**Chapter 4. Results of the offline land surface model**

**4.4 The diurnal difference in the dry and wet seasons (South Asia).28**

Figure 27 shows the difference in temperature, wet-bulb temperature, and mixing

ratio in the dry season, respectively. On dry season days, the gradient of humidity

between irrigated surfaces and the atmosphere is large. Therefore, evaporation works

more effectively than the night and wet seasons. However, according to equation (13),

the moistening effect is much larger than the temperature decrease. Thus, the wet-bulb

temperature curve is similar to the mixing ratio change. Specifically, the curve of

mixing ratio change increased from 1906 to 2010 because the irrigation amount in

South Asia also increases and makes the evaporation go larger. During the nighttime,

the temperature decreases because of sunsets. Besides, the moisture in the atmosphere

goes higher from evaporation in the daytime. Therefore, the relative humidity is larger

at night than at daytime. Evaporation is less due to the lower gradient of the mixing

ratio between the surface and atmosphere and solar radiation. Thus, the red curve in

figure 27 has the same trend as the blue curve, but the absolute values are lower.

Figure 28 shows the difference in temperature, wet-bulb temperature, and the

mixing ratio in wet seasons, respectively. In these figures, the daytime and nighttime are

similar. This is because the background atmosphere is wet and the gradient between the

surface and atmosphere is small both day and night. Therefore, the wet-bulb

temperature doesn’t increase as large as in dry seasons but still has the same trend.

4.5 The yearly trend of wet-bulb temperature in South Asia and North China

In this section, we explore six variables to deeply understand the mechanism of

irrigation moistening by comparing two different regions, South Asia and North China.

Figure 29 shows the difference in variables due to irrigation. Figure 29d illustrates the

irrigation amount increase over time. This is due to the increasing population and the

food demand getting higher, particularly after the 1950s (Siebert et al. 2015, Guo et al.

2022). Because of these higher amounts of water in the soil, the specific humidity near

the surface gets higher, making evaporation efficient. Accordingly, we calculate the

correlation coefficient of irrigation amount to temperature, wet-bulb temperature,

mixing ratio, and latent heat flux. The coefficients are -0.993, 0.994, 0.997, and 0.991,

respectively. Therefore, the relations between these variables are highly correlated.

To analyze what makes the evaporation work, we investigate the bulk formula

which is the concept of the mixture in the boundary layer (Lawrence et al. 2019) as

below:

(1) The definition of the bulk formula:

𝐿𝐻 = 𝜌𝐿_{3}𝐶_{4}𝑈_{&"}(𝑞_{!}− 𝑞_{5})

( 19 )

(2) Differentiate it on both sides:

𝑑𝐿𝐻 ∝ 𝑈_{&"}𝑑(𝑞_{!}− 𝑞_{5}).

( 20 )

Therefore, the difference in latent heat flux between the two models is in proportion to

the specific humidity difference. Figure 29f shows the decomposition of latent heat flux.

The main reason that causes the evaporation to work is the difference of specific

humidity in the atmosphere and surface, here we call (𝑞_{!} − 𝑞_{5})_{!67} afterward and the

subscript means the simulation model. When irrigation turns on, the (𝑞_{!}− 𝑞_{5})_{%''} goes

higher because the specific humidity gets larger near the surface. Also, the key factor

𝑑(𝑞_{!}− 𝑞_{5}) can be written as:

𝑑(𝑞_{!}− 𝑞_{5}) = (𝑞_{!}− 𝑞_{5})_{%''}− (𝑞_{!}− 𝑞_{5})_{,-.} = (𝑞_{!})_{%''}− (𝑞_{!})_{,-.}

( 21 )

Note that this is a bounded model, so the specific humidity of the atmosphere is the

same in both models. Note that figure 29f is similar to figure 29e but not the same. This

comes from the coefficient ahead in equation (19) is not the same when the model does

the irrigation.

In plain language, the mechanism is that evaporation makes the surface moisturize,

which causes evaporation to work efficiently. This gives rise to latent heat flux and the

mixing ratio goes high. Also, the temperature goes down due to the cooling effect. The

result of wet-bulb temperature obeys the mixing ratio curve because the moistening

effect is the key faction to dominate.

Figure 30 is the profile of North China, the irrigation amount is less than South

Asia by one order. Thus, the evaporation-related variables change less. However,

although the irrigation amount increases over time, latent heat flux decreases between

1920 to 1950 and 2000 to 2010. Figures 31a and b show the specific humidity at 10m

and 2m high. It grows about 10^{-3} (kg/kg) and 10^{-4} (kg/kg) from 1920 to 1950 and 2000

to 2010. That is, the background atmosphere is moisturized. According to our discussion

above, the evaporation is less because of the specific humidity difference in the two

models, that is, (𝑞_{!})_{%''} minus (𝑞_{!})_{,-.}, gets lower. Therefore, the related variables (i.e.

wet-bulb temperature, mixing ratio, etc.) have the same trend as latent heat flux

although the irrigation amount remains nearly the same.

Also, we find that the irrigation amount increases rapidly from 1950 to 1960. This

might come from two factors at the same time. The first one is the green revolution

which is the food demand from the increasing population. The second one is the

background atmosphere becomes dry. Figure 31a shows the decreasing specific

humidity in the upper layer from 1950 to 1960. That is to say, the model is forced to

irrigate this region due to the increasing irrigation fraction and the dry climate.

Therefore, the latent heat flux increases rapidly because the specific humidity near the

surface gets much higher compared to the control simulation. Therefore, the mixing

ratio and wet-bulb temperature increase a lot over this period.