Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime

*Milan Gomboš, Branislav Kandra, Andrej Tall and Dana Pavelková*

## **Abstract**

Rainfall and evaporation belong to the basic components of the hydrological cycle. Rainfalls are a decisive natural source of water in the soil. For water replenishment in the natural environment, it is important not only the sum of the rainfall for the balanced period but also the time distribution. In the case of long non-rainfall periods, the soil profile is dried. In the sufficiently long non-rainfall period, the water reserves in the unsaturated zone of the soil profile change and the actual evapotranspiration is reduced. There is a meteorological and then dry soil formation. For the design of adaptation measures, it is necessary to quantify the mentioned hydrological processes. These were investigated in the central area of the Eastern Slovak Lowland between 1970 and 2015. Significant non-rainfall periods, their periodicity and statistical characteristics have been identified. In the course of significant non-rainfall intervals during the vegetation periods the water reserves in the root layer of the soil were analysed up to a depth of 1 m, the actual and potential evapotranspiration, the evapotranspiration deficit, the groundwater level and the air temperature. The longest non-rainfall periods exceeded 30 days.

**Keywords:** rainfall, evaporation, non-rainfall periods, evapotranspiration deficit, soil drought

## **1. Introduction**

Precipitation and evapotranspiration are basic compounds of hydrologic cycle. Precipitation is crucial natural source of water in the soil. Precipitation amount and temporal distribution of the rainfall is important for water refilling of the environment for balanced periods. Drying of soil profile occurs during long rainless periods. Meteorological drought and subsequently soil drought occurs in the case of the sufficiently long rainless period. Therefore it is necessary to know size and statistical characteristics of rainless periods (RLP).

For the analysis of the impacts of the length of the non-precipitation period on the soil water regime, it is necessary to analyse the second critical component of the hydrological cycle. It is a process of evaporation and quantification of the vapour. The evaporation of water in nature is physically the process of converting water to vapour. Due to the high vapour heat (2450 kJ kg<sup>−</sup><sup>1</sup> at the evaporating surface temperature of 20°C) it is an energy-intensive process. In nature, it is the decisive

regulator of energy flows. The evaporation from the soil and plants is called evapotranspiration. The intensity of evapotranspiration over time is affected by the power consumption required for the phase conversion of water to vapour and the amount of this water in the environment. Consequently, evapotranspiration is seasonal in the course of the year. The decisive amount of water evaporates in the vegetal half of the year—from April to September. The maximum possible evapotranspiration under given meteorological conditions is potential evapotranspiration (ET0). Its size is the result of the energy balance on the active surface. Really evaporated water from the soil and plants is called the actual evapotranspiration (ETa). It depends on the positive energy balance, the turbulent exchange between the plant and the atmosphere, the water content of the soil profile, and the plant's ability to regulate the intake and discharge of water from its own organism. If there is sufficient water in the environment, then the actual evapotranspiration is the same as the potential evapotranspiration. If ET0 > ETa, there is an evapotranspiration deficit. This in the root zone of the soil profile indicates the water supply deficit and the beginning of the soil profile drying. Current climate changes are reflected in the redistribution of precipitation over the course of the year and the increase in the air temperature. In other words, the distribution of water and energy in the hydrological system is redistributed. These changes are reflected in changes in evaporation and consequently in changes in the water balance of the area [1–6]. The authors of the chapter have the hypothesis that not only the height of precipitation but also their time distribution during the year has the effect on the occurrence of soil drought.

The aim of the chapter is to identify significant non-precipitation periods, to quantify their time duration, probability properties, development trends and impacts on changes in the critical components of the water regime in the soil environment. In the course of significant non-precipitation intervals during vegetation periods, the water reserves in the root layer of the soil up to a depth of 1 m, the actual and potential evapotranspiration, the evapotranspiration deficit, the groundwater level and the air temperature were analysed.

#### **2. Materials and methods**

The identification of non-precipitation periods and the process of their impact on the components of the water regime of the soil environment were examined in the Milhostov locality in the Eastern Slovak Lowlands (ESL).

The analysis concerned the growing seasons from 1970 to 2015. During the analysis, the following values were analysed at 1-day calculation step and one-day input data: non-rainfall periods, soil water storage to the depth of 1 m; movement of the groundwater level; air temperature; and daily totals of actual and potential evapotranspiration, rainfall and evapotranspiration deficiency.

The research was based on field measurements of hydrophysical characteristics, volume humidity monitoring over the soil profile vertical line, laboratory work and numerical simulation of the water regime using GLOBAL mathematical model [1–6]. The part of the research works was also the verification of the mathematical model using results of the monitoring carried out in the examined locality.

#### **2.1 Description of the investigated area**

These hydrological processes were examined in Milhostov, the area located in the central part of the ESL, Slovakia (48°40′11.08″, N; 21°44′18.02″, E; 100 m). The selected area is characteristic of the ESL. Typical soil of the area is gleyic fluvisol, a medium-heavy soil where clay particles forms 11–39% of the content.

**69**

Genuchten.

**Figure 1.**

*0.002–0.05 mm).*

*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime*

The profile is made of clay, clay-loam and silty clay layers **Figure 1**.

of the soil profile by 0.1 m layers to a depth of 1.0 m.

**Figure 2** shows the course of the clay, dust and sand content via the vertical line

*Texture of the examined soil profile as defined by the USDA triangle (sand 0.05–2.0 mm, clay <0.002 mm, silt* 

In terms of climate, the examined area, as well as the rest of the ESL, is located

in the transitional climate region between the maritime and the continental climate. In terms of temperature, the area is homogeneous. Long-term mean temperature in the area between the years 1961 and 2015 is 9.4°C; minimum mean daily temperature is −20.5°C, maximum mean daily temperature is +30.6°C. The absolute minimum temperature in the area during the analysed period was −29.1°C (January 01, 1987) and the absolute maximum daily temperature was +38.2°C (July 22, 2007). The warmest month is July, the coldest is January. The mean annual amount of rainfall in the area is 558 mm (years 1961–2015). Daily maximum rainfall total was 82.5 mm (June 26, 1995). Rainfall conditions in the area are heavily influenced by the air circulation. Heaviest rainfall is induced by the humid and warm air flowing from the south. Air currents from the other directions do not usually bring rainfall because it falls on the Carpathians. The maximum duration of the continuous period with no rainfall was 35 days. The maximum annual long-term mean duration of the period with no rainfall is 17 days. Long-term mean

The clay, silt and sand content via the vertical line of the soil profile to 1 m depth. **Figure 2** shows that the most ratio of the studied profile is formed by the dusty component. The profile is up to 0.7 m relatively homogeneous. In the range between 0.7 and 1.0 m, the ratio of the individual components of the microstructure significantly changes. For this reason, two material layers were considered in the calculations. **Table 1** lists their retention lines parameters according to Van

*DOI: http://dx.doi.org/10.5772/intechopen.82399*

*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime DOI: http://dx.doi.org/10.5772/intechopen.82399*

**Figure 1.** *Texture of the examined soil profile as defined by the USDA triangle (sand 0.05–2.0 mm, clay <0.002 mm, silt 0.002–0.05 mm).*

The profile is made of clay, clay-loam and silty clay layers **Figure 1**.

**Figure 2** shows the course of the clay, dust and sand content via the vertical line of the soil profile by 0.1 m layers to a depth of 1.0 m.

The clay, silt and sand content via the vertical line of the soil profile to 1 m depth. **Figure 2** shows that the most ratio of the studied profile is formed by the dusty component. The profile is up to 0.7 m relatively homogeneous. In the range between 0.7 and 1.0 m, the ratio of the individual components of the microstructure significantly changes. For this reason, two material layers were considered in the calculations. **Table 1** lists their retention lines parameters according to Van Genuchten.

In terms of climate, the examined area, as well as the rest of the ESL, is located in the transitional climate region between the maritime and the continental climate. In terms of temperature, the area is homogeneous. Long-term mean temperature in the area between the years 1961 and 2015 is 9.4°C; minimum mean daily temperature is −20.5°C, maximum mean daily temperature is +30.6°C. The absolute minimum temperature in the area during the analysed period was −29.1°C (January 01, 1987) and the absolute maximum daily temperature was +38.2°C (July 22, 2007). The warmest month is July, the coldest is January. The mean annual amount of rainfall in the area is 558 mm (years 1961–2015). Daily maximum rainfall total was 82.5 mm (June 26, 1995). Rainfall conditions in the area are heavily influenced by the air circulation. Heaviest rainfall is induced by the humid and warm air flowing from the south. Air currents from the other directions do not usually bring rainfall because it falls on the Carpathians. The maximum duration of the continuous period with no rainfall was 35 days. The maximum annual long-term mean duration of the period with no rainfall is 17 days. Long-term mean

*Hydrology - The Science of Water*

year has the effect on the occurrence of soil drought.

groundwater level and the air temperature were analysed.

the Milhostov locality in the Eastern Slovak Lowlands (ESL).

evapotranspiration, rainfall and evapotranspiration deficiency.

**2. Materials and methods**

**2.1 Description of the investigated area**

regulator of energy flows. The evaporation from the soil and plants is called evapotranspiration. The intensity of evapotranspiration over time is affected by the power consumption required for the phase conversion of water to vapour and the amount of this water in the environment. Consequently, evapotranspiration is seasonal in the course of the year. The decisive amount of water evaporates in the vegetal half of the year—from April to September. The maximum possible evapotranspiration under given meteorological conditions is potential evapotranspiration (ET0). Its size is the result of the energy balance on the active surface. Really evaporated water from the soil and plants is called the actual evapotranspiration (ETa). It depends on the positive energy balance, the turbulent exchange between the plant and the atmosphere, the water content of the soil profile, and the plant's ability to regulate the intake and discharge of water from its own organism. If there is sufficient water in the environment, then the actual evapotranspiration is the same as the potential evapotranspiration. If ET0 > ETa, there is an evapotranspiration deficit. This in the root zone of the soil profile indicates the water supply deficit and the beginning of the soil profile drying. Current climate changes are reflected in the redistribution of precipitation over the course of the year and the increase in the air temperature. In other words, the distribution of water and energy in the hydrological system is redistributed. These changes are reflected in changes in evaporation and consequently in changes in the water balance of the area [1–6]. The authors of the chapter have the hypothesis that not only the height of precipitation but also their time distribution during the

The aim of the chapter is to identify significant non-precipitation periods, to quantify their time duration, probability properties, development trends and impacts on changes in the critical components of the water regime in the soil environment. In the course of significant non-precipitation intervals during vegetation periods, the water reserves in the root layer of the soil up to a depth of 1 m, the actual and potential evapotranspiration, the evapotranspiration deficit, the

The identification of non-precipitation periods and the process of their impact on the components of the water regime of the soil environment were examined in

The research was based on field measurements of hydrophysical characteristics,

These hydrological processes were examined in Milhostov, the area located in the central part of the ESL, Slovakia (48°40′11.08″, N; 21°44′18.02″, E; 100 m). The selected area is characteristic of the ESL. Typical soil of the area is gleyic fluvisol, a

volume humidity monitoring over the soil profile vertical line, laboratory work and numerical simulation of the water regime using GLOBAL mathematical model [1–6]. The part of the research works was also the verification of the mathematical

model using results of the monitoring carried out in the examined locality.

medium-heavy soil where clay particles forms 11–39% of the content.

The analysis concerned the growing seasons from 1970 to 2015. During the analysis, the following values were analysed at 1-day calculation step and one-day input data: non-rainfall periods, soil water storage to the depth of 1 m; movement of the groundwater level; air temperature; and daily totals of actual and potential

**68**

#### **Figure 2.**

*Content of clay, silt and sand to the soil profile vertical to 1 m depth.*


#### **Table 1.**

*Parameters of retention lines of material layers of the soil profile.*

wind speed 10 m above the ground is 2.468 m s<sup>−</sup><sup>1</sup> . Daily long-term mean pressure of water vapour is 0.999 kPa where the daily mean minimum is 0.083 kPa and the maximum is 2.760 kPa. Daily long-term mean relative humidity is 77.4%, where the daily mean minimum is 33% and the maximum is 100%. With regard to phenological characteristics and vegetation of the area, there are no noticeable temporal or local changes.

### **2.2 Description of the experiment**

Methodical process of the research consists of two phases: rainless periods selection, model verification, calculation of water regime components and results interpretation. Climatic station of Milhostov (N 48°39,786′; E 21°43,298′) was chosen for selection of statistically important rainless periods. Station is located at central part of Eastern Slovak Lowland (ESL) and represents wider area of lowland. Daily precipitation amounts of the 1961–2015 period was examined for the station. 20,080 daily precipitation amounts (including zero) were analysed for the period. Length of RLP was identified separately for whole years of examined periods and separately for vegetal periods (VP). Selections of RLP were applied for VP examination in two ways. Periods with zero daily precipitation amounts were

**71**

*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime*

considered in first selection (s0). Daily precipitation amounts lower than 2 mm were considered as zero in the second selection (s2). These precipitation are likely to be catched by the plant cover and subsequently vaporised without influencing soil water supply. Selection of rainless periods during VP was done only of those which occurred during vegetal periods (April–September). However, periods that starts before VP and overlap to VP and those that starts during VP and finished after VP were considered as well. Rainless periods of the 1961–2015 were probabil-

Just (s0) selection was applied during examination of entire year periods. Basic statistical characteristics were calculated after identification of RLP. Probability characteristics of occurrence of different RLP temporal duration were calculated by binomial distribution. The results are indicated in the form of frequency curves. Development of number of rainless days during individual years and VP was evaluated. For example, 10 longest RLP during 1961–2015 were selected for every

The database for needs of the experiment was collected by the field monitoring, laboratory measurements and the numerical simulation via the mathematical model

The field monitoring concerned the measuring of the groundwater level and volumetric moisture within a soil profile, vertically to the depth of 0.8 m and horizontally by 0.1 m thick layers. The field works included also soil sampling. Gathered soil samples were processed in the laboratory and basic characteristics of the soil profile were determined. The Climatic and Agroecology Research Institute is located in the examined area. During the years 1970–2015, the institute provided hydro-meteorological data and plant characteristics necessary for the numerical simulation via the mathematical model 'GLOBAL'. The results of the water storage monitoring to the depth of 0.8 m are available as well. The model was verified using the data from the extremely dry growing season in 2007. The growing season of 2007 was the second driest season of the analysed period. The driest season was that

Once the model was verified, the development of *ET0*, *ETa* and water storage in a soil profile to the depth of 1 m was calculated with one-day calculation step. In addition, the value of evapotranspiration deficiency was calculated using Eq. (1):

*D* = *ET*<sup>0</sup> − *ETa* (1)

The simulation was conducted for the growing seasons from 1970 to 2015. *ET0*, *ETa* and *D* totals during the growing seasons were analysed with regard to water storage (WS), rainfall and groundwater level (GWL). For *ET0*, *ETa* and *D*, linear trends were calculated and the correlation analysis between the analysed units was performed. The development of *WS* in the extremely dry season was analysed with

The model 'GLOBAL' is a mathematical model to enable simulating water movement in soil and calculating the distribution of soil moisture potential, i.e. soil moisture in real time [7–12]. The model is based on the numerical solution of a nonlinear partial differential Richards' equation describing water movement in aerated

> ( \_\_\_\_ ∂*hw*

<sup>∂</sup>*<sup>z</sup>* <sup>+</sup> <sup>1</sup>)] <sup>−</sup> \_\_\_\_\_

*S*(*z*,*t*)

*<sup>c</sup>*(*hw*) (2)

*DOI: http://dx.doi.org/10.5772/intechopen.82399*

ity-evaluated in every selection group.

selection.

'GLOBAL'.

of the year 2015.

one-day step.

**2.3 Brief description of the model 'GLOBAL'**

∂*hw*

<sup>∂</sup>*<sup>t</sup>* <sup>=</sup> \_\_\_\_\_ <sup>1</sup> *c*(*hw*) \_\_\_∂ <sup>∂</sup>*<sup>z</sup>* [*k*(*h*)

soil zone, which is as follows:

\_\_\_\_

#### *Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime DOI: http://dx.doi.org/10.5772/intechopen.82399*

considered in first selection (s0). Daily precipitation amounts lower than 2 mm were considered as zero in the second selection (s2). These precipitation are likely to be catched by the plant cover and subsequently vaporised without influencing soil water supply. Selection of rainless periods during VP was done only of those which occurred during vegetal periods (April–September). However, periods that starts before VP and overlap to VP and those that starts during VP and finished after VP were considered as well. Rainless periods of the 1961–2015 were probability-evaluated in every selection group.

Just (s0) selection was applied during examination of entire year periods. Basic statistical characteristics were calculated after identification of RLP. Probability characteristics of occurrence of different RLP temporal duration were calculated by binomial distribution. The results are indicated in the form of frequency curves. Development of number of rainless days during individual years and VP was evaluated. For example, 10 longest RLP during 1961–2015 were selected for every selection.

The database for needs of the experiment was collected by the field monitoring, laboratory measurements and the numerical simulation via the mathematical model 'GLOBAL'.

The field monitoring concerned the measuring of the groundwater level and volumetric moisture within a soil profile, vertically to the depth of 0.8 m and horizontally by 0.1 m thick layers. The field works included also soil sampling. Gathered soil samples were processed in the laboratory and basic characteristics of the soil profile were determined. The Climatic and Agroecology Research Institute is located in the examined area. During the years 1970–2015, the institute provided hydro-meteorological data and plant characteristics necessary for the numerical simulation via the mathematical model 'GLOBAL'. The results of the water storage monitoring to the depth of 0.8 m are available as well. The model was verified using the data from the extremely dry growing season in 2007. The growing season of 2007 was the second driest season of the analysed period. The driest season was that of the year 2015.

Once the model was verified, the development of *ET0*, *ETa* and water storage in a soil profile to the depth of 1 m was calculated with one-day calculation step. In addition, the value of evapotranspiration deficiency was calculated using Eq. (1):

$$D = -ET\_0 - ET\_a \tag{1}$$

The simulation was conducted for the growing seasons from 1970 to 2015. *ET0*, *ETa* and *D* totals during the growing seasons were analysed with regard to water storage (WS), rainfall and groundwater level (GWL). For *ET0*, *ETa* and *D*, linear trends were calculated and the correlation analysis between the analysed units was performed. The development of *WS* in the extremely dry season was analysed with one-day step.

#### **2.3 Brief description of the model 'GLOBAL'**

The model 'GLOBAL' is a mathematical model to enable simulating water movement in soil and calculating the distribution of soil moisture potential, i.e. soil moisture in real time [7–12]. The model is based on the numerical solution of a nonlinear partial differential Richards' equation describing water movement in aerated soil zone, which is as follows:

$$\frac{\partial h\_w}{\partial t} = \frac{1}{c \langle h\_w \rangle} \frac{\partial}{\partial z} \left[ k \left( h \right) \left( \frac{\partial h\_w}{\partial z} + \mathbf{1} \right) \right] - \frac{S(z, t)}{c \langle h\_w \rangle} \tag{2}$$

*Hydrology - The Science of Water*

wind speed 10 m above the ground is 2.468 m s<sup>−</sup><sup>1</sup>

*Parameters of retention lines of material layers of the soil profile.*

*Content of clay, silt and sand to the soil profile vertical to 1 m depth.*

**2.2 Description of the experiment**

of water vapour is 0.999 kPa where the daily mean minimum is 0.083 kPa and the maximum is 2.760 kPa. Daily long-term mean relative humidity is 77.4%, where the daily mean minimum is 33% and the maximum is 100%. With regard to phenological characteristics and vegetation of the area, there are no noticeable temporal or

**Layer Alpha n θs Θ<sup>r</sup>** 0.0–0.7 m 0.0084 1.5202 0.43 0.12 0.7–1.0 m 0.0482 1.1593 0.39 0.07

Methodical process of the research consists of two phases: rainless periods selection, model verification, calculation of water regime components and results interpretation. Climatic station of Milhostov (N 48°39,786′; E 21°43,298′) was chosen for selection of statistically important rainless periods. Station is located at central part of Eastern Slovak Lowland (ESL) and represents wider area of lowland. Daily precipitation amounts of the 1961–2015 period was examined for the station. 20,080 daily precipitation amounts (including zero) were analysed for the period. Length of RLP was identified separately for whole years of examined periods and separately for vegetal periods (VP). Selections of RLP were applied for VP examination in two ways. Periods with zero daily precipitation amounts were

. Daily long-term mean pressure

**70**

local changes.

**Figure 2.**

**Table 1.**

#### *Hydrology - The Science of Water*

where *hw*—soil moisture potential; *z*—vertical coordinate; *<sup>k</sup>*(*hw*)—unsaturated hydraulic conductivity of soil; *<sup>S</sup>*(*z*,*t*)—intensity of water uptake by plant roots from unit soil volume per unit of time (cm3 /cm3 ).d<sup>−</sup><sup>1</sup> ; and *<sup>c</sup>*(*hw*) <sup>=</sup> \_\_\_\_ ∂θ ∂*hw* , *θ*—volume soil moisture (cm3 /cm3 ).

The simulation using the model 'GLOBAL' can be performed with one-day calculation step. In that instance, daily values are used as the input values for creating the boundary conditions. This also applies to the meteorological inputs and the plant cover input parameters. The model 'GLOBAL' includes also soil hydrophysical characteristics such as: retention curves, soil saturated and unsaturated hydraulic conductivity, hydrolimits and some physical soil characteristics (porosity, specific weight and volumetric mass density and moisture of saturated soil). In the model, hydrophysical characteristics are expressed by analytical equations. Moisture retention curve is described by van Genuchten model.

Potential evapotranspiration *ET0* is calculated by Penman-Monteith equation. For determining actual transpiration and evaporation, the method developed at IH SAS was used. This method assumes that the evapotranspiration depends on the value of leaf area index (*LAI*). The intensity of potential evaporation *Eeo* is calculated from the value of potential evapotranspiration *ET0* as follows:

$$E\_{ev} = \,^\*ET\_0 \,. \exp\left(-m\_1 \,.LAI\right) \tag{3}$$

The value of empirical coefficient (m1 = 0.463) was gained by field measurements in a maize field. Actual evapotranspiration and its structure is calculated based on the values of potential evapotranspiration ET0 and the relation between relative evapotranspiration Eeo/ET0 and soil profile moisture, i.e.

$$ET\_r = \frac{E\_{to}}{ET\_0} = f(\Theta) \tag{4}$$

**73**

duration of RLP.

**Figure 3.**

**Table 2.**

*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime*

**Parameters Year VP VP** Selection f(0) f(0) f(2) Mean 3.57 3.67 6.15 Standard error 0.06 0.08 0.17 Median 2 2 4 Mode 1 1 1 Standard deviation 3.52 3.51 6.31 Sample variance 12.41 12.30 39.84 Kurtosis 10.98 9.66 8.47 Skewness 2.64 2.47 2.45 Range 34 34 52 Minimum 1 1 1 Maximum 35 35 53 Sum 12,185 6429 8567 Count 3409 1751 1393 Confidence level (95.0%) 0.12 0.16 0.33

results that only little differences are between course of yearly and vegetal selections of s0. Length of RLP with p = 50% probability of exceedance is for this selection of VP 13 days and for the year 15.5 days. This value is 23.3 days for selection s2 during the vegetal period. The course of probability of exceedance curve is in case of s2 selection moved and more steep. This indicates greater variability and longer

*Empirical and theoretical probability of exceedance curves of maximal year durations of rainless periods.*

Numbers of days without rainfall are indicated in **Figure 4** for individual years and their vegetal periods for selections s0 and s2. Developmental trends are for all cases parallel with timeline. It is testified by the fact that number of rainy

*DOI: http://dx.doi.org/10.5772/intechopen.82399*

*Basic statistical characteristics of rainless periods.*

The calculation method is based, inter alia, on the assumption that the median soil moisture in the root zone used for the calculation of transpiration, or the value of moisture in the upper layer of a soil profile used for the calculation of evaporation, depends on the intensity of evaporation. The higher is the intensity of evaporation, the higher is the value of *θk*, at which the evaporation starts to decrease. The verification of the method via the model 'GLOBAL' has shown a very high concordance between the calculated values and the values measured in real conditions. The outputs of the modelling are moisture and soil moisture potential distribution, daily totals of the following: interception, evaporation and its components, infiltration, existing water deficiency in soil and other.

#### **3. Results and discussion**

#### **3.1 Identification of non-precipitation periods**

Basic characteristics of descriptive statistics are indicated in **Table 2**. It results that 12,185 days (60.68%) were with no precipitation in 1 year selection data series. Days without rainfall were grouped to 3409 periods. 63.87% of days without rainfall were in the case of VP and s0 selection and 85.12% days without rainfall in the case of VP and s2 selection. The longest RLP duration was 35 days for s0 selection and 53 days for s2 selection.

Eloquent image of probability of occurrence of maximal year durations of RLP gives probability of exceedance curves. Curves are indicated in **Figure 3**. There of


*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime DOI: http://dx.doi.org/10.5772/intechopen.82399*

#### **Table 2.**

*Hydrology - The Science of Water*

moisture (cm3

unit soil volume per unit of time (cm3

tion curve is described by van Genuchten model.

*ETr* <sup>=</sup> \_\_\_\_ *Eeo*

tion, existing water deficiency in soil and other.

**3.1 Identification of non-precipitation periods**

**3. Results and discussion**

53 days for s2 selection.

/cm3 ).

where *hw*—soil moisture potential; *z*—vertical coordinate; *<sup>k</sup>*(*hw*)—unsaturated hydraulic conductivity of soil; *<sup>S</sup>*(*z*,*t*)—intensity of water uptake by plant roots from

; and *<sup>c</sup>*(*hw*) <sup>=</sup> \_\_\_\_ ∂θ

∂*hw*

= *f*(θ) (4)

, *θ*—volume soil

/cm3 ).d<sup>−</sup><sup>1</sup>

The simulation using the model 'GLOBAL' can be performed with one-day calculation step. In that instance, daily values are used as the input values for creating the boundary conditions. This also applies to the meteorological inputs and the plant cover input parameters. The model 'GLOBAL' includes also soil hydrophysical characteristics such as: retention curves, soil saturated and unsaturated hydraulic conductivity, hydrolimits and some physical soil characteristics (porosity, specific weight and volumetric mass density and moisture of saturated soil). In the model, hydrophysical characteristics are expressed by analytical equations. Moisture reten-

Potential evapotranspiration *ET0* is calculated by Penman-Monteith equation. For determining actual transpiration and evaporation, the method developed at IH SAS was used. This method assumes that the evapotranspiration depends on the value of leaf area index (*LAI*). The intensity of potential evaporation *Eeo* is calcu-

*Eeo* = *ET*<sup>0</sup> . exp(−*m*<sup>1</sup> . *LAI*) (3)

The value of empirical coefficient (m1 = 0.463) was gained by field measurements in a maize field. Actual evapotranspiration and its structure is calculated based on the values of potential evapotranspiration ET0 and the relation between

*ET*<sup>0</sup>

The calculation method is based, inter alia, on the assumption that the median soil moisture in the root zone used for the calculation of transpiration, or the value of moisture in the upper layer of a soil profile used for the calculation of evaporation, depends on the intensity of evaporation. The higher is the intensity of evaporation, the higher is the value of *θk*, at which the evaporation starts to decrease. The verification of the method via the model 'GLOBAL' has shown a very high concordance between the calculated values and the values measured in real conditions. The outputs of the modelling are moisture and soil moisture potential distribution, daily totals of the following: interception, evaporation and its components, infiltra-

Basic characteristics of descriptive statistics are indicated in **Table 2**. It results that 12,185 days (60.68%) were with no precipitation in 1 year selection data series. Days without rainfall were grouped to 3409 periods. 63.87% of days without rainfall were in the case of VP and s0 selection and 85.12% days without rainfall in the case of VP and s2 selection. The longest RLP duration was 35 days for s0 selection and

Eloquent image of probability of occurrence of maximal year durations of RLP gives probability of exceedance curves. Curves are indicated in **Figure 3**. There of

lated from the value of potential evapotranspiration *ET0* as follows:

relative evapotranspiration Eeo/ET0 and soil profile moisture, i.e.

**72**

*Basic statistical characteristics of rainless periods.*

*Empirical and theoretical probability of exceedance curves of maximal year durations of rainless periods.*

results that only little differences are between course of yearly and vegetal selections of s0. Length of RLP with p = 50% probability of exceedance is for this selection of VP 13 days and for the year 15.5 days. This value is 23.3 days for selection s2 during the vegetal period. The course of probability of exceedance curve is in case of s2 selection moved and more steep. This indicates greater variability and longer duration of RLP.

Numbers of days without rainfall are indicated in **Figure 4** for individual years and their vegetal periods for selections s0 and s2. Developmental trends are for all cases parallel with timeline. It is testified by the fact that number of rainy

#### **Figure 4.**

*Number of days without precipitation in individual years 1961–2015.*

and rainless days is for individual years and their vegetal periods balanced in the long term view. Only duration of rainless events of non-vegetal periods changes in examined periods. It is confirmed by the results that are graphically shown in **Figure 5**. There are indicated numbers of days of rainless periods that lasts 10 days or more for VP of individual years. From the figure results that trend development of both selections s0 and s2 is stable without change (parallel to the timeline) during vegetal periods. Elongated trend of rainless periods with duration of 9 days or more was identified in case of s0 yearly selection. These results show that this trend

**75**

**Figure 6.**

*growing season of 2007.*

*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime*

rainless periods predominantly occurred in 1960s and after the year 2000.

Extremely dry year 2015 does not appear in s0 selection, however, it was identified in s2 selection. 35 day continuous period during which was total precipitation amount of 2.5 mm occurred. This year was unique in that 91 rainless days between 28.5.2015 and 2.9.2015 were associated in 4 seasons by 18, 22, 16 and 35 days in

During the verification of the model GLOBAL the assessment of the weekly values of integral soil water content to the depth of 0.8 m expressed in millimetres of water column was conducted. The selection of the layer for the calculation

*Ten longest rainless periods in every selection series, their theoretical probability of incidence and periodicity.*

*Comparison between the monitored and the modelled soil water storage up to the depth of 0.80 m during the* 

is caused by rainless events during non-vegetal periods. Stated fact has influence on creation of water storage during before-spring periods and enlarges risk of drought. As an example, 10 longest rainless periods with date of its occurrence, theoretical probability and periodicity of incidence is indicated in **Table 3** for every selection series (year, s0, VP, s0 and VP, s2). The absolutely longest continuous period without rainfall for s0 selection (year, VP) had 35 days and occurred between 25.9.1962 and 29.10.1962. Maximal continuous rainless event extends to 53 days in case of s2 selection for the vegetal period. This event occurred in time interval 19.7.1967–9.9.1967. Precipitation amount was only 1.6 mm in this time interval. This time interval can be considered as the rainless period. From **Table 3** results that the most important

*DOI: http://dx.doi.org/10.5772/intechopen.82399*

selection s2.

**Table 3.**

**3.2 Model verification**

**Figure 5.** *Number of days during rainless periods with duration of 9 days or more.*

#### *Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime DOI: http://dx.doi.org/10.5772/intechopen.82399*

is caused by rainless events during non-vegetal periods. Stated fact has influence on creation of water storage during before-spring periods and enlarges risk of drought.

As an example, 10 longest rainless periods with date of its occurrence, theoretical probability and periodicity of incidence is indicated in **Table 3** for every selection series (year, s0, VP, s0 and VP, s2). The absolutely longest continuous period without rainfall for s0 selection (year, VP) had 35 days and occurred between 25.9.1962 and 29.10.1962. Maximal continuous rainless event extends to 53 days in case of s2 selection for the vegetal period. This event occurred in time interval 19.7.1967–9.9.1967. Precipitation amount was only 1.6 mm in this time interval. This time interval can be considered as the rainless period. From **Table 3** results that the most important rainless periods predominantly occurred in 1960s and after the year 2000.

Extremely dry year 2015 does not appear in s0 selection, however, it was identified in s2 selection. 35 day continuous period during which was total precipitation amount of 2.5 mm occurred. This year was unique in that 91 rainless days between 28.5.2015 and 2.9.2015 were associated in 4 seasons by 18, 22, 16 and 35 days in selection s2.

## **3.2 Model verification**

During the verification of the model GLOBAL the assessment of the weekly values of integral soil water content to the depth of 0.8 m expressed in millimetres of water column was conducted. The selection of the layer for the calculation


**Table 3.**

*Hydrology - The Science of Water*

**74**

**Figure 5.**

**Figure 4.**

*Number of days during rainless periods with duration of 9 days or more.*

and rainless days is for individual years and their vegetal periods balanced in the long term view. Only duration of rainless events of non-vegetal periods changes in examined periods. It is confirmed by the results that are graphically shown in **Figure 5**. There are indicated numbers of days of rainless periods that lasts 10 days or more for VP of individual years. From the figure results that trend development of both selections s0 and s2 is stable without change (parallel to the timeline) during vegetal periods. Elongated trend of rainless periods with duration of 9 days or more was identified in case of s0 yearly selection. These results show that this trend

*Number of days without precipitation in individual years 1961–2015.*

*Ten longest rainless periods in every selection series, their theoretical probability of incidence and periodicity.*

**Figure 6.**

*Comparison between the monitored and the modelled soil water storage up to the depth of 0.80 m during the growing season of 2007.*

#### *Hydrology - The Science of Water*

depended on the depth to which the soil water storage was monitored in field. The results of the simulation and the measurements are shown in **Figure 6**. The diagram shows a very high concordance between the calculated and the measured values which is proven by the results in **Figure 7**. It is a quantile-quantile plot which shows the linear trend and the correlation coefficient between the measured and the modelled values. The R-squared statistic indicates that the model as fitted explains 86.37% of the variability in measurement. The correlation coefficient equals 0.93, indicating a relatively strong relationship between the variables. Other basic characteristics of the descriptive statistics are listed in **Table 4**.

The results show that, especially in terms of moisture, the model GLOBAL <sup>θ</sup> <sup>&</sup>gt; TP tends to overestimate the real state. When the moisture is lower, it tends to underestimate it. In addition, the t-test was applied to compare the mean values and the F-test to compare the standard deviations of the measured and the modelled values. The results of the tests are shown in **Table 5**. The tests showed that the null hypothesis regarding the equality of the mean values and standard deviations of

#### **Figure 7.**

*Representation of the linear dependence via the correlation coefficients between the measured and the modelled daily values of integral soil water content to the depth of 0.8 m in Milhostov.*


**77**

**Figure 8.**

1998).

**Table 5.**

*Results of the t-test and F-test.*

*Analysis of Non-Rainfall Periods and Their Impacts on the Soil Water Regime*

t-statistic = −0.177316 Two-sided P-value = 0.860112

F-statistic = 0.627217 Two-sided P-value = 0.293035

Null hypothesis Mean measurement = Mean simulation Alternative hypothesis Mean measurement ≠ Mean simulation

Null hypothesis Sigma measurement = Sigma simulation Alternative hypothesis Sigma measurement ≠ Sigma simulation

Conclusion Do not reject the null hypothesis for alpha = 0.05

Conclusion Do not reject the null hypothesis for alpha = 0.05

the measured and simulated values cannot be rejected. The results indicate that the model is suitable for the examined area and it can be used for the simulation of the water regime in the unsaturated soil zone. It should be noted that the model has been verified and successfully applied in other areas around Slovakia (Novák et al.,

**Figure 8** shows the contour lines representing the volume moisture and it was made based on the moisture values monitored up to the depth of 0.8 m by 0.10 m thick layers in Milhostov during the growing season of 2007. The picture shows that

**Table 6** lists the basic characteristics of the descriptive statistics applied to the following: seasonal, monthly and daily totals of ET0, D, P; average soil water storage during the growing season to the depth of 1.0 m and the mean location of GWL under the surface during the growing season. **Table 6** shows that the longterm mean evaporation during the growing season in the form of ETa is 315.17 mm (59.4% of ET0) while evaporation ET0 is 530.63 mm. This leads to the long-term evaporation deficiency of 215.45 mm, which is 40.6% of ET0. Long-term mean rainfall total during the growing season is 70.0% (371.44 mm) of ET0. Long-term mean

*Contour lines of the volumetric moisture up to 0.80 m during the growing season of 2007.*

*DOI: http://dx.doi.org/10.5772/intechopen.82399*

**F-test to compare standard deviations**

**t-Test to compare means**

the whole profile was dry to the subsoil layers.

**3.3 Results of numerical simulation**
