Water

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Water (水)

Mount Usu / Sarobetsu post-mined peatland
From left: Crater basin in 1986 and 2006. Cottongrass / Daylily

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Water for life (生命にとっての水)

Plants live with water because of photosynthesis (光合成)

Plants [ algae | moss | fern | seed plant ]
Physiology [ water culture , water stress ]
Ecology [ hydrosphere | wetland ]

Water types used by plants

1. rainfall (降雨)

Worldwide average: 880 mm/yr - highly heterogenous distribution

2. stream water (河川水)

[ water potential | pH ]

3. groundwater (地下水)

phreatophyte (地下水植物): plants utilizing groundwater

Ex. Poenix dactylifera (ナツメヤシ) - developing oasis, Prosopis juliflora (メスキート)

Hydraulic redistribution

4. mist and dew

cloud forest or mist forest - how to measure!

Water transportation (水移動)

(Slatyer & Taylor 1960)

Water potential (水ポテンシャル)

Quantifier: ψ, or ψw
Dimension: L^-1MT^-2
Unit: Pa

Water transport: from high to low water potential →
The following equation is ture whenever water transportation occurs from soil to air through plant

ψ_l < ψ_x < ψ_r < ψ_s
← ← ← ← ← ←
l: leaf, x: xylem, r: root, s: soil

Law. Darcy's law (ダルシーの法則, Darcy 1856)
ψ_h = ψ_m + ψ_g (Pa or cm)

ψ_h: hydraulic potential (water potential)
ψ_m: tention (張力)
ψ_g: relative height of the quantity of water in the gravitational field

J = -K·(dh/ds) (m³/m²s = m/s)

J: flux rate
K: hydraulic conductivity (透水係数)

K = K(φm(Θ))

Θ: volume fractiion of the bulk soil containing water
Q = KAt·h/l = K·D

t: unit time

Permeability (浸透性)

Terms: permeable, adj 浸透(透過)される, permeate, vt -に浸透する

Deficiency and evapotranspiration (etp)

Ideal

water potential

Actual

-ψ_π: osmosis potential, -ψ_p: water potential, -ψ: equivalent state

Active transport (水能動輸送)

Materials: Barley roots
active transport

[ stable isotope ( 安定同位体 )]

Water for plant (植物における水)

Def. transpiration (蒸散), T_p: the evaporation of water from plants

stomatal transpiration
cuticular transpiration
lenticular transpiration

Vapor water deficit (VPD, 飽差)

Water-use efficiency, WUE (水利用効率)

Def. WUE: the ratio of water used in plant metabolism to water lost by the plant through transpiration (at a unit time)
a) instantaneous water-use efficiency (photosynthetic WUE)

ratio of the rate of carbon assimilation (photosynthesis, P_s) to the rate of transpiration
= P_s/T_p

b) integrated water-use efficiency (water-use efficiency of productivity)

the ratio of biomass (dry weight, D_w) produced to the rate of transpiration
= D_w/T_p

Transpiration ratio (蒸散係数) = water requirement (要水量)

the amount of water required to produce a unit of plant biomass
= 1/WUE

crop ≈ 200-1000: 200-1000 kg of water is requred to prodcue 1 kg of biomass

Ex. To assimilate 1 g of organic substances, plants require water:

Trees: 200-400 g / Herbs: 400-700 g

pH (potential of hydrogen, ピーエッチ)

1909 Soerensen: proposed the concept of pH
A measure of the acidity or basicity of an aqueous solution, expressed by the concentration of hydrogen ion
Def. ionic product of water (水のイオン積), Kw ≡ [H⁺]·[OH^-]

→ depending only on temperature (T)
Ex. room temperature → Kw ≈ 1.0 × 10^-14

T (°C) → Kw
_0 → 0.113 × 10^-14
10 → 0.292 × 10^-14
20 → 0.681 × 10^-14
25 → 1.008 × 10^-14

Def. Hydrogen-ion exponent (水素イオン指数), pH = -log[H⁺]
= Potential hydrogen, or power of hydrogen
pH is defined as minus the decimal logarithm of the hydrogen ion activity in a solution. So, pH is a dimensionless quantity.

pH = -log₁₀(H⁺) = log₁₀(1/H⁺),

where H⁺ is the activity of hydrogen ions.
As wall as pH, we can define pOH = -log[OH^-], and pKw = -logKw
→ pKw = pH + pOH = 14

Ex. Pure water: H₂O ⇔ H⁺ + OH^- → [H⁺] = [OH^-] = 10^-7

K = [H⁺][OH^-]/[H2O] = 1.8 × 10^-16 (mol) = 55.5 (mol)

[H⁺][OH^-] = 1.8 × 10^-16 × 55.5 = 1.0 × 10^-14, [H⁺] = [OH^-] = 1 × 10^-7 ∴ pH = log[H⁺] = 7

pH_____0____1____2_____3____4____5_____6____7
[H⁺]___10⁰__10^-1__10^-2__10^-3__10^-4__10^-5__10^-6__10^-7
[OH^-]__10^-14_10^-13_10^-11_10^-12_10^-10_ 10^-9__10^-8__10^-7
______acidic ←←←←←←←←←←←←←←←← neutral
____________→→→→→→→→→→→→→→→→ alkali
pH__________8____9____10___11___ 12___ 13___ 14
[H⁺]________10^-8_ 10^-9__10^-10_ 10^-11_10^-12_ 10^-13_10^-14
[OH^-]_______10^-6_ 10^-5__10^-4__10^-3__10^-2__10^-1__10⁰

Def. H⁺ activity (プロトン活量)

CH⁺ = r[H⁺]

r: activity coefficient (活量係数)
fA: [H⁺]↑ → r = 1, [H⁺]↓ → r > 1

Ex. 0.1 M HCl: -log[H⁺] = 1.09 = log-1(2.91) = 8.1 × 10^-2, r = 0.81