# Management models

## Management Model: Irrigation 

### Introduction

The WiForAgri irrigation model is a system for monitoring, **forecasting and alerting the water content of the cropland.** 

On the basis of the agronomic-cultural characteristics of the agricultural lot, which can be selected through the initial setting interface of the model, the **DSS will carry out the daily water balance of the soil,** according to the standard FAO methodology (Irrigation and Drainage Paper No.56), analyzing the terms entering and leaving the ground and will provide a series of information on a daily basis describing the current water status, including: 

* Daily and long-term (precision) **evapotranspiration**. 
* **Soil water deficit versus field capacity** (maximum water volume retained by the soil). 
* **The residual water content that can be easily extracted from crops** (without undergoing stress conditions). 
* The terms of **effective rain and capillary rising.**

![Figure 1 - Exchanges of water between the atmosphere, the soil and the aquifer evaluated by the DSS daily through the water balance equation, in order to determine the water deficit of the soil with respect to an ideal condition (field capacity)](https://1959260061-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LDGLlFs-4e4Wr2T8FYa%2F-LoW-cLxY-EicNNrif_9%2F-LoW1KEMpP9kDhUkihbI%2Fbilancio_idrico4.png?alt=media\&token=6c79762f-b441-458e-815a-31cc0bbeaf58)

![Figure 2 - Conceptual scheme of compensation of irrigation losses of the soil system of plants through irrigation interventions.](https://1959260061-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Ff4cRzKqKDgSAs8egc84d%2Fuploads%2FBH7BoZgpgaz8IMgqFqRa%2FIRRIGATION%20scheme.png?alt=media\&token=48549aa7-773a-484e-8517-a949d9db0ba6)

In addition to this information, provided in graphic format for immediate reading, the model integrates an **automatic alert system** (SMS and/or Email) **capable of notifying the user of the approaching critical moment for which irrigation is required.** It will therefore be possible to avoid an excessive and harmful water deficit for plants and for production by knowing in advance a state of water criticality that requires irrigation intervention. 

**The optimal irrigation volume (irrigation recommended** for each irrigation intervention - in cubic meters or liters per hectare) **will be provided by the model** in order to prevent episodes of over-irrigation, saturation of the soil and therefore root anoxia and waste of water resources. If the user supplies an excessive volume of water, the system will indicate the liters of water lost/wasted for each single irrigation intervention deemed excessive. 

**The irrigation management DSS will also be interfaced with the fertilization model** which will evaluate a series of aspects linked jointly to irrigation and fertilization: 

* losses due to leaching of nitrates into the subsurface aquifer 
* the quantities of nitrogen (N) that can be administered in conjunction with irrigation interventions (in fertigation systems).

### **Input Data: user**

For the correct functioning of the model, the user must: 

* provide one-off (setup data) agronomic-cultural information on the irrigated agricultural lot and on its land; 
* provide daily any irrigations carried out; 
* periodically update the phenological phases of the irrigated crops. 

The following table shows the data entered by the user.

{% tabs %}
{% tab title="Setting Data" %}

1. **Date of sowing** (for crops if sown) 
2. **Type of crop:** Vine, Corn, Soybean, Rape, Sorghum, Fruit trees (Apple, Pear, and others) 
3. **Soil type:** Sandy, sandy, silty, clayey silty, and others. 
4. **Type of irrigation system:** sprinkler (sprinkler), drip (microirrigation), central pivot (pivot), and others. 
5. **Height of plants at full growth**
6.  **Known depth of water table**
   {% endtab %}

{% tab title="Setting data (optional)" %}

1. **Mulch type (at sowing):** Artificial, natural. 
2. **Mulch coverage (%)** compared to the soil surface. 
3. **Maximum agricultural yield** at the end of the crop cycle (in t/ha)
   {% endtab %}

{% tab title="Daily Data" %}

1. **Irrigations carried out** in the current day with quantities in cubic metres/ha, or l/ha; 
2. **Observed BBCH phenological stages** of irrigated crop (optional)\*

{% hint style="info" %}
The model estimates the evolution of the main BBCH phenological phases based on the type of crop. **The user can choose to manually enter the pheno-phases during the growing season to make the model more accurate in estimating water balance.**
{% endhint %}
{% endtab %}
{% endtabs %}

### Input Data: sensors

The DSS needs the following daily weather data to work (collected by the WiForAgri stations) 

1. **Average daily temperature** \[°C] 
2. **Minimum daily temperature** \[°C] 
3. **Maximum daily temperature** \[°C] 
4. **Average daily wind speed** \[m/s] - optional 
5. **Minimum daily relative humidity** \[%] 
6. **Total daily rainfall** \[mm]

### Daily output data

1. **Water deficit** at the start of the current day \[mm] 
2. **Effective and maximum possible daily evapotranspiration** \[mm] 
3. Total reserve and **easily usable reserve** \[mm] 
4. **Irrigation water losses** due to deep drainage \[litres/ha] - daily and cumulative losses since the beginning of the season 
5. **Current water status:** indicates if the condition of water stress for plants (loss of productivity) occurs at the beginning of the current day.

### Output Data: end of cycle

1. **Total effective evapotranspiration** referred to the entire crop cycle \[mm] 
2. **Maximum total evapotranspiration referred** to the entire crop cycle \[mm] 
3. Difference between maximum and actual evapotranspiration for the whole cycle \[mm] 
4. **Maximum agricultural yield** at crop maturity \[t/ha] 
5. **Effective agricultural yield** at crop maturity (estimated) \[t/ha] 
6. Agricultural yield loss \[t/ha] 
7. Total irrigated water \[mm] 
8. Total irrigation water lost to deep drainage \[mm] 
9. Total rainfall \[mm]

### Modeling functionality

In the daily routine of the model all the partials of water entering and leaving the system are weighed (in mm shown on a vertical section of the ground representing the rhizosphere) and, making the balance, it is checked at what point is the daily water deficit with respect to to an optimal situation (field capacity). The objective of the model is, by sending alarms to the user, to allow the user to program emergency irrigation in advance and to keep the soil water deficit within optimal limits for crops. 

#### The daily water balance equation of the model is as follows:

                                       ***`RZWDi = RZWDi-1 – Rei – Ii + ETEi + (ROi + Di) - CRi`***               

Where:

* All terms are reported in mm/day. 
* **RZWDi is the water deficit** with respect to the ideal water situation (land to field capacity) at the end of the current day. 
* **RZWDi-1 is the past water deficit** of the day before the current day.
* **Rei is the value of actual rain** that fell on the current day 
* **Ii** is the value of the net irrigation done in the current day.
* **ETEi** is the value of effective evapotranspiration. 
* **ROi** is the amount of water leaving the system for surface runoff.
* **Di** is the amount of water leaving the deep drainage system. 
* **CRi** is the rise of water in the system by capillarity. (\*particular situation: surface water table).

As can be seen, the negative terms are appositive for the system i.e. they reduce the water deficit (irrigation, rainfall, upflow of water by capillarity). Positive terms, on the other hand, are aspirative for the system, i.e. they increase the water deficit (actual evapotranspiration, water lost through runoff/drainage). 

Considering the soil-root system figuratively as a reservoir and its water content (in % - moisture) as the water level of the reservoir, we can see that the water content (moisture) can fall within three livability zones for plants (Figure 3).

![Figure 3 - Moisture content of the root ball and habitability zones for plants](https://lh3.googleusercontent.com/KRsAHPoatJc08kCs0WtW245kX_UsMHeDyJQp9FtbfW7cK1fJbrGHkV5sjcY0Pfp5hUlbMWfX3i84kjhf9MehAcf6hVzY50V3gCpY81uCHaZIgT3y2gMt-v0BwGtv3w8g4gO6b0H3)

* **In the saturation zone (blue zone),** the soil is saturated with water following a heavy rain event. The roots are subjected to stress and may become waterlogged. However, in a crop system with a well-designed drainage system, the saturation water content drops quickly and quickly stabilises at the ideal field capacity condition (the same day). 
* **At the point of field capacity (C.C.)** the soil is in its best water supply state, i.e. the air/water ratio is healthy and the soil is at its maximum water supply state without saturation occurring (macropores are free).
* **As the water content decreases** due to the variables exiting the system over time (essentially evapotranspiration, i.e. absorption of water for vegetation viability), the daily water content progressively decreases with respect to field capacity, and a condition of daily water deficit (RZWDi) is thus created, compared to the ideal condition, which is weighed in the daily water balance equation (Eq.1). 
* **Within the optimal water supply zone (RFU), however,** there is no reduction in effective evapotranspiration (ETE=ETM) and thus productivity does not fall. Consequently, the aim of the model is to maintain the soil water content within this no-stress zone for plants.

{% hint style="success" %}
The model then calculates the RZWDi water deficit on a daily basis and, when this reaches the stress point (lower limit) or rather when the RZWDi=RFU condition occurs, it sends an output/alarm signal to trigger irrigation that will return the soil water content from the stress point to field capacity. **In this way, the water content will fluctuate within the readily available reserve zone (RFU) and the plants will never experience stress and reduced productivity.**
{% endhint %}

### Water Balance

The following table provides some details on the calculation methods of the individual components considered in the irrigation model.

{% tabs %}
{% tab title="RFU" %}
**The model calculates the amount of this reserve (RFU) on a daily basis, which depends on the type of soil (grain size) and the extraction capacity of the individual species/crop grown.** This reserve indicates the portion of water that can be easily utilised by the plants themselves without undergoing stress mechanisms (closure of stomata and reduction of evapotranspiration).
{% endtab %}

{% tab title="Effective irrigation" %}
**The model will calculate the effective irrigation term on the basis of the efficiency that varies per type of system used.** Micro-irrigation systems have a very high efficiency (around 90%) while sprinkler systems have a lower efficiency.
{% endtab %}

{% tab title="Evapotranspiration" %}
**The model calculates the potential evapotranspiration (ET0), which expresses the evapotranspirative potential of the atmosphere through the Hargraves-Semani equation for the reference territory. It then corrects it through the crop coefficient (Kc) to determine the total evapotranspiration of the reference crop on a daily basis.** 

The Kc coefficient is estimated by means of the official FAO methodology (Irrigation and Drainage Paper No.56), i.e. it is calibrated daily by weighing the determining agro-climatic factors (wind, humidity, plant height, rainfall intensity and frequency, and finally soil type) using various equations. Through this calibration, the model is in fact able to integrate all climatic factors that increase or decrease it compared to a day with average climatic conditions into the calculation of evapotranspiration.
{% endtab %}

{% tab title="Agricultural yield" %}
The model for calculating the agricultural yield loss at the end of the cycle is based on the equation developed by FAO and already used in the AcquaCrop FAO model, **which relates the reduction in evapotranspiration to the loss of productivity relative to a ceiling (maximum agricultural yield) through a crop-specific response factor.**
{% endtab %}

{% tab title="Effective rain + capillary rise" %}
**The gross rainfall measured through the WiForAgri monitoring stations is reprocessed by excluding the portion of rain intercepted by vegetation (initial losses) and not immediately available to crops. It is then quantified on the actual portion that contributes to the reduction of the soil water deficit.** The term capillary rise is determined specifically on the type of soil and the depth of the water table relative to the base of the root system
{% endtab %}
{% endtabs %}

![Figure 5 - Development of the Kc coefficient during the vegetative cycle periods.](https://1959260061-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Ff4cRzKqKDgSAs8egc84d%2Fuploads%2FmiMlNGcpSN3OeEqhSdcW%2Firrigation_kc.png?alt=media\&token=88ad9fa1-0216-4b2f-814f-0225da12403b)

### Reference Bibliography

**AIAM.** (1998). Applicazioni di modelli di bilancio idrico e di produttività delle colture. Atti del workshop nazionale di Agrometeorologia AIAM ’98, Firenze 2 aprile 1998.

**Ali M. & Mubarak S.** (2017). Effective Rainfall Calculation Methods for Field Crops: An Overview, Analysis and New Formulation. Asian Research Journal of Agriculture. 7. 1-12. 10.9734/ARJA/2017/36812.

**Allen R., & Pereira L., Raes D., Smith M.** (1998). FAO Irrigation and drainage paper No. 56. Rome: Food and Agriculture Organization of the United Nations. 56, 26-40.

**Carr M.** (2013). Crop Yield Response to Water. FAO Irrigation and Drainage Paper 66. By P. Steduto, T. C. Hsiao, E. Fereres and D. Raes. Rome, Italy: Food and Agriculture Organization of the United Nations (2012), 500

**Garcia D., Ramos A., Marín S.** (2013). Modeling kinetics of aflatoxin production by Aspergillus flavus in maize-based medium and maize grain. International journal of food microbiology. 162. 182-9. 10.1016/j.ijfoodmicro.2013.01.004.

**Kuo Sheng-Feng & Lin Bor-Jang & Shieh Horng-Je.** (2019). CROPWAT MODEL TO EVALUATE CROP WATER REQUIREMENTS IN TAIWAN.

**Lupia F., Altobelli F., Nino P., Vanino S.** (2014). Il calcolo dei consumi irrigui delle aziende agricole con il modello MARSALa.

**Lupia F., Vanino S., Santis F., Altobelli F., Barberio G., Nino P., Bellini G. Carbonetti G., Greco M., Salvati L., Mateos L., Perini L. & Laruccia N.** (2013). A model-based irrigation water consumption estimation at farm level.

**Savana A. P., & Frenken K.** (2002). Crop water requirements and irrigation scheduling. FAO irrigation manual, module 4, Harare, 132.

**Steduto P., Hsiao T., Fereres E.** (2009). AquaCrop—The FAO Crop Model to Simulate Yield Response to Water: I. Concepts and Underlying Principles. Agronomy Journal - AGRON J. 101. 10.2134/agronj2008.0139s.

## Management Model: Fertilisation

### Introduction

The WiForAgri fertilisation model is characterised by a high level of **customisation and extreme user-friendliness.** In a nutshell, the model will provide **daily estimates** of the need for **NPK nutrients** (nitrogen, phosphorus and potassium) to be administered, **avoiding deficiencies and/or over-fertilisation** (a source of waste and pollution). The fertilisation model also co-operates with the irrigation model and can also be used for combined water and nutrient administrations (fertigation system). 

Through the use of the fertilisation DSS, the user will be able to **achieve the following objectives:** 

* **Optimise the timing and intensity of fertilisation interventions** in a manner appropriate to the nutrient requirements of the specific crop plants, the simulation soil and the current climate year; 
* **Reduce the rate of nitrate leaching** to water sources susceptible to nitrate pollution; 
* **Administer the correct amount of NPK fertiliser in the correct way** and at the correct time depending on the agronomic factors involved.

### Input Data

The input data required from the user are divided into: 

* **setup data** requested once at the beginning of the cultivation cycle (e.g. plot size and location, type of soil);
* **daily data** entered by the user during the cycle itself (fertilisation and any irrigation carried out).

#### **Setup Data**

* **Concentration of Nitrate (NO3) and initial Ammonium (NH4+)** in soil (soil analysis). 
* **Concentration of soil organic matter, total nitrogen and total calcium carbonate** (soil analysis). 
* **Concentration of Nitrate in irrigation water** for the calculation of additional Nitrate (irrigation water analysis) - optional data.

{% hint style="success" %}
**High customisation and accurate calibration:** for each user-selectable crop, the model automatically selects as many as 71 specific calibration parameters (in addition to those entered by the user) that serve to optimise and accurately customise the model calculation for each crop and each specific soil-plant-climate ecosystem.
{% endhint %}

#### **Daily Data**

* **Amount of fertiliser (nitrogen) applied** today (kg/ha); 
* **Type of fertiliser used** (ready or slow release).

### Daily output data

* **Amount of residual nitrogen in the soil (kg/ha) - nitrogen balance:** 
  * Need to administer nitrogen (N); 
  * Need to administer phosphorus (P) and potassium (K); 
  * Suggested dosage for P and K based on the N dosage of the fertilisation carried out;
* **Amount of nitrogen released and available to plants (kg/ha)** related to fertilisation carried out during the crop cycle; 
* **Amount of nitrogen released by mineralisation** of soil organic matter (kg/ha); 
* **Quantity of mineral nitrogen intercepted** by root growth (kg/ha); 
* **Amount of nitrogen absorbed by plants** (kg/ha);
* **Amount of residual nitrogen in the soil** (kg/ha), a parameter required for activating alarms and quantifying nitrogen administrations); 
* **Volume of irrigation water administered** (in litres/ha) - if configured together with the irrigation model.

### Modelling functionality

The model will carry out the daily estimation of the various components linked to rhizospheric nitrogen dynamics and report them as **output variables in tabular and graphical form** to give detailed indications of the components entering and leaving the root system. It will make a daily estimate of the **residual nitrogen level in the soil, which, depending on the vegetative phase considered (initial, average, final), will be matched to a minimum alarm threshold.**

{% hint style="info" %}
The threshold level (minimum amount of residual nitrogen in the soil) will be used by the model for setting mail/SMS alarms.
{% endhint %}

**The model within it is divided into three sub-models:** 

* **Crop Growth Sub-model** that estimates plant growth in terms of both biomass and root system volume. 
* **Nitrogen Balance Sub-model** that estimates the additive and subtractive nitrogen terms in the rhizosphere and, by taking stock, monitors the level of nitrogen within the root systems. P and K requirements are estimated from N requirements according to crop-specific NPK proportional tables. 
* **Water Balance sub-model** that evaluates the volumes of water entering and leaving the system.

### Nitrogen Balance

* **Uptake of crop nitrogen** using a dynamic approach, capable of assessing the growth of the crop mass (SDW - Shoot Dry Weight) net of any stress factors (thermal and water effects, negative on growth). 
* **Mineralisation of organic matter.** 
* Presence of **nitrates in irrigation water.** 
* **Increased interception of mineral nitrogen stock** by progressive growth of the root system.

![Figure 3 - Conceptual diagram of the relationships between the various components of the nitrogen balance within the sub-model](https://1959260061-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LDGLlFs-4e4Wr2T8FYa%2F-LlHkCzQx0Q2QuW8dlM8%2F-LlHv6_DFzjEWhj1M-px%2Fimage.png?alt=media\&token=9e4cced2-5d48-43d2-b629-df9e5046b248)

{% hint style="warning" %}
**The model, considering the brevity of the growing season, assumes that atmospheric nitrogen deposition and gaseous emissions (volatilisation, denitrification) are equivalent and thus cancel each other out.**
{% endhint %}

![Figure 4 - Simulative three-dimensional representation of interaction between the actual root system and the wet soil in double-row fertigation systems.](https://1959260061-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LDGLlFs-4e4Wr2T8FYa%2F-LofK9-kAzJs1x1swjk4%2F-LofTRTKv2zdZSUjQgk-%2Fbulbo_umido.png?alt=media\&token=0aa95186-b3ce-4fce-8284-dcf5cefc2b7f)

### Additional functionality: ZVN zones

Activated at the user's choice, the mode developed for **ZVN (nitrate-vulnerable) zones** ensures that a volumetric dose of irrigation water is recommended so that **the depth of soil wetted by the system does not exceed the actual root depth.**                                                                                                 This mode makes it possible, through more frequent and less intense irrigation, to prevent the percolation of groundwater below the root zone, thus limiting the leaching of nitrates to the sub-surface water table.

### Reference Bibliography	

**Ainechee G., Boroomand-Nasab S., Behzad M.** (2009). Simulation of soil wetting pattern under point source trickle irrigation. J. Appl. Sci. 9, 1170–1174. doi: 10.3923/jas.2009.1170.1174

**Benedetti A., Frangi A., Nardi P., Sinopoli A.M., Trinchera A.** (2005). Tipizzazione del rilascio nei concimi “non a pronto effetto” - Prime indicazioni operative. Atti Convegno Milano, 25 gennaio 2005.

**Conversa G., Bonasia A., Di Gioia F., Elia A.** (2015). A Decision Support System (GesCoN) for Managing Fertigation in Vegetable Crops. Part II – Model calibration and validation under different environmental growing conditions on field grown tomato. Frontiers in Plant Science. 6. 10.3389/fpls.2015.00495.

**Elia A., Conversa G.** (2015). A Decision Support System (GesCoN) for managing fertigation in open field vegetable crops. Part I - Methodological approach and description of the software. Frontiers in Plant Science. 6. 1-18. 10.3389/fpls.2015.00319.

**Mary B., Guérif J.** (1994). Intérêts et limites des modèles de prévision de l’évolution des matières organiques et de l’azote dans le sol. Cahiers Agric. 3, 247–25

**Mualem Y.** (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12, 513–522. doi: 10.1029/WR012i003p00513

**Schwartzman M., Zur B.** (1986). Emitter spacing and geometry of wetted soil volume. J. Irrig. Drain. Eng. ASCE 112 (3), 242–253

**van Genuchten M. T.** (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898. doi: 10.2136/sssaj1980.03615995004400050002x