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A distributed water-heat coupled model for mountainous watershed of an inland river basin of Northwest China (I) model structure and equations

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Environmental Geology

Abstract

It is absolutely necessary to quantify the hydrological processes in earth surface by numerical models in the cold regions where although most Chinese large rivers acquire their headstreams, due to global warming, its glacier, permafrost and snow cover have degraded seriously in the recent 50 years. Especially in an arid inland river basin, where the main water resources come from mountainous watershed, it becomes an urgent case. However, frozen ground’s impact to water cycle is little considered in the distributed hydrological models for a watershed. Took Heihe mountainous watershed with an area of 10,009 km2, as an example, the authors designed a distributed heat-water coupled (DWHC) model by referring to SHAW and COUP. The DWHC model includes meteorological variable interception model, vegetation interception model, snow and glacier melting model, soil water-heat coupled model, evapotransporation model, runoff generation model, infiltration model and flow concentration model. With 1 km DTM grids in daily scale, the DWHC model describes the basic hydrological processes in the research watershed, with 3∼5 soil layers for each of the 18 soil types, 9 vegetation types and 11 landuse types, according to the field measurements, remote sensing data and some previous research results. The model can compute the continuous equation of heat and water flow in the soil and can estimate them continuously, by numerical methods or by some empirical formula, which depends on freezing soil status. However, the model still has some conceptual parameters, and need to be improved in the future. This paper describes only the model structure and basic equations, whereas in the next papers, the model calibration results using the data measured at meteorological stations, together with Mesoscale Model version 5 (MM5) outputs, will be further introduced.

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Abbreviations

a :

adjustable parameter for soil evaporation

a 1 :

empirical constants (clay: 0.13; sand type soil: 0.1)

a 2 :

empirical constant (clay: −0.129; sand type soil: 0.058)

a 3 :

empirical constant (0.6245 for both clay and sand type soil)

b :

adjustable parameter for vegetation transpiration

b 1 :

empirical constants (clay: 0.00144; sand type soil: 0.00158)

b 2 :

empirical constant (clay: 1.32; sand type soil: 1.336)

b 3 :

empirical constant (clay: 0.0036; sand type soil: 0.00375)

b 4 :

empirical constant (clay: 0.8743; sand type soil: 0.9118)

C :

soil heat capacity (J °C−1cm−3)

C i :

specific heat of ice (J g−1 °C−1)

C l :

specific heat of water (J g−1 °C−1)

C s :

specific heat of soil grains (J g−1 °C−1)

d 1 :

empirical constant (default 0.5)

d 2 :

empirical constants (default 0.1)

d 3 :

empirical constants (default 10)

E :

evapotranspiration in a DTM grid (mm)

E 0 :

potential evaporation (mm)

E c :

evaporation of canopy interception (mm)

E s :

soil evaporation (mm)

E v :

vegetation transpiration (mm)

f lat :

ratio of latent heat of ice to the total heat content of the soil, Q total,tf , at the temperature T f

g :

gravity constant (9.8  ms−2)

H :

sensitive heat content (J cm−2d−1)

h 1 :

empirical constants (default 0.06)

h 2 :

empirical constants (default 0.01)

h 3 :

empirical constant (default 2.0)

I∼III:

soil layer number

k′0 :

corrected k 0 considering frozen effects (cm d−1)

k 0 :

saturated hydraulic conductivity of unfrozen soil (cm d−1)

k h :

thermal conductivity for unfrozen soil (J s−1  m−1 °C−1)

k h,i :

thermal conductivity for fully frozen soil (J s−1  m−1 °C−1)

k h,s :

thermal conductivity for sub-frozen soil (J s−1  m−1 °C−1)

k hm :

thermal conductivity for unfrozen mineral soil (J s−1  m−1 °C−1)

k hm,i :

thermal conductivity of fully frozen mineral soil (J s−1  m−1 °C−1)

k ho :

thermal conductivity for unfrozen humus (J s−1  m−1 °C−1)

k ho,i :

thermal conductivity of a fully frozen organic soil (J s−1  m−1 °C−1)

k mat :

saturated matrix conductivity (cm d−1)

k w :

unsaturated hydraulic conductivity (cm d−1)

l :

flow length in a DTM grid (m)

LAI:

leaf area index

LAImax :

maximal LAI in a year

L f :

latent heat of freezing (334 × 103  J kg−1)

m 1 :

adjustable parameter for flow time

m 2 :

adjustable parameter for flow time

n :

parameter accounting for pore correlation and flow path tortuosity (default 1)

P :

daily precipitation (mmH2O)

P ground :

precipitation falling to the ground after the interception process (mmH2O)

Q :

thermal quality of the soil layer

q :

infiltration rate (cm d−1)

Q total :

heat content of sub-frozen or unfrozen soil (J cm−1)

\({{\varvec{\Delta}}{Q}_{\rm total}}\) :

change of the total heat content of the soil layer (J cm−1)

Q total,tf :

total heat content of soil at T f (J cm−1)

r :

freezing-point depression

R 0 :

surface runoff (mm d−1)

R glacier :

glacier meltwater (mm d−1)

R I :

subsurface flow of soil layer I (mm d−1)

R snow :

snow meltwater (mm d−1)

T :

air temperature

t :

flow time between two adjacent DTM grids

T 0 :

soil surface temperature

T f :

a threshold temperature value below which the soil is assumed to be completely frozen except of a residual unfrozen amount (−8°C)

T s :

soil temperature (°C)

T s,change :

increase or decrease of soil temperature (°C)

V cov :

vegetation coverage

V p :

precipitation that intercepted by vegetation canopy (mmH2O)

V p,total :

canopy storage amount (mmH2O)

V p0 :

vegetation interception capacity (mmH2O)

V pmax :

saturated interception capacity (mmH2O)

V sto :

canopy storage amount before one precipitation (mmH2O)

w :

soil total mass of water (g)

w ice :

mass of water available for freezing (g)

z :

soil layer depth (cm)

λ:

pore size distribution index

β:

slope of a DTM grid (%)

θ:

soil volume water content (%)

θ c :

field capacity (%)

θ l :

soil volume liquid water content (%)

θ m :

soil volume water content at ψmat, θ m = θ s −4% (%)

θ i :

soil volume solid water content (%)

θ i,change :

mass change of the solid water content (g)

θ r :

residual water content (%)

θ s :

saturated volume water content (porosity,%)

θwilt :

water content at wilting point (%), defined as a tension of 15,000 cm water, i.e. ψwilt

θ x :

threshold volume water content (%) at the threshold tension, ψ x

ρ d :

soil dry bulk density (g cm−3)

ρ G :

soil grains density (g cm−3)

ρ i :

ice density (g cm−3)

ρ l :

liquid water density (g cm−3)

ρ s :

soil density (g cm−3)

ψ:

soil water tension (cmH2O)

ψ′:

corrected water tension for sub-frozen or fully frozen soil layer (cmH2O)

ψ a :

air entry tension (cmH2O)

ψmat :

matrix tension (cmH2O)

ψwilt :

threshold tension (15,000 cmH2O) at wilting point

ψ x :

threshold tension (cmH2O)

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Acknowledgments

This work has been mainly supported by Chinese National Sciences Foundation Committee and Chinese Academy of Sciences (KZCX2-YW-301-3 and 40401012). The authors would also thank Dr. Jason Yan for English improvements.

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Authors and Affiliations

  1. Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, 730000, China

    Ren-sheng Chen, Shi-hua Lu, Er-si Kang, Xi-bin Ji, Zhihui Zhang, Yong Yang & Wenwu Qing

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  1. Ren-sheng Chen
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  2. Shi-hua Lu
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Correspondence to Ren-sheng Chen.

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Chen, Rs., Lu, Sh., Kang, Es. et al. A distributed water-heat coupled model for mountainous watershed of an inland river basin of Northwest China (I) model structure and equations. Environ Geol 53, 1299–1309 (2008). https://doi.org/10.1007/s00254-007-0738-2

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