Assessing the effects of severe rainstorm-induced mixing on a subtropical, subalpine lake

Abstract

Severe rainstorms cause vertical mixing that modifies the internal dynamics (e.g., internal seiche, thermal structure, and velocity filed) in warm polymictic lakes. Yuan Yang Lake (YYL), a subtropical, subalpine, and seasonally stratified small lake in the north-central region of Taiwan, is normally affected by typhoons accompanied with strong wind and heavy rainfall during the summer and fall. In this study, we used the field data, statistical analysis, spectral analysis, and numerical modeling to investigate severe rainstorm-induced mixing in the lake. Statistical determination of the key meteorological and environmental conditions underlying the observed vertical mixing suggests that the vertical mixing, caused by heat loss during severe rainstorms, was likely larger than wind-induced mixing and that high inflow discharge strongly increased heat loss through advection heat. Spectral analysis revealed that internal seiches at the basin scale occurred under non-rainstorm meteorological conditions and that the internal seiches under the rainstorm were modified on the increase of the internal seiche frequencies. Based upon observed frequencies of the internal seiches, a two-dimensional model was simulated and then appropriate velocity patterns of the internal seiches were determined under non-rainstorm conditions. Moreover, the model implemented with inflow boundary condition was conducted for rainstorm events. The model results showed that the severe rainstorms promoted thermal destratification and changed vertical circulation of the basin-scale, internal seiche motion into riverine flow.

Appendices

Appendices

Appendix 1. Estimate of inflow/runoff temperature

Inflow temperature was evaluated relate to the daily averaged air temperature using a nonlinear regression equation (Mohseni et al. 1998), given by

$$ {T}_{\mathrm{in}}={T}_{\mathrm{in}, \min }+\frac{T_{\mathrm{in}, \max }-{T}_{\mathrm{in}, \min }}{1+ \exp \left[{\gamma}_{\mathrm{a}}\left(T{}_{\mathrm{a},\mathrm{ip}}-{T}_{\mathrm{a}}\right)\right]} $$

(A1)

where T _in,min and T _in,max denote the minimum and maximum inflow temperatures, respectively, T _a,ip is the air temperature at inflection point, γ _a is the steepest slope of T _in at inflection point. Nonlinear correlation plots between air temperature and inflow temperatures measured at the location A (see Fig. 1a) from 2007 to 2010 are shown in Fig. A1. The above equation was implemented to the non-typhoon case (Fig. A1a). The linear regression (T _in = m ⋅ T _a + b) was used for the typhoon case (Fig. A1b). The inflow/runoff temperatures from spring 2004 to summer 2006 were computed using the nonlinear correlation Eq. A1 and the linear regression with the coefficients (T _in,min, T _in,max, T _a,ip, γ _a, m, and b), which were determined by the data from 2007 to 2010.

Appendix 2. Runoff model and evapotranspiration

The Clark Unit Hydrograph method (Clark 1945) was used to estimate the inflow/runoff discharge from precipitation in the watershed. The key parameters, likely sensitive in the calibration tests, are the infiltration (normally determined on the basis of the soil type, land cover/land use, and antecedent-moisture conditions) and the time of concentration (typically given by the time for the first drop of precipitation at the hydraulically most distant point in the watershed to reach the watershed outlet). Both parameters were tuned by adjusting water elevation peaks, caused by rainstorms.

Forest evapotranspiration (E _T, mm/day) was estimated using Priestley–Taylor equation (Priestley and Taylor 1972), capable of minimizing the number of parameters on the practical operation. The equation is given by

$$ {E}_{\mathrm{T}}={\alpha}_{\mathrm{E}}{\rho}_0\frac{s}{s+\gamma}\frac{H_{\mathrm{n}}-{H}_x}{L_{\mathrm{E}}} $$

(A2)

where γ = c _pa p _a/(ε _E L _E), psychrometric constant with the ratio of molecular weight of water to dry air, ε _E (=0.622), α _E is the Priestley–Taylor empirical constant (maximum = 1.26), s is slope of the saturated vapor pressure gradient, s = 0.04145 exp(0.06088T _a) by the American Society of Association Executives (ASAE) Standards (1998), H _n is net radiation, MJ/(m² day), and H _x is stored heat in soil, MJ/(m² day), given by

$$ {H}_x={K}_{\mathrm{G}}{H}_{\mathrm{n}} \exp \left(-0.5\mathrm{LAI}\right) $$

(A3)

where K _G is 0.4 for daytime (H _n > 0), and 1.6 to 2.0 for night time (H _n < 0), and LAI is the leaf area index, measured in the forest of the YYL catchment (Kao et al. 2000).

Appendix 3. Dominant wind direction

The dominant wind directions were plotted with the 10-min interval data (shown in Fig. A2) for the non-typhoon case (corresponding to Fig. 7a) and two typhoon cases: the weaker typhoon of 200413 (Fig. 7b) and the strong typhoon of 200505 (Fig. 7c).

Notation

The following symbols are used in this paper:

ΔT _rms :

Root Mean Square deviation of water temperature

α _E :

Priestly–Taylor empirical constant

α _lwa :

Albedo of incoming longwave radiation

α _sw :

Albedo of shortwave radiation

β :

Coefficient of thermal expansion

γ _a :

Steepest slope at inflection point expansion

ε _E :

Ratio of molecular weight of water to dry air

ε _w :

Emissivity of the water body

λ :

Stefan–Boltzmann constant

τ :

Wind shear stress

ω :

Angular frequency

ψ and φ :

Stream function

ζ :

Vertical fluid displacement

ζ _rms :

Internal seiche amplitude

ρ ₀ :

Reference water density

ρ :

Water density

ρ _a :

Air density

A ₀ :

Surface area of the lake

C :

Cloud cover fraction

c _c and c _e :

Dimensionless coefficient

C _D :

Drag coefficient

c _p :

Specific heat capacity of water

c _pa :

Specific heat capacity of air

E :

Evaporation

E _T :

Evapotranspiration

e _a :

Air vapor pressure

e _s :

Vapor pressure at water surface

g :

Gravitational acceleration

H _adv :

Heat advection

H _c :

Sensible heat flux

H _e :

Latent heat flux

H _lw :

Net longwave radiation

H _net :

Net heat flux on the water surface

H _sw :

Shortwave radiation

H _x :

Stored heat in soil

L _E :

Heat of vaporization

L :

Cross section distance

LAI:

Leaf area index

N :

Buoyancy frequency

P :

Amount of precipitation

p :

Pressure in water column

p _a :

Air pressure

Q _in :

Inflow discharge

Q _net :

Net water storage

Q _out :

Outflow discharge

S _t :

Schmidt stability

s :

Slope of the saturated vapor pressure gradient

T _a :

Air temperature

T _in :

Inflow water temperature

T _out :

Outflow water temperature

T _s :

Water surface temperature

t :

Time

u and w :

Velocities in horizontal and vertical directions

u _* w :

Water friction velocity

w _* :

Penetrative convection velocity

W _10m :

Wind speed on the 10 m height from the water surface

V :

Lake volume

x and y :

Horizontal and vertical directions

z _g :

Center of the gravity

z _m :

Maximum depth

z _t :

Height of the thermocline

Fig. A1

Nonlinear and linear correlations with daily average air temperatures and inflow temperatures (red lines) and 95 % confidence interval (blue dotted lines), a the non-typhoon case using the empirical Eq. A1 and b the typhoon case using the linear regression

Fig. A2

Dominant wind directions during a the non-typhoon case (typical diurnal thermal cycle), b the weaker typhoon 200413 (distant to YYL), and c the strong typhoon 200505 (close to YYL). Bold numbers are the number of occurrences of wind direction with the 10° interval