03. Module I (Agro‐climatic analysis) - un-fao/gaezv5 GitHub Wiki

The main purpose of Module I is the compilation of a geo-referenced climatic resources inventory providing a variety of relevant agro-climatic indicators. They give a general characterization of climatic resources and of their suitability for agricultural use. Once generated in Module I, several agro-climatic layers are then used as input for estimation of crop yields and production in Module II (Biomass and yield), quantification of agro-climatic constraints in Module III and for estimating agro-ecological suitability and attainable yields in Module V (integration of climatic and edaphic evaluation). Figure below provides a brief overview of the information flow in Module I.

Figure: Information flow in Module I

Monthly and daily climatic variables are used in GAEZ for the calculation of soil water balances and agro-climatic indicators relevant to plant production. Below we summarize some key variables simulated in Module I.

Day-time and night-time temperatures

The temperatures during day-time (T_day, °C) and night-time (T_night, °C) are calculated as follows:

$$ T_{\text{day}} = T_a + \left( \frac{T_x - T_n}{4\pi} \right) \times \left( \frac{11 + T_0}{12 - T_0} \right) \times \sin\left( \pi \times \left( \frac{11 - T_0}{11 + T_0} \right) \right) $$

$$ \text { Tnight }=T a-\left(\frac{T x-T n}{4 \pi}\right) \times\left(\frac{11+T_{0}}{T_{0}}\right) \times \sin \left(\pi \times\left(\frac{11-T_{0}}{11+T_{0}}\right)\right) $$ where $T a$ is average 24 -hour temperature, $T x$ and $T n$ are maximum and minimum daily temperature, and $T_{o}$ is calculated as a function of day-length (DL, hours). $$ T_{0}=12-0.5 \times D L $$

Day-length is calculated in the model and is a function of the latitude of a grid-cell and depends on the day of the year.

Reference evapotranspiration (ETo)

The reference evapotranspiration (ETo) represents evapotranspiration from a defined reference surface, which closely resembles an extensive surface of green, well-watered grass of uniform height (12 cm), actively growing and completely shading the ground. GAEZ calculates ETo from the attributes in the climate database for each grid-cell according to the Penman-Monteith equation (Allen et al., 1998; Doorenbos and Pruitt, 1977; Monteith, 1965, 1981). A description of the implementation of the Penmann-Monteith equations in GAEZ is provided in Appendix 3-1.

Maximum evapotranspiration (ETm)

In Module I, the calculation of maximum evapotranspiration (ETm) for a ‘reference crop’ assumes that sufficient water is available for uptake in the rooting zone. The value of ETm is related to ETo through applying crop coefficients for water requirement (Kc), reflecting phenological development and leaf area. The Kc values are crop and climate specific. They vary generally between 0.3–0.5 at initial crop stages (emergence) to 1.0–1.2 at reproductive stages.

$$ ETm = Kc \times ETo $$

For the reference crop as modeled in GAEZ, values of Kc depend on the thermal characteristics of a grid cell. For locations with a year-round temperature growing period, i.e., when average daily temperature stays above 5⁰C for the entire year, the Kc value applied for the reference crop is always 1.0. When the temperature growing period is < 365 days, the Kc value increases linearly from 0.4 at the start of the temperature growing period until reaching the reference value 1.0 after 30 days to account for increasing water demand as the crop canopy develops after the cold period. When assessing specific crops, as is done in Module II, empirically determined Kc values for the calculation of crop specific ETm are available from various sources (Allen et al., 1998) and differ by the development stage of the crop.

Actual evapotranspiration (ETa)

The actual uptake of water by the ‘reference’ crop is characterized by the actual evapotranspiration (ETa, mm/day) resulting in the daily calculations of the reference crop water balance. The calculation of ETa differentiates two possible cases depending on the availability of water for plant extraction:

• Adequate soil water availability (ETa=ETm), and
• Limiting soil water availability (ETa<ETm).

When water is not limiting, the ETa value is equal to the maximum evapotranspiration (ETm) of the ‘reference’ crop. At limiting water conditions, ETa is a fraction of ETm, depending on soil water availability as explained in following sections.

ETa for adequate soil water availability

The value of ETa is set to be equal to ETm as long as the water balance (Wb) is above or equal the threshold of “readily” available soil water (Wr). This characterizes a situation when crops are able to “easily” extract sufficient water and therefore no water stress occurs. The potentially total available soil moisture Wx is the product of total available soil water holding capacity (Sa) and rooting depth (D). In the operation of Module I the rooting depth D in the reference water balance is assumed to be 1 m. The share of Wx below which soil moisture starts to become difficult to extract is referred to as ‘p’, the soil moisture depletion fraction. The fraction p varies with the evaporative demand of the atmosphere, crop type, and soil characteristics. Estimates are available from various sources (FAO 1998). The value of p normally varies from 0.3 for shallow rooted plants at high rates of ETm (>8 mm/day) to 0.7 for deep-rooted plants at low rates of ETm (<3 mm/day). In general, the value of p declines with increasing evaporative demand. The threshold of readily available soil moisture is in turn calculated from Wx and the soil moisture depletion fraction (p).

$$ Wx = Sa \times D $$

$$ Wr = p \times Wx $$

A condition of ‘adequate soil moisture availability’ is defined when (i) daily precipitation (P) is greater or equal to ETm and/or (ii) precipitation P plus the difference between water balance (Wb) and threshold of readily available water (Wr) is greater than ETm. These conditions imply that there is sufficient “easily” extractable water to meet the crop water demand (ETm):

$$ ETa = ETm $$

when:

$$ P \ge ETm $$

or when:

$$ P < ETm $$

$$ P + Wb - Wr > ETm $$

ETa calculation for limited soil water availability

When soil water is limiting, i.e., when above conditions are not met and P + Wb-Wr < ETm, then ETa falls short of ETm. In this case, ETa is calculated as a fraction ρ of ETm. The variable ρ is the ratio of current water balance (Wb) and the threshold of readily available soil water (Wr).

$$ \rho = \frac{Wb}{Wr} $$

ETa is then calculated as daily precipitation P plus the ρ fraction of ETm.

$$ ETa = P + \rho \times ETm $$

This procedure assumes rainfall is immediately available to plants on the day of precipitation, prior to replenishing soil moisture.

Snow balance calculation

In seasonally cold climates the calculation of a snow balance (Sb, mm) affects the water balance procedure outlined above. The snow balance increases when precipitation falls as snow and decreases with snowmelt and snow sublimation. Precipitation (P) is assumed to fall as snow (Psnow) when maximum temperature (Tx) is below a certain temperature threshold (Ts).

Snowmelt (Sm) is calculated as a function of daily maximum temperature, the snow melt parameter (δ) and depends on the previously accumulated snow balance. The snow melt factor δ is set to 5.5 mm/⁰C.

$$ Sm = \min(\delta \times (T_x - T_s), S_b) $$

The sublimation factor (ks) is used to discount a fraction of maximum evapotranspiration as sublimated snow. This fraction (ks*ETm) is subtracted from the snow balance:

$$ S_{b_j} = S_{b_{j-1}} - S_m - (k_s \times E_{Tm}) + P^{snow} $$

The sublimation factor (ks) is assumed to be 0, 0.1 or 0.2 of reference evapotranspiration (ETm, mm), depending temperature:

ks = 0.0, when Tx < Ts; Ts is assumed as 0⁰C in GAEZ

ks = 0.1, when Tx > Ts and Ta < 0⁰C

ks = 0.2, when Tx > Ts and 0⁰C <Ta<5⁰C

Once the water balance for the ‘reference crop’ is calculated, five important indicators are generated. These are:

1. Maximum evapotranspiration of ‘reference’ crop (ETm);
2. Actual evapotranspiration of ‘reference’ crop (ETa);
3. Water balance for ‘reference’ crop (Wb);
4. Snow balance (Sb), and
5. Excess water of ‘reference’ crop water balance (We).

After simulating the water balance for the ‘reference’ crop in Module I, various raster maps of related variables are produced and used for further computations in subsequent AEZ modules.

Temperature is a major determinant of crop growth and development. In GAEZ, the effect of temperature on crops is characterized in each grid-cell by thermal regimes. Thermal regimes are represented by six types of indicators: (i) thermal climates; (ii) thermal zones; (iii) length of temperature growing periods; (iv) accumulated temperature sums, (v) temperature profiles, and (vi) permafrost zones.

Latitudinal thermal climates provide a classification that is used in Module II for the assessment of potential crop-LUT presence in each grid cell. The delineation of thermal climates is based on (i) the average monthly temperature, (ii) proportions of respectively summer, winter rainfall, and (iii) the temperature amplitude as a measure of continentality (i.e., difference between temperatures of warmest and coldest month). Thermal climates are derived from monthly temperatures corrected to "sea level temperature" with a fixed lapse rate of 0.55⁰C/100m. There is a further subdivision for rainfall seasonality in the subtropics and for temperature amplitude in temperate and boreal zones. In this way, latitudinal climates approximate temperature seasonality and ranges of prevailing day-lengths, which is used as a proxy for matching short-day, day-neutral and long-day crop requirements.

Thermal climates are derived from monthly temperatures corrected to sea level. The thermal climates have been subdivided for rainfall seasonality in the subtropics and for temperature seasonality in temperate and boreal zones. The tropics have been subdivided into lowland and highland zones.

Table: Classification of thermal climates

Climate	Rainfall and Temperature Seasonality
Tropics	All months with monthly mean temperatures, corrected to sea level, above 18°C
	Tropical lowland: Tropics with actual mean temperatures above 20°C
	Tropical highland: Tropics with actual mean temperatures below 20°C
Subtropics	One or more months with monthly mean temperatures, corrected to sea level, below 18°C, but all above 5°C, and 8–12 months above 10°C
	Subtropics summer rainfall:
	Northern hemisphere: P/ETo in April-September ≥ P/ETo in October-March.
	Southern hemisphere: P/ETo in October-March ≥ P/ETo in April-September.
	Subtropics winter rainfall:
	Northern hemisphere: P/ETo in October-March ≥ P/ETo in April-September.
	Southern hemisphere: P/ETo in April-September ≥ P/ETo in October-March.
	Subtropics low rainfall: Annual rainfall less than 250 mm
Temperate	At least one month with monthly mean temperatures, corrected to sea level, below 5°C and four or more months above 10°C
	Oceanic temperate: Seasonality less than 20°C
	Sub-continental temperate: Seasonality 20–35°C
	Continental temperate: Seasonality more than 35°C
Boreal	At least one month with monthly mean temperatures, corrected to sea level, below 5°C and 1–3 months above 10°C
	Oceanic boreal: Seasonality less than 20°C
	Sub-continental boreal: Seasonality 20–35°C
	Continental boreal: Seasonality more than 35°C
Arctic	All months with monthly mean temperatures, corrected to sea level, below 10°C
	Arctic

See GAEZ v5 dataset on thermal climates on the FAO Agro-Informatic Data Catalog (link).

Thermal zones, which are based on actual temperatures, reflect the prevailing temperature regimes of major thermal climates.

• Warm in tropical zones refers to annual mean temperatures above 20⁰C, cool, cold, very cold tropics refers to annual mean temperature below 20⁰C;
• Moderately cool refers to actual temperature conditions characterized by one or more months with monthly average temperatures below 18⁰C but all above 5⁰C and 8–12 months above 10⁰C;
• Cool refers to conditions with at least one month with monthly mean temperatures below 5⁰C and four or more months above 10⁰C;
• Cold refers to conditions with at least one month with monthly mean temperatures below 5⁰C and 1–3 months above 10⁰C, and
• Very cold refers to polar conditions i.e., all months with monthly mean temperatures below 10⁰C.

See GAEZ v5 dataset on thermal zones on the FAO Agro-Informatic Data Catalog (link).

The time during the year when daily temperatures are conducive to crop growth and development is represented in AEZ by temperature growing periods. The length of the ‘temperature growing period’ (LGPt) is calculated as the number of days in the year when average daily temperature (Ta) is above a temperature threshold “t”. In AEZ three standard temperature thresholds for temperature growing periods are used: (i) periods with Ta > 0⁰C (LGPt0), (ii) periods with Ta > 5⁰C (LGPt5), which is considered as the period conducive to plant growth and development, and (iii) periods with Ta > 10⁰C (LGPt10), which is used as a proxy for the period of low risks for late and early frost occurrences and termed ‘frost-free period’.

See GAEZ v5 dataset on ‘frost-free’ period (LGPt10, days) on the FAO Agro-Informatic Data Catalog (link).

For crop suitability assessments, individual crop/LUT heat unit requirements are matched with temperature sums during the crop/LUT growth cycle duration, defined as the sum of mean daily temperatures calculated from a base temperature of 0⁰C, resulting in optimum, sub-optimum or non-suitable ranges.

Heat requirements of crops are expressed in accumulated temperatures. Reference temperature sums (TS) are calculated for each grid-cell by accumulating daily average temperatures (Ta) for days when Ta is above the respective threshold “t” as follows: (i) 0⁰C (TS0), (ii) 5⁰C (TS5), and (iii) 10⁰C (TS10).

See GAEZ v5 dataset on annual temperature sum, days with Ta > 10 °C on the FAO Agro-Informatic Data Catalog (link).

Temperature profiles are defined in terms of 9 classes of “temperature ranges” for days with Ta <-5⁰C to >30⁰C (at 5⁰C intervals) in combination with distinguishing increasing and decreasing temperature trends within the year. In Module II of GAEZ, these temperature profiles are matched with crop-specific temperature profile requirements providing either optimum match, sub-optimum match or assessing a crop as not suitable for the respective location.

Table: Temperature profile classes

Average Temperature (Ta, °C)	Temperature Trend (Increasing)	Temperature Trend (Decreasing)
> 30	A1	B1
25–30	A2	B2
20–25	A3	B3
15–20	A4	B4
10–15	A5	B5
5–10	A6	B6
0–5	A7	B7
-5–0	A8	B8
< -5	A9	B9

Daily data of minimum and maximum temperatures are used in GAEZ to compute various statistics of extreme temperature events. Several indicators are calculated to capture the risk of occurrence of high temperature events. For instance, the agro-climatic analysis produces a count of the number of ‘hot’ days, here defined as days when daily maximum temperature exceeds 35⁰C, which is indicative of periods when temperature may damage development and yields of cool-loving crops such as wheat. Besides ‘hot’ days (Tmax > 35⁰C), the module also counts the annual number of days with maximum temperature above 30⁰C, 40⁰C and 45⁰C. Among these, the GAEZ analysis produces a count of ‘very hot’ days, defined as daily maximum temperature exceeding 40⁰C. These thresholds were chosen to indicate periods when even thermophilic crops like maize may suffer from high temperatures.

Number of ‘frost’ days (with Tmin < 0°C)

On the cold side of the temperature range in a grid-cell, one such index of interest to planning in agriculture counts the number of ‘frost’ days in a year, defined here as days when minimum daily temperature falls below 0°C. The module also counts the annual number of days when minimum temperature falls below respectively 5⁰C, 10⁰C, 15⁰C and 20⁰C.

See GAEZ v5 dataset on average annual number of days with frost on the FAO Agro-Informatic Data Catalog (link)

Occurrence of continuous or discontinuous permafrost conditions are used in the suitability assessment. Permafrost areas are characterized by sub-soil at or below the freezing point for two or more years. Permafrost or ‘gelic’ soils are considered unsuitable for crops and therefore their identification is essential for the land resources assessment in GAEZ. Average air temperature and the physical and chemical characteristics of the soils are the main features influencing the presence of permafrost. Consequently, GAEZ considers permafrost in two ways: (i) it determines different reference permafrost zones based on climatic conditions, and (ii) it relies on soil classification; soils with a ‘gelic’ connotation within or outside permafrost zones are considered to belong to the continuous permafrost zone.

In GAEZ, the procedures proposed by Nelson and Outcalt (1987) are applied to calculate an air Frost Index (FI) which is used to characterize climate-derived permafrost conditions into four classes:

• Continuous permafrost;
• Discontinuous permafrost;
• Sporadic permafrost, and
• No permafrost.

Reference permafrost zones are determined based on prevailing daily mean air temperature (Ta). The air frost index (FI) is calculated and used to characterize permafrost areas. For this calculation, accumulated degree-days, above and below 0⁰C, are used to calculate the thawing index (DDT) and the freezing index (DDF).

The thawing index DDT is calculated as:

$$ DDT = \sum_{j=1}^{12} Ta_j, \quad \text{for months when } Ta_j > 0^\circ C $$

The freezing index DDF is calculated as:

$$ DDF = \sum_{j=1}^{12} |Ta_j|, \quad \text{for months when } Ta_j \leq 0^\circ C $$

The frost index FI is then calculated according to Nelson and Outcalt (1987):

$$ FI = \sqrt{DDT \times DDF} $$

The value of FI is regarded a measure of the probability of occurrence of permafrost and used to classify grid-cells in four distinct permafrost classes (table below). In the GAEZ assessment, those grid-cells characterized as continuous permafrost (class 1) or discontinuous permafrost (class 2) are considered unsuitable for crop production. Regular yield and suitability calculations are performed in class 3 and 4.

See GAEZ v5 dataset on reference permafrost zones on the FAO Agro-Informatic Data Catalog (link).

Table: Classification of permafrost areas used in the GAEZ assessment

Permafrost Class	Value of Frost Index (FI)	Probability of Permafrost* (%)
Continuous permafrost	> 0.625	> 67
Discontinuous permafrost	0.570 < FI < 0.625	33–67
Sporadic permafrost	0.495 < FI < 0.570	5–33
No permafrost	< 0.495	< 5

*Probability of permafrost occurrence was calculated based on datasets from Nelson and Outcalt (1987) and analyzed at IIASA.

In Module I, GAEZ calculates a daily reference soil water balance for each grid-cell and estimates actual evapotranspiration (ETa) for a reference crop. In the Module II, soil moisture balance calculations are performed considering specific crop/LUTs and their specific water requirements.

Daily soil moisture balance calculation procedures follow the methodologies outlined in “Crop Evapotranspiration” (Allen et al., 1998). The quantification of a crop-specific water balance determines crop “actual” evapotranspiration (ETa), a measure used for calculating water-constrained crop yields by comparing ETa with a crop’s evaporative demand ETm. The volume of water available for plant uptake is calculated by means of a daily soil water balance (Wb). The Wb accounts for accumulated daily water inflow from precipitation (P) or snowmelt (Sm) and outflow from actual evapotranspiration (ETa), and excess water lost due to runoff and deep percolation (We).

$$ Wb_j = \min \left( Wb_{j-1} + Sm_j + P_j - ETa_j,; Wx \right) $$

where j is the day of the year; Wx is the maximum water available to plants. The snowmelt (Sm) is accounted within the snow balance calculation procedures and excess water (We) is the amount of water that exceeds Wx. The upper limit Wx of the water available to plants depends on the soil’s physical and chemical characteristics that influence available soil water holding capacity (AWC) and volume. Wx is the product of available soil water (Sa) and rooting depth (D).

$$ Wx = Sa \times D $$

The maximum Sa value is a soil-specific attribute defined as the difference between soil moisture content at field capacity (Sfc) and permanent wilting point (Swp) over the rooting zone. Therefore, at any given day, an actual soil water content (Wb) will be available to plants if Swp < Wb < Sfc (Figure below). However, water extraction becomes more difficult as soil water content (Wb) is less than a critical threshold (Wr) defined by p, the “soil water depletion factor”, and the available soil water capacity (AWC).

Figure: Schematic representation of water balance calculations

The values of AWC and rooting depth limitations due to soil are derived from soil information contained in the Harmonized World Soil Database v1.2 (Nachtergaele et al., 2012). Details on the estimation of AWC values are provided in section 6-5 in the context of soil evaluation procedures. Any water input into the soil that exceeds Wx is “lost” as excess water (We) and is considered “not available” in further GAEZ calculations. It accounts for the water lost either by runoff or deep percolation.

The agro-climatic potential productivity of land depends largely on the number of days during the year when temperature regime and moisture supply are conducive to crop growth and development. This period is termed the length of the growing period (LGP). The LGP is determined based on prevailing temperatures and the above-described water balance calculations for an assumed reference crop. In a formal sense, LGP refers to the number of days when average daily temperature is above 5⁰C and ETa of this reference crop exceeds a specified fraction of ETm. In the current GAEZ parameterization, LGP days are considered when ETa ≥ 0.4×ETm, which aims to capture periods when sufficient soil moisture is available that would allow the establishment of the reference crop. Specifically, the reference water balance underlying LGP calculations assumes an effective soil depth D of 1m and a soil water holding capacity Smax of 100 mm. The reference water balance is calculated year-round (for 365 days) and the Kc values used to relate reference crop potential evapotranspiration (ETm) to Penman-Monteith reference evapotranspiration (ETo) are listed in the table below. the

Table: Kc values applied in Module I reference water balance

Daily temperature condition	Remarks	Kc
Areas with year-round temperature growing period	LGPt > 5 = 365 days
Daily Ta ≥ 5°C; LGPt>5 = 365 days	In areas with year-round LGPt > 5 the Kc value stays at 1	1.0
Areas with dormancy period or cold break	LGPt > 5 is less than 365 days
Daily Ta ≤ 0°C; Tmax < 0°C	Precipitation falls as snow and is added to snow bucket	0.0
Daily Ta ≤ 0°C; Tmax ≥ 0°C	Snow-melt takes place; minor evapotranspiration	0.1
0°C < Daily Ta < 5°C; temperature trend upward	Biological activities before start of growing period	0.2
Daily Ta ≥ 5°C; LGPt>5 < 365 days; case 1	Kc used for days until start of growing period	0.5
Daily Ta ≥ 5°C; LGPt>5 < 365 days; case 2	Kc increases from 0.5 to 1.0 during first month of LGP	0.5–1
Daily Ta ≥ 5°C; LGPt>5 < 365 days; case 3	Kc = 1 until daily Ta falls below 5°C	1.0
0°C < Daily Ta < 5°C; temperature trend downward	Reduced biological activities before dormancy	0.2

See GAEZ v5 dataset on reference length of growing period (days) on the FAO Agro-Informatic Data Catalog (link).

Length of growing period data is also used for the classification of land into generalized moisture regimes classes. The GAEZ moisture regimes classes and their definitions are presented in the table below.

Table: Moisture regimes

Length of growing period (days)	Moisture regime
0	Hyper-arid
<60	Arid
60 to 119	Dry semi-arid
120 to 179	Moist semi-arid
180 to 269	Sub-humid
270 to 364	Humid
≥ 365 (year-round growing period)	Per-humid

The moisture regime within an LGP is characterized by different water supply conditions as follows: Growing period days without water stress (days when ETa=ETm): When ETa equals ETm, the crop water requirements are fully met (i.e., no water stress for plants occurs). From a soil water balance point of view these LGP days can further be differentiated as follows:

1. Daily rainfall is higher than crop water requirements (P > ETm) and available soil moisture Sa is below maximum (Sa < Smax). Excess rainfall now adds to replenish the available soil moisture storage.
2. Daily rainfall is higher than crop water requirements, P > ETm, and available soil moisture is at its maximum (Sa = Smax). In this case excess precipitation is lost to surface runoff and/or deep percolation.
3. Days when rainfall falls short of crop water requirements (P < ETm) but easily available soil moisture exceeds crop water requirements. In this case ETa equals ETm and the soil moisture content in the soil profile is decreasing.

Growing period days with water stress (days when ETa<ETm): ETa falls short of ETm. The crop experiences water stress as not enough readily available water can be obtained from rainfall or moisture stored in the soil profile. Water stress implies that crop growth and yield formation are reduced.

Discontinuous growing periods

Total annual LGP days may be in one continuous period or may occur as two or more discontinuous growing periods. When available moisture becomes insufficient (ETa < 0.4×ETm), LGP ends and/or is interrupted by a dry period. In the case of temperature limitations (Ta < 5°C), LGP is interrupted by either a dormancy break or a cold-break. This distinction is determined on the basis of temperature limits for survival of hibernating crops. During a dormancy period hibernating crops can survive as opposed to a cold-break when temperature drops below a crop specific critical temperature limit.

GAEZ can store up to five individual continuous component LGPs. Various soil moisture supply stages during the LGP are recorded and several indicators are calculated, including:

1. Total number of growing period days;
2. Number of growing period days, during which ETa=ETm;
3. Number of growing period days when P>ETm;
4. Number of individual growing periods;
5. Number of growing period days in individual growing periods;
6. Begin date of individual growing periods, and
7. End date of individual growing periods.

The difference between annual potential and actual evapotranspiration as simulated in the reference water balance and is termed here the reference annual water deficit (WDe, mm), WDe = ETm-ETa. It measures the discrepancy between evaporative demand of a well-watered vegetation and the actual moisture supply under rain-fed conditions. Note that WDe is computed as an agro-climatic indicator, without consideration of actual soil conditions, and the reference water balance is calculated using a soil water holding capacity Smax of 100 mm. In Module V, when the crop specific water deficits are determined, the actual soil and terrain conditions of a grid cell are taken into account in crop water balance calculations.

The moisture availability index compares the amount of incoming precipitation to the evaporative demand of the reference crop assumed in the calculation of the Penman-Monteith equation used for reference evapotranspiration ETo. An index value of 100 means that precipitation equals reference potential evapotranspiration, i.e., that precipitation on average over the year matches the evaporative demand of the vegetation. Values below 100 indicate the occurrence of some water deficit; values above 100 mean that precipitation exceeds evaporative demand on an annual basis. In the GAEZ analysis, a moisture availability index is calculated for different periods: for year-round conditions; for 6-month periods (April to September, October to March), and for 3-month periods (January to March, April to June, July to September, and October to December). The indicators provide a general understanding of soil moisture conditions and of the level of water stress occurring overall and within certain periods of a year.

The GAEZ analysis uses daily data of precipitation. This allows the computation of various statistics, including the number of rain-days in a year, here defined as days with precipitation P ≥ 1 mm.

See GAEZ v5 dataset on average number of rain-days (days) on the FAO Agro-Informatic Data Catalog (link).

The comprehensive climate database in GAEZ is used to generate several additional indicators to portray various aspects that characterize the agro-climatic conditions of a grid cell. For instance, these indicators relate to (i) the possibility of cultivating multiple sequential crops under rain-fed and irrigated conditions, (ii) a general estimate of climate related bio-productivity, and (iii) the quantification of widely used climate classification (Koeppen-Geiger).

In the GAEZ crop suitability analysis, the LUTs considered refer to single cropping of sole crops, i.e., each crop is presumed to occupy the land only once a year and in pure stand. Consequently, in areas where the growing periods are sufficiently long to allow more than one crop to be grown in the same year or season, single crop yields of annual crops do not reflect the full potential of total time available each year for rain-fed or irrigated crop production. To assess the multiple cropping potential, a number of multiple cropping zones have been defined through matching both growth cycle and temperature requirements of individual suitable crops with time available for crop growth. For rain-fed conditions this period is approximated by the LGP, i.e., the number of days during which both temperature and moisture conditions permit crop growth. Under irrigation conditions the length of the temperature growing period and annual accumulated temperature sums are decisive.

According to the above considerations, nine different multiple cropping zones were classified:

• Zone of no cropping (too cold or too dry for rain-fed crops);
• Zone of single cropping;
• Zone of limited double cropping (relay cropping; single wetland rice may be possible);
• Zone of double cropping (note, in Zone D sequential double cropping including wetland rice is not possible);
• Zone of double cropping with rice (sequential double cropping with one wetland rice crop is possible in Zone E);
• Zone of double rice cropping or limited triple cropping (may partly involve relay cropping; a third crop is not possible in case of two wetland rice crops);
• Zone of triple cropping (sequential cropping of three short-cycle crops; two wetland rice crops are possible in Zone G), and
• Zone of triple rice cropping (sequential cropping of three wetland rice crops is possible).

Delineation of multiple cropping zones for rain-fed conditions is solely based on agro-climatic attributes calculated during AEZ analysis. The following attributes were used in the definition of cropping zones:

• LGP: length of growing period, i.e., number of days when temperature and soil moisture permit crop growth;
• LGPt5: number of days with mean daily temperatures above 5⁰C;
• LGPt10: number of days with mean daily temperatures above 10⁰C;
• TS0: accumulated temperature (degree-days) on days when mean daily temperature ≥ 0⁰C;
• TS10: accumulated temperature (degree-days) on days when mean daily temperature ≥ 10⁰C;
• TSG5: accumulated temperature on growing period days when mean daily temperature ≥ 5⁰C, and
• TSG10: accumulated temperature on growing period days when mean daily temperature ≥ 10⁰C.

Tables below summarize the delineation criteria for multiple cropping zones under rain-fed conditions in respectively the lowland tropics and all other thermal zones.

Table: Delineation of multiple cropping zones under rain-fed conditions in lowland tropics

Zone	LGP	LGPt5	LGPt10	TS0	TS10	TSG5	TSG10
A *	-	-	-	-	-	-	-
B	≥45	≥120	≥90	≥1600	≥1200	-	-
C**	≥220	≥220	≥120	≥5500	-	≥3200	≥2700
C	≥200	≥200	≥120	≥6400	-	≥3200	≥2700
C	≥180	≥200	≥120	≥7200	-	≥3200	≥2700
D**	≥270	≥270	≥165	≥5500	-	≥4000	≥3200
D	≥240	≥240	≥165	≥6400	-	≥4000	≥3200
D	≥210	≥240	≥165	≥7200	-	≥4000	≥3200
E***	n.a.	n.a.	n.a.	n.a.	n.a.	n.a.	n.a.
F	≥300	≥300	≥240	≥7200	-	≥5100	≥4800
G***	n.a.	n.a.	n.a.	n.a.	n.a.	n.a.	n.a.
H	≥360	≥360	≥360	≥7200	≥7000	-	-

• Is a residual zone and applies if conditions for zone B (‘single cropping’) are not met.

** Three alternative sets of conditions are tested in lowland tropics and a grid cell is assigned the C or D class when at least one set of conditions is met.

*** Due to a relatively small temperature amplitude (i.e., calculated temperature difference between warmest month and coldest month in a year) in lowland tropics the multiple cropping zones of type E and G, which combine cool and warm season crops, are not considered in this climate.

Table: Delineation of multiple cropping zones under rain-fed conditions in all other thermal zones

Zone	LGP	LGPt5	LGPt10	TS0	TS10	TSG5	TSG10
A*	-	-	-	-	-	-	-
B	≥45	≥120	≥90	≥1600	≥1200	-	-
C	≥180	≥200	≥120	≥3600	≥3000	≥3200	≥2700
D	≥210	≥240	≥165	≥4500	≥3600	≥4000	≥3200
E	≥240	≥270	≥180	≥4800	≥4500	≥4300	≥4000
F	≥300	≥300	≥240	≥5400	≥5100	≥5100	≥4800
G	≥330	≥330	≥270	≥5700	≥5500	-	-
H	≥360	≥360	≥330	≥7200	≥7000	-	-

• Is a residual zone and applies if conditions for zone B (‘single cropping’) are not met.

See GAEZ v5 dataset on multiple cropping zones classes for rain-fed conditions on the FAO Agro-Informatic Data Catalog (link).

See GAEZ v5 dataset on multiple cropping zones classes for irrigated conditions on the FAO Agro-Informatic Data Catalog (link).

Reference LGPs account for both temperature and soil moisture conditions and do not necessarily account for significant differences in wetness conditions especially within long LGPs (> 225 days), For the purpose of better reflection of wetness conditions, so-called equivalent LGPs are used. Equivalent LGP is defined on the basis of regression analysis of the reference LGP and the humidity index P/ETo as follows. A quadratic polynomial is used to express the relationship between the number of growing period days and the annual humidity index. Parameters were estimated using data of all grid-cells with essentially year-round temperature growing periods, i.e., with LGPt5 = 365.

$$ LGPeq = \begin{cases} 14.0 + 293.66 \times \left( \frac{P}{E_{To}} \right) - 61.25 \times \left( \frac{P}{E_{To}} \right)^2 & \text{when } \left( \frac{P}{E_{To}} \right) \leq 2.4 \\ 366 & \text{when } \left( \frac{P}{E_{To}} \right) > 2.4 \end{cases} $$

The equivalent LGP is used in the assessment of agro-climatic constraints, which relate environmental wetness with the occurrences of pest and diseases and workability constraints for harvesting conditions and for high moisture content of crop produce at harvest time.

Net primary productivity (NPP) is estimated as a function of incoming solar radiation and soil moisture at the rhizosphere. Actual crop evapotranspiration (ETa) has a close relationship with NPP of natural vegetation as it is quantitatively related to plant photosynthetic activity which is also driven by radiation and water availability.

NPP is computed based on daily values of actual evapotranspiration (ETa) simulated in the reference water balance and serves as a climate related indicator of rain-fed biological activity.

In GAEZ, NPP is estimated according to Zhang and Zhou (1995) as follows:

$$ NPP = \sum \frac{E_{Ta} \times A_0}{d} $$

The ∑ETa are accumulated estimates of daily ETa from the GAEZ water balance calculations for the specific water holding capacity of individual soil types. The variable A0 is a proportionality constant depending on diffusion conditions of CO2 and d is an expression of sensible heat. The ratio A0/d can be approximated by a function of the radiative dryness index (RDI) (Uchijima and Seino, 1988).

$$ \frac{A_0}{d} \approx f(RDI) = RDI \times \exp \left( -\sqrt{9.87 + 6.25 \times RDI} \right) $$

with:

$$ RDI = \frac{\sum_{j=1}^{12} Rn_j}{\sum_{j=1}^{12} P} $$

where, ΣRn is accumulated net radiation for the year and ΣP is precipitation for the year.

In GAEZ, two separate evaluations of the NPP function are performed:

• For NPP estimates under natural, i.e., rain-fed conditions, RDI is calculated from prevailing net radiation and precipitation of a grid cell and ETa is determined by the GAEZ reference water balance:

$$ NPP_{rf} = \sum \left( E_{Ta} \times RDI \times \exp \left( -\sqrt{9.87 + 6.25 \times RDI} \right) \right) $$

• For an NPP estimate applicable under irrigation conditions, ETa = ETm is assumed and a RDI of 1.375 is used, a value which results in a maximum for the function term approximating the A0/d ratio:

$$ NPP_{ir} = \sum \left( E_{Ta} \times 1.375 \times \exp \left( -\sqrt{9.87 + 6.25 \times 1.375} \right) \right) $$

NPP is computed using daily values of estimated actual evapotranspiration (ETa) of the reference water balance and serves as a climate related indicator of rain-fed biological activity. Separate NPP potential calculations are performed for moisture supply under natural conditions and for conditions when adequate water is supplied (e.g. by irrigation) to ensure daily ETa = ETo.

See GAEZ v5 dataset on Net Primary Production (NPP) potential under rain-fed conditions (kg C/ha) on the FAO Agro-Informatic Data Catalog (link).

The Köppen climate classification is a widely used, vegetation-based, empirical climate classification system developed by Wladimir Köppen in the early 20th century (Köppen, 1900) and later updated by Rudolf Geiger (Geiger, 1954, 1961) with the aim was to devise formulas that would define climatic boundaries in such a way as to correspond to different observed vegetation zones (biomes).

Köppen’s classification is based on a subdivision of terrestrial climates into five major types, which are represented by the capital letters A (tropical), B (dry), C (temperate), D (cold), and E (polar). Each of these climate types, except for B, is defined by temperature criteria. Type B designates climates in which the controlling factor on vegetation is dryness (rather than coldness). Dry climates are divided into arid (BW) and semi-arid (BS) subtypes. Other climate types are sub-divided according to seasonal precipitation characteristics. The level-2 classification distinguishes 14 classes.

The computations in Module I produce also a level-3 classification with 31 classes where additional temperature criteria are applied for a further subdivision in temperate and cold climates (classes with capital letters B and C).

See GAEZ v5 dataset on Koeppen-Geiger climate classification (level-2) on the FAO Agro-Informatic Data Catalog (link).

Module I produces two binary intermediate output files, which respectively contain for each grid cell the calculated indicators of thermal and moisture conditions. These files are then used to generate tabulations by administrative or watershed territorial units and a variety of GIS raster maps of the agro-climatic analysis results (see table below) for visualization and download. Several indicators are also used as input variables to the computations in Modules II, III, and V.

The indicators are calculated for average climate conditions, for time-series of individual years (TS) and, based on time-series results, for 30-year statistics (TS30) including for each variable the mean, median, 10% and 90% quantiles, standard deviation and coefficient of variation.

Table: Agro-climatic indicators provided in GAEZ v5

Type	Description	Unit
ET0	Reference evapotranspiration (Penman-Monteith)	mm
ETa	Actual evapotranspiration of FAO reference crop	mm
fss	Snow-adjusted air frost number	Scalar
fst	Air frost number	Scalar
KG2	Koeppen-Geiger climate classification (2-character)	Class
KG3	Koeppen-Geiger climate classification (3-character)	Class
ld1	Longest component growing period	Days
lgb	Starting day of longest component growing period	Day-of-Yr
lgd	Total number of growing period days	Days
lgp	Length of growing period zones	Class
lt2	Temperature growing period LGPt5: Number of days when Ta ≥ 5 °C	Days
lt3	Temperature growing period LGPt10: Number of days when Ta ≥ 10 °C	Days
mc2	Thermal Zones class	Class
mci	Multi-cropping class, irrigation conditions	Class
mcl	Thermal Climate class	Class
mcr	Multi-cropping class, rain-fed conditions	Class
ndd	Maximum number of consecutive dry days (P < 1mm) during LGPt5	Days
ndr	Number of rain days, i.e., days with P ≥ 1mm	Days
nhum	Number of humid months (with P > ETo)	Months
nn00	Number of ‘frost’ days with minimum temperature Tmin < 0 °C	Days
nn05	Number of days with minimum temperature Tmin < 5 °C	Days
nn10	Number of days with minimum temperature Tmin < 10 °C	Days
nn20	Number of days with minimum temperature Tmin < 20 °C	Days
np1	Potential net primary productivity, irrigation conditions	kg C/ha
np2	Potential net primary productivity, rain-fed conditions	kg C/ha
nx30	Number of days with maximum temperature Tmax > 30 °C	Days
nx35	Number of ‘hot’ days with maximum temperature Tmax > 35 °C	Days
nx40	Number of ‘very hot’ days with maximum temperature Tmax > 40 °C	Days
nx45	Number of ‘extremely hot’ days with maximum temperature Tmax > 45 °C	Days
prc	Annual precipitation	mm
prf	Permafrost zone	Class
rfm	Fournier index	mm
ri2	P/ETo ratio (*100) for temperature growing period when Ta ≥ 5 °C	Scalar
rid	Annual Moisture Availability index (100×P/ETo)	Scalar
riS	Seasonal P/ETo ratio (×100) for April-September	Scalar
riW	Seasonal P/ETo ratio (×100) for October-March	Scalar
rQ1	Quarterly P/ETo ratio (×100) for January-March	Scalar
rQ2	Quarterly P/ETo ratio (×100) for April-June	Scalar
rQ3	Quarterly P/ETo ratio (×100) for July-September	Scalar
rQ4	Quarterly P/ETo ratio (×100) for October-December	Scalar
ta0	Mean temperature of coldest month	°C
td2	Annual temperature amplitude (Ta of warmest month – Ta of coldest month)	°C
tmp	Mean annual temperature	°C
ts2	Annual accumulated temperature sum for days with Ta ≥ 5 °C	∑°C
ts3	Annual accumulated temperature sum for days with Ta ≥ 10 °C	∑°C
wde	Annual water deficit of FAO reference crop (= ETo – ETa)	mm