between EXP9 and EXP2 (middle column), as well as the difference between EXP8 and EXP9 (right column) in the inputs of air temperature and snowfall, as well as the simulated sensible heat flux, evapotranspiration, and ground surface temperature averaged over 1996-2005. The spatial maps for EXP2 are also given for reference (left column).


(a) EXP2

(b) EXP9 – EXP2

(c) EXP8 – EXP9

Figure 17. Same as Figure 16, but for the simulated snow depth, snow water equivalent, surface wetness and root zone wetness averaged over 1996-2005.


Figure 18. Examples of diurnal variation of NLR in each season of 2001 derived from ground Tair observations in the studied basin.


Figure 19. Comparison of the ground-based NLRs for the selected 60 very cloudy and 60 very sunny days averaged over each month in 2001. Here, regarding solar radiations, we assume that the biggest and least five days are the ones having least uncertainties to be confirmed to be sunny or cloudy.


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