Since no useful information is available for an estimate of the direct runoff volume on the whole region, natural water resource was determined using a distributed monthly water balance model described by Mendicino & Versace (2007) and Mendicino et al. (2008a), which extends the approach proposed by Thornthwaite & Mather (1955) and simulates soil moisture variations, evapotranspiration, and runoff on a 5 km regular grid (Fig. 1) using data sets that include climatic drivers, vegetation, and soil properties. This model does not consider the horizontal motion of water on the land surface, or in the soil (hence no flow routing algorithms are required), and it is based on a simplified mass balance:

$$
\Delta \mathcal{W} = P + SM - SA - ET - Q \tag{1}
$$

where ΔW is the change in soil moisture storage, P the precipitation, SM the snow melt, SA the snow accumulation, ET the actual evapotranspiration, and Q is the runoff (all the quantities are evaluated in mm month-1). In the model, potential evapotranspiration PET is estimated through the Priestley-Taylor method (Priestley & Taylor, 1972), requiring only temperature, air pressure and net radiation data, overcoming the lack of observed wind speed and air humidity data in the analyzed area before the year 2000. In the case of net radiation, monthly values were obtained starting from a modified version of the model originally suggested by Moore et al. (1993). Actual evapotranspiration ET is calculated starting from PET and considering the Accumulated Potential Water Loss (APWL), such as suggested by Thornthwaite & Mather (1955), which represents the total amount of unsatisfied potential evapotranspiration to which the soil has been subjected.

Because of the significant reforestation campaigns carried out in Calabria after the Second World War, whose results were evident already at the end of 1950s, the starting period for the analysis was assumed to be 1957. The assumption of constant soil use (derived by the Corine Land Cover 2000 project) is justified by the coarse resolution of the model (5 km grid). The model schematized in figure 1 was improved also considering: i) that a portion of the rainfall is directly transformed into "instantaneous" runoff (depending on the ratio between actual soil moisture and soil water holding capacity WHC, in its turn derived by combining soil use with a detailed soil texture map of Calabria); ii) an additional very simple snow module, which partitions snow and rain precipitation and regulates snow melt just referring to the current monthly temperature in the cell; iii) that the hydraulic subsoil characteristics are simulated with reservoirs whose rates of depletion vary with the predominating geo-lithological characteristics in the single cells of the model (Mendicino et

Fig. 1. Schematization of the water balance model and overlay of the 5 km regular grid in the analyzed region.

consider the horizontal motion of water on the land surface, or in the soil (hence no flow

where ΔW is the change in soil moisture storage, P the precipitation, SM the snow melt, SA the snow accumulation, ET the actual evapotranspiration, and Q is the runoff (all the quantities are evaluated in mm month-1). In the model, potential evapotranspiration PET is estimated through the Priestley-Taylor method (Priestley & Taylor, 1972), requiring only temperature, air pressure and net radiation data, overcoming the lack of observed wind speed and air humidity data in the analyzed area before the year 2000. In the case of net radiation, monthly values were obtained starting from a modified version of the model originally suggested by Moore et al. (1993). Actual evapotranspiration ET is calculated starting from PET and considering the Accumulated Potential Water Loss (APWL), such as suggested by Thornthwaite & Mather (1955), which represents the total amount of

Because of the significant reforestation campaigns carried out in Calabria after the Second World War, whose results were evident already at the end of 1950s, the starting period for the analysis was assumed to be 1957. The assumption of constant soil use (derived by the Corine Land Cover 2000 project) is justified by the coarse resolution of the model (5 km grid). The model schematized in figure 1 was improved also considering: i) that a portion of the rainfall is directly transformed into "instantaneous" runoff (depending on the ratio between actual soil moisture and soil water holding capacity WHC, in its turn derived by combining soil use with a detailed soil texture map of Calabria); ii) an additional very simple snow module, which partitions snow and rain precipitation and regulates snow melt just referring to the current monthly temperature in the cell; iii) that the hydraulic subsoil characteristics are simulated with reservoirs whose rates of depletion vary with the predominating geo-lithological characteristics in the single cells of the model (Mendicino et

Fig. 1. Schematization of the water balance model and overlay of the 5 km regular grid in the

analyzed region.

*W P SM SA ET Q* (1)

routing algorithms are required), and it is based on a simplified mass balance:

unsatisfied potential evapotranspiration to which the soil has been subjected.

al., 2005). The different characteristics of subsoil leaded to the subdivision of the region into three categories: I) areas with a high capability of producing perennial flow (rocks with high permeability not in the plain); II) areas with mean capability of producing perennial flow (rocks with mean permeability); III) areas with low capability of producing perennial flow (rocks with low permeability or with high permeability in the plain).

The monthly water balance model was validated considering about 2900 monthly runoff values observed in 14 Calabrian catchments during the period 1955-2006 (Fig. 2). Figure 2 also shows the quite satisfactory performance of the model that, besides reproducing the monthly average behaviour of each considered catchment, provided values of the slopes of the regression curves obtained comparing observed and simulated runoff values varying from a minimum of 0.791 (Alli Orso) to a maximum of 1.135 (Esaro La Musica), while the correlation coefficients *r* varied from 0.447 (Coscile Camerata) to 0.939 (Corace Grascio).

Fig. 2. Spatial distribution of the gauged catchments and comparison between all observed and simulated runoff during the period 1960-2006.

The monthly water balance model was applied on the whole territory of Calabria for the period 1960-2006 on a 5 km regular grid, where each cell was independent from the others, determining the main components of the hydrological balance in the whole region: precipitation, actual evapotranspiration, soil moisture storage, groundwater volume and instantaneous, surface and subsurface runoff. In several areas of the region a negative trend was observed for many of these variables. Specifically, while the potential evapotranspiration trend was strongly related to increasing temperature, actual evapotranspiration was affected also by changes (reduction) in precipitation. Considering the whole region, the average annual actual evapotranspiration estimated in the analyzed period is 581 mm, equal to about 57.8% of the average cumulated annual rainfall (potential evapotranspiration is about 110%). Figure 3 (left side) shows the average monthly values in the whole region for actual and potential evapotranspiration. The months where a significant difference can be observed are the months from May to September. In these months (the less rainy and warmest ones), evaporation of soil moisture accumulated in wintertime exceeds rainfall, requiring irrigation in most of the agricultural areas. Figure 3 (right side) also shows the trend of cumulated annual actual evapotranspiration. The decrease in time of this quantity due to rainfall reduction is partly balanced by the increasing temperatures, hence the negative trend is not significant. It is noteworthy that peaks and troughs are generally dependent on rainy (e.g. 2005) or not rainy (e.g. 2001) years, even though rainfall distribution during the single year also affects the evapotranspirative phenomenon. The correlation coefficient between cumulated annual actual evapotranspiration and precipitation in the period 1960-2006 was 0.638.

Fig. 3. Left: average monthly values in Calabria of actual (AE) and potential evapotranspiration (PE), precipitation (P) and temperature (T) during the period 1960-2006. Right: trend of cumulated annual actual evapotranspiration.

## **3. Water demand and availability**

The water balance between available water resource and water demand is the starting point for a correct water management. One of the main problems occurring in this phase is the general lack of observed data, obliging to synthetic estimates of water availability and several levels of approximation in the assessment of water needs, mainly for irrigation and for determining the management rules of the reservoirs.

In this context, the water balance on the Calabrian region was carried out considering also withdrawals from springs, streams, reservoirs and wells for irrigation and for potable uses, adopting two sequential simulation models. The former is a modified version of the distributed hydrological model, where the natural water balance is integrated with the withdrawal for irrigation and potable uses, producing (output variable) a residual availability. This water availability is used in a second GIS-based model considering the effects of diversions and reservoirs.

In the first model, inside a single 5 km squared cell can co-exist both wells and springs used to feed small irrigation systems or few users, located in the same cell, and wells and springs used for water mains collecting water outside the cell. If both the points where the water is withdrawn and used are inside the same cell (this happens only for wells for irrigation purposes), the schematization shown in figure 4a is adopted, hypothesizing that inside the cell a known volume is transferred monthly from the subsoil reservoir to the surface as an "added" precipitation (owing to the irrigation). This volume has to be summed to the meteorological precipitation and is subjected to the cycle simulated by the water balance, increasing the soil moisture and actual evapotranspiration and eventually feeding the

months (the less rainy and warmest ones), evaporation of soil moisture accumulated in wintertime exceeds rainfall, requiring irrigation in most of the agricultural areas. Figure 3 (right side) also shows the trend of cumulated annual actual evapotranspiration. The decrease in time of this quantity due to rainfall reduction is partly balanced by the increasing temperatures, hence the negative trend is not significant. It is noteworthy that peaks and troughs are generally dependent on rainy (e.g. 2005) or not rainy (e.g. 2001) years, even though rainfall distribution during the single year also affects the evapotranspirative phenomenon. The correlation coefficient between cumulated annual actual

evapotranspiration and precipitation in the period 1960-2006 was 0.638.

Fig. 3. Left: average monthly values in Calabria of actual (AE) and potential

Right: trend of cumulated annual actual evapotranspiration.

for determining the management rules of the reservoirs.

**3. Water demand and availability**

effects of diversions and reservoirs.

evapotranspiration (PE), precipitation (P) and temperature (T) during the period 1960-2006.

The water balance between available water resource and water demand is the starting point for a correct water management. One of the main problems occurring in this phase is the general lack of observed data, obliging to synthetic estimates of water availability and several levels of approximation in the assessment of water needs, mainly for irrigation and

In this context, the water balance on the Calabrian region was carried out considering also withdrawals from springs, streams, reservoirs and wells for irrigation and for potable uses, adopting two sequential simulation models. The former is a modified version of the distributed hydrological model, where the natural water balance is integrated with the withdrawal for irrigation and potable uses, producing (output variable) a residual availability. This water availability is used in a second GIS-based model considering the

In the first model, inside a single 5 km squared cell can co-exist both wells and springs used to feed small irrigation systems or few users, located in the same cell, and wells and springs used for water mains collecting water outside the cell. If both the points where the water is withdrawn and used are inside the same cell (this happens only for wells for irrigation purposes), the schematization shown in figure 4a is adopted, hypothesizing that inside the cell a known volume is transferred monthly from the subsoil reservoir to the surface as an "added" precipitation (owing to the irrigation). This volume has to be summed to the meteorological precipitation and is subjected to the cycle simulated by the water balance, increasing the soil moisture and actual evapotranspiration and eventually feeding the aquifer from which it has been withdrawn. Instead, if the cell where the water is withdrawn does not coincide with the cell where it is used (that is only the case of regional water mains) then the schematization shown in figure 4b is adopted. The source cell is subjected to a reduction of the volume of the subsoil reservoir, while the water is hypothesized to reach directly the water stream in the destination cell, feeding the surface runoff with a restitution coefficient equal to 0.7.

Fig. 4. Schematization of the modified water balance model considering withdrawals for irrigation and potable uses.

Summarizing, the proposed model allows that every month for each cell a volume *cellout* can be extracted from the subsoil reservoir, which is equal to the withdrawals for irrigation and potable purposes, that a volume *cellin\_irr* can be added like a supplementary precipitation representing the water derived from the same cell and used for irrigation, and finally, that a volume *cellin\_pot* can be added like a supplementary surface runoff accounting for the water come in the cell to satisfy the potable uses. All the data related to potable and irrigation withdrawals were derived from several official sources, even if sometimes incomplete, and were aggregated at the resolution of the water balance model. Figure 5 shows the distribution of the regional water mains and of the local water distribution systems.

The modified natural water balance is the input of the commercial GIS-based model Mike Basin (DHI Software), accounting for the effects of diversions and reservoirs aimed at satisfying irrigation, hydro-power, civil and industrial requirements (Fig. 6). The lack of actual information about the management rules of reservoirs led to hypothesize several working schemes for the definition of the optimal water balance. Finally, for all the analyzed reservoirs the minimum flow requirements were considered following two different approaches: the former proposed by the Regional Basin Authority (very conservative, especially for some typical Calabrian rivers, called *fiumare*¸ characterized by no flow conditions for a relevant part of the year) and; the latter based on the Q7,10 flow, i.e. the lowest 7 consecutive-day average flow characterized by a 10 years time period.

In the case of the irrigation demand (i.e. water requirements for balancing evapotranspiration losses), a detailed analysis was carried out on each irrigation district (Fig. 7) during the irrigation season April – September. Specifically, the assessment of the effective water consumption was determined by considering different seasonal (spring, summer, autumn) soil use spatial distributions (e.g. in Table 1). For each soil use the seasonal irrigation demand (m3/ha) of the crops (Table 2) was achieved. The same was split monthly taking into account that the highest request is obtained during the trimester June – August (Table 3). An adequately detailed knowledge of the irrigation network allowed the correct estimate of the possible uptake of volumes to/from other cells. It is noteworthy to highlight that all the information related to soil use and water requirements were aggregated at the resolution of the model, i.e. 5×5 km2, for the whole region.

In the proposed analysis the quite small volumes related to industrial areas were neglected.

Fig. 5. Left: regional water mains (479 springs, 281 wells and about 2000 conveying pipes). Right: local water distribution systems (over 1200 springs and wells).

Water balance results showed that, for average conditions, the residual annual water availability is great, even if some weaknesses arise. Among these, the strong differences in the seasonal precipitation, which is mainly concentrated in the wet winter period (80-90%), require an accurate management of the volumes stored in natural and artificial reservoirs for facing the hot and dry Mediterranean summer. Furthermore, the decrepitude of several conveying pipes has to be considered with remarkable water losses, and the negative precipitation trend due to climate change that seems to be relevant in Calabria (a preliminary analysis about future climate scenarios in Calabria is shown in the 6th section). The weaknesses pointed out in normal conditions suggested water resources availability should be analyzed when drought conditions occur. Specifically, through the use of the Standardized Precipitation Index (SPI, McKee et al., 1993) intensity and duration of

droughts were determined on the whole Calabrian region.

(Fig. 7) during the irrigation season April – September. Specifically, the assessment of the effective water consumption was determined by considering different seasonal (spring, summer, autumn) soil use spatial distributions (e.g. in Table 1). For each soil use the seasonal irrigation demand (m3/ha) of the crops (Table 2) was achieved. The same was split monthly taking into account that the highest request is obtained during the trimester June – August (Table 3). An adequately detailed knowledge of the irrigation network allowed the correct estimate of the possible uptake of volumes to/from other cells. It is noteworthy to highlight that all the information related to soil use and water requirements were

In the proposed analysis the quite small volumes related to industrial areas were neglected.

Fig. 5. Left: regional water mains (479 springs, 281 wells and about 2000 conveying pipes).

Water balance results showed that, for average conditions, the residual annual water availability is great, even if some weaknesses arise. Among these, the strong differences in the seasonal precipitation, which is mainly concentrated in the wet winter period (80-90%), require an accurate management of the volumes stored in natural and artificial reservoirs for facing the hot and dry Mediterranean summer. Furthermore, the decrepitude of several conveying pipes has to be considered with remarkable water losses, and the negative precipitation trend due to climate change that seems to be relevant in Calabria (a preliminary analysis about future climate scenarios in Calabria is shown in the 6th section). The weaknesses pointed out in normal conditions suggested water resources availability should be analyzed when drought conditions occur. Specifically, through the use of the Standardized Precipitation Index (SPI, McKee et al., 1993) intensity and duration of

Right: local water distribution systems (over 1200 springs and wells).

droughts were determined on the whole Calabrian region.

aggregated at the resolution of the model, i.e. 5×5 km2, for the whole region.

Fig. 6. Example of water system schematization realized within the GIS-based model Mike Basin.

Table 1. Seasonal soil use for a generic irrigation district.

For each of the most significant Calabrian basins, and for each month of the period 1960- 2006, a mean SPI areal value was calculated for different time scales (1-, 3-, 6-, 12-, 24- and 48-months), with the aim of highlighting the longest and most intense drought periods (Fig. 8). Drought indices are essential at all levels of the planning process. The reader is referred to section 5 for a brief review of the most diffused ones.

Usually, the beginning of a drought period can be defined when SPI values are lower than -1.0, and its end when the values come back positive. Nevertheless, based on a historical analysis of the official declarations of "natural disaster" in Calabria due to drought, even a 12-month SPI value equal to -0.7 was observed to be adequate as a drought threshold. Hence, when a generic month presented a 12-month SPI value lower than -0.7, it was considered a drought month, and the correspondent total runoff simulated with the water balance model was taken into account. The aggregation, from January to December, of the average runoff estimated during the drought months leaded to the definition of a so-called "scarce year" whose runoff values, even if statistically less probable than the ones of the single months, pointed out the possibility of extremely critical situations in Calabria, with a reduction of total runoff up to 43%. This analysis introduces issues related both to the management of water shortage and to the mitigation of drought through the use of restrictive measures. The development and implementation of strategic and emergency plans are primary tools to face the different aspects of drought phenomenon, as it is shown in the next paragraph.

Fig. 7. Calabrian irrigation districts and network systems.

Table 2. Seasonal irrigation demand (m3/ha) of the crops.

even if statistically less probable than the ones of the single months, pointed out the possibility of extremely critical situations in Calabria, with a reduction of total runoff up to 43%. This analysis introduces issues related both to the management of water shortage and to the mitigation of drought through the use of restrictive measures. The development and implementation of strategic and emergency plans are primary tools to face the different

aspects of drought phenomenon, as it is shown in the next paragraph.

Fig. 7. Calabrian irrigation districts and network systems.

Table 2. Seasonal irrigation demand (m3/ha) of the crops.

 Monthly irrigation demand (m3/ha) of the crops.

Fig. 8. Temporal evolution of SPI values in a generic Calabrian river basin. Red squares correspond to drier periods.

## **4. Water resource management under shortage conditions**

In its 2007 Communication (COM, 2007) the European Commission stated that the challenge of water scarcity and droughts needs to be addressed both as an essential environmental issue and as a precondition for sustainable economic growth in Europe, and highlighted the necessity of progressing towards full implementation of the EU Water Framework Directive (WFD) 2000/60. The WFD is the EU's flagship Directive on water policy, explicitly defining long-term planning as the main tool for ensuring good status of water resources. Nevertheless, it does not indicate criteria and actions to face risk of drought, delegating National Legislations to concretely realize its framework (after a series of yearly follow-up reports, a policy review is foreseen for 2012 at the EU level).

In Italy the EU WFD was taken into account with the Legislative Decree 152/2006 on environmental protection. Though this act is quite recent, it seems to be far from being adequate to actually cope with drought, mainly because it does not stress the necessity of passing from a reactive to a proactive approach, based on preparedness and mitigation actions planned in advance with the contribution of all the involved stakeholders, ready to be implemented when drought phenomena occur.

Within a comprehensive drought management planning process, Rossi et al. (2007) proposed the identification of three main tools: Strategic Water Shortage Preparedness Plan, Water Supply System Management Plan and Drought Contingency Plan. Following, an example of application of the proposed guidelines is shown for the planning of the best mix of measures needed for coping with drought phenomena on one of the most important agricultural areas in southern Italy, the Low Esaro and Sibari Plain (Mendicino et al., 2008b). It is noteworthy that in the proposed example (water shortage planning in the agricultural sector) water demand is strictly correlated to the amount of water needed from crops for facing lack of precipitation and high potential evapotranspiration during summer (see Table 3). Hence, in this case the planning process is triggered by the need of coping with the high water loss due to evapotranspiration in a particularly dry period of the year. As it is explained in the next sections, this objective can be reached by means of demand reduction, water supply increase or impacts minimization measures, and considering long-, mediumand short-term actions.

#### **4.1 Methods and tools**

The Agricultural Strategic Water Shortage Preparedness Plan (ASP) is aimed at obtaining the reduction of drought vulnerability in the analyzed area through the implementation in normal conditions of long term mitigation measures, consisting in a series of structural and non-structural actions applied in the water supply system. Usually, structural measures are economically expensive and require the use of many human resources. However, their effects are easier to be foreseen than the effects produced by the nonstructural mitigation actions, in their turn usually more accepted by all the stakeholders. The long term mitigation measures are specifically indicated in the systems characterized by a low level of reliability and are oriented at improving the water balance in the analyzed system. These actions not only enhance the reliability of the system through fulfilling water requirements, but also reduce its vulnerability with respect to future drought events, fulfilling three main objectives: i) water demand reduction; ii) water supply increase and improvement of the efficiency of the system; iii) minimization of the impacts. Within the actions reducing water demand, some are directly aimed at reducing evapotranspiration by adopting appropriate agronomic techniques, such as e.g. irrigating during non windy periods for minimizing wind drift losses, or early defoliation to reduce crop transpiration surface (for a deeper description, the reader is referred to Pereira, 2007). In table 4 the long term measures that can be potentially adopted in agriculture are listed, subdivided considering their main objectives.

long-term planning as the main tool for ensuring good status of water resources. Nevertheless, it does not indicate criteria and actions to face risk of drought, delegating National Legislations to concretely realize its framework (after a series of yearly follow-up

In Italy the EU WFD was taken into account with the Legislative Decree 152/2006 on environmental protection. Though this act is quite recent, it seems to be far from being adequate to actually cope with drought, mainly because it does not stress the necessity of passing from a reactive to a proactive approach, based on preparedness and mitigation actions planned in advance with the contribution of all the involved stakeholders, ready to

Within a comprehensive drought management planning process, Rossi et al. (2007) proposed the identification of three main tools: Strategic Water Shortage Preparedness Plan, Water Supply System Management Plan and Drought Contingency Plan. Following, an example of application of the proposed guidelines is shown for the planning of the best mix of measures needed for coping with drought phenomena on one of the most important agricultural areas in southern Italy, the Low Esaro and Sibari Plain (Mendicino et al., 2008b). It is noteworthy that in the proposed example (water shortage planning in the agricultural sector) water demand is strictly correlated to the amount of water needed from crops for facing lack of precipitation and high potential evapotranspiration during summer (see Table 3). Hence, in this case the planning process is triggered by the need of coping with the high water loss due to evapotranspiration in a particularly dry period of the year. As it is explained in the next sections, this objective can be reached by means of demand reduction, water supply increase or impacts minimization measures, and considering long-, medium-

The Agricultural Strategic Water Shortage Preparedness Plan (ASP) is aimed at obtaining the reduction of drought vulnerability in the analyzed area through the implementation in normal conditions of long term mitigation measures, consisting in a series of structural and non-structural actions applied in the water supply system. Usually, structural measures are economically expensive and require the use of many human resources. However, their effects are easier to be foreseen than the effects produced by the nonstructural mitigation actions, in their turn usually more accepted by all the stakeholders. The long term mitigation measures are specifically indicated in the systems characterized by a low level of reliability and are oriented at improving the water balance in the analyzed system. These actions not only enhance the reliability of the system through fulfilling water requirements, but also reduce its vulnerability with respect to future drought events, fulfilling three main objectives: i) water demand reduction; ii) water supply increase and improvement of the efficiency of the system; iii) minimization of the impacts. Within the actions reducing water demand, some are directly aimed at reducing evapotranspiration by adopting appropriate agronomic techniques, such as e.g. irrigating during non windy periods for minimizing wind drift losses, or early defoliation to reduce crop transpiration surface (for a deeper description, the reader is referred to Pereira, 2007). In table 4 the long term measures that can be potentially adopted in agriculture are

reports, a policy review is foreseen for 2012 at the EU level).

be implemented when drought phenomena occur.

listed, subdivided considering their main objectives.

and short-term actions.

**4.1 Methods and tools**

Table 4. Main long term drought mitigation measures in agriculture (adapted from Rossi et al., 2007, and Georgia Dept. Of Natural Resources, 2003).

Since the ASP has to be drawn up choosing among several combinations of long-term mitigation measures, a suitable evaluation procedure has to be adopted. A multi-criteria technique could provide an as objective as possible comparison among different alternatives, according to a series of economic, environmental and social criteria, and taking into account the point of view of all the stakeholders. The tool adopted in this study for multi-criteria analysis is the software NAIADE (Munda, 1995).

The ASP should be prepared by the Basin or Hydrographic District Authorities, which are the bodies responsible for planning, and corresponds to the Drought Management Plan included into the River Basin Management Plan provided in the WFD.

Once the long-term mitigation measures are defined, an Agricultural Water Supply System Management Plan (AMP) has to be developed with the aim of: defining the best mix of long and short-term measures to avoid the beginning of a real water emergency; estimating the costs and the financing sources for the chosen mitigation measures, and; fostering the stakeholder participation and exchanges. It is prepared by the authority responsible for agricultural water management (i.e. the Land Reclamation Consortium), and the operative measures defined have to be adopted according to the values of early warning indicators, showing Normal, Pre-Alert or Alert conditions. The threshold values of the indicators can be chosen through an objective function or, if several aspects have to be accounted for, through a multi-criteria analysis.

In table 5 the short term measures that can be potentially adopted in agriculture are shown, subdivided on the basis of their principal objectives. With respect to the long-term mitigation measures, in this case the actions in the "demand reduction" category implicitly accept a certain percentage of water stress for the crops, because they are only aimed to reduce water consumption, without taking into account crop conditions. On the contrary, former long-term mitigation measures suggested some structural actions (i.e. actions to be adopted always) aimed at limiting some additional evapotranspiration due, e.g., to not correct irrigation practices, and that could be avoided without consequences for the crop. In brief, adopting the AMP evapotranspiration losses could be not completely compensated, and the farmers should be supported in assessing how to minimize water stress effects adopting even more specific agronomic techniques.

Table 5. Main short term mitigation measures in agriculture (adapted from Rossi et al., 2007).

If a particularly severe drought occurs, and the indicators signal Alarm conditions, the Agricultural Drought Contingency Plan (ACP) has to be adopted, defining the most appropriate short-term measures to reduce the impact of emergency situations. In this case the efforts are turned to protect the essential activities of the agricultural system, and the threshold values of the indicators have to be chosen taking into account this objective, preferably using a probabilistic approach, that allows the decision-makers to evaluate the effective risk of having water deficit for different scenarios. The ACP should be prepared by the Basin or Hydrographic District Authorities, with the collaboration of the Civil Protection.

Such as in the AMP, also in the ACP the assessment of crop losses can be made through production functions. In the case of extreme and particularly prolonged drought also the damage to perennial crops, the excessive decrease of the water tables of the aquifers, sea water intrusion, ecological damages to aquatic flora and fauna have to be considered. Some of this damage can be irreversible and can also influence crop production in the following years.

## **4.2 Case study**

210 Evapotranspiration – Remote Sensing and Modeling

In table 5 the short term measures that can be potentially adopted in agriculture are shown, subdivided on the basis of their principal objectives. With respect to the long-term mitigation measures, in this case the actions in the "demand reduction" category implicitly accept a certain percentage of water stress for the crops, because they are only aimed to reduce water consumption, without taking into account crop conditions. On the contrary, former long-term mitigation measures suggested some structural actions (i.e. actions to be adopted always) aimed at limiting some additional evapotranspiration due, e.g., to not correct irrigation practices, and that could be avoided without consequences for the crop. In brief, adopting the AMP evapotranspiration losses could be not completely compensated, and the farmers should be supported in assessing how to minimize water stress effects

> Public information campaign for water saving Restriction of irrigation of annual crops Pricing (discourage excessive water use) Mandatory rationing

Improvement of existing water systems efficiency (leak detection programs, new operating rules, etc.) Use of emergency sources (additional sources of low quality and/or high exploitation cost) Over exploitation of aquifers (use of strategic reserves) Increased diversion by relaxing ecological or recreational use constraints

> Temporary reallocation of water resources Public aids to compensate income losses Tax reduction or delay of payment deadline Public aids for crops insurance

**Category Short-term actions**

Table 5. Main short term mitigation measures in agriculture (adapted from Rossi et al., 2007). If a particularly severe drought occurs, and the indicators signal Alarm conditions, the Agricultural Drought Contingency Plan (ACP) has to be adopted, defining the most appropriate short-term measures to reduce the impact of emergency situations. In this case the efforts are turned to protect the essential activities of the agricultural system, and the threshold values of the indicators have to be chosen taking into account this objective, preferably using a probabilistic approach, that allows the decision-makers to evaluate the effective risk of having water deficit for different scenarios. The ACP should be prepared by the Basin or

Such as in the AMP, also in the ACP the assessment of crop losses can be made through production functions. In the case of extreme and particularly prolonged drought also the damage to perennial crops, the excessive decrease of the water tables of the aquifers, sea water intrusion, ecological damages to aquatic flora and fauna have to be considered. Some of this damage can be irreversible and can also influence crop production in the

Hydrographic District Authorities, with the collaboration of the Civil Protection.

adopting even more specific agronomic techniques.

Demand reduction

Water supply increase

Impacts minimization

following years.

The core of the analyzed water supply system is the Farneto Dam (Fig. 9), closing the Esaro Catchment (about 245.4 km2) in southern Italy. The dam is aimed at: (i) containing the ordinary floods and mitigating the extraordinary ones, according to the condition that the reservoir level is maintained almost empty from October to March; (ii) supplying water (about 30 hm3 from April to September) to the downstream agricultural area (about 85 km2), sited in the Low Esaro and Sibari Plain. At present about 63% of the irrigable area is based on open channel irrigation systems.

Fig. 9. Study area for the development of the planning process.

## **4.3 Applying the Agricultural Strategic Plan**

Table 6 shows 13 selected alternatives (from A to M), obtained combining the following six long-term mitigation measures: 0) System in current configuration; 1) Modernization of the irrigation network for reducing water losses and evaporation (it has been calculated that the efficiency of the actual scenario is equal to 67%, while the efficiency of the "modernized" scenario will be 80%; Mendicino et al., 2008b); 2) Construction of farm ponds; 3) Construction of a new upstream dam; 4) Economic incentives and educational activities for water saving; 5) Allowing the dam to store a little volume during the winter (i.e. dam not empty in March).

Table 6. Long-term mitigation measures and alternatives.

The alternatives were compared within the DSS tool NAIADE according to 4 economic criteria (construction costs of infrastructures, operation and maintenance costs, crop yield losses and amount of public aids needed), 2 environmental criteria (failures to meet ecological requirements and reversibility of the alternatives) and 4 social criteria (system vulnerability, temporal reliability, realization time of the infrastructures and employment increase). Since the observed period is short in order to evaluate the criteria and is characterized by few drought events, two monthly synthetic temperature and precipitation series of 1000 years were generated as input of the water balance model providing the corresponding runoff values.

Within the analysis carried out with NAIADE the final ranking of the alternatives comes from the intersection of two separate rankings. The former + is based on the "better" and "much better" preference relations, hence it points out how an alternative is "better" than the others. The latter is based on the "worse" and "much worse" preference relations, and indicates how an alternative is "worse" than the others.

The two rankings are different, since one alternative could result slightly better than the others with respect to few criteria and at the same time could result worse with respect to many criteria, or vice versa. In figure 10 the partial rankings and the final ranking are shown. The most efficient alternative is the "J", where measures 1, 4 and 5 are considered together. The alternative "M", mainly characterized by the construction of a new upstream dam, is the best only in the + ranking. A sensitivity analysis, carried out to assess the robustness of the achieved solution, showed a substantial stability of the ranking, constantly confirming alternative J as the optimal one. It is pointed out that alternative J is made up also by measure 1), allowing a reduction of evaporation losses.

Fig. 10. Partial and final ranking of the drought mitigation alternatives in the Esaro River Basin.

## **4.4 Applying the Agricultural Management Plan**

212 Evapotranspiration – Remote Sensing and Modeling

losses and amount of public aids needed), 2 environmental criteria (failures to meet ecological requirements and reversibility of the alternatives) and 4 social criteria (system vulnerability, temporal reliability, realization time of the infrastructures and employment increase). Since the observed period is short in order to evaluate the criteria and is characterized by few drought events, two monthly synthetic temperature and precipitation series of 1000 years were generated as input of the water balance model providing the

Within the analysis carried out with NAIADE the final ranking of the alternatives comes from the intersection of two separate rankings. The former + is based on the "better" and "much better" preference relations, hence it points out how an alternative is "better" than

The two rankings are different, since one alternative could result slightly better than the others with respect to few criteria and at the same time could result worse with respect to many criteria, or vice versa. In figure 10 the partial rankings and the final ranking are shown. The most efficient alternative is the "J", where measures 1, 4 and 5 are considered together. The alternative "M", mainly characterized by the construction of a new upstream dam, is the best only in the + ranking. A sensitivity analysis, carried out to assess the robustness of the achieved solution, showed a substantial stability of the ranking, constantly confirming alternative J as the optimal one. It is pointed out that alternative J is made up

Fig. 10. Partial and final ranking of the drought mitigation alternatives in the Esaro River

is based on the "worse" and "much worse" preference relations, and

corresponding runoff values.

indicates how an alternative is "worse" than the others.

also by measure 1), allowing a reduction of evaporation losses.

the others. The latter -

Basin.

The AMP is aimed at defining the indicators and the triggers for establishing the Normal, Pre-Alert and Alert conditions for the agricultural areas of the system. It has to take into account the guidelines provided by the ASP. In fact, it has to select the best combination among the optimal long-term mitigation measure previously determined (J) and the several short-term measures that can be adopted to manage water deficits on the analyzed area. Whereas the long-term measure J is adopted continuously, the short-term measures vary following the status of the system. Specifically, for this case study:

With the aim of determining the threshold values of the indices indicating the passage from one status to another, for every month from April to September a multicriteria analysis of the effects through NAIADE was carried out. The conflicting objectives to minimize are:

For each month, starting from April, an impact matrix was achieved where, on the basis of the criteria selected for the fulfillment of the objectives, the optimal combination of the thresholds triggering the Pre-Alert and Alert status was selected (Fig. 11). The selected index for the definition of the drought thresholds is the volume stored in the dam from May to

Fig. 11. Pre-Alert and Alert thresholds defined in the AMP.

September, while for the month of April a meteorological index was chosen, since owing to the rules adopted for dam management, at the end of March the dam level is not a significant index. For the month of April an analysis was carried out relating the yearly irrigation deficit to the 6 month-SPI calculated in March (considering in this way the first six months of the hydrologic year, from October to March). In the selection of the threshold values a rule was followed considering that, if the multicriteria analysis provides more optimal solutions, the one with the lowest irrigation deficit is selected.

#### **4.5 Applying the Agricultural Contingency Plan**

The first objective of the ACP is the definition of indices and their thresholds for univocally establishing the beginning of an emergency situation. Since the hydrologic analysis in April shows that the water demand is always less than the water availability in the Farneto del Principe Dam, and that every year the volume stored increases during this month, the thresholds are selected starting from May, choosing as an index, such as in the AMP, the volume stored in the dam. Furthermore, since using the 1000-year series of generated meteorological data the application of the two previous Plans determined a very high temporal reliability of the system (98.7%), it is not useful to evaluate the emergency thresholds considering the few residual years. Hence, the adopted approach was based on a probabilistic analysis of the system failures and deficit percentage of the demand.

Specifically, hypothesizing that all the short-term measures were already adopted, the 1000 year series of generated meteorological data, for every month and for different fixed initial volumes stored, were used to assess the probability of having failures in fulfilling demand either in the same month or in the subsequent irrigation period, and the deficit percentage with respect to demand. The results, allowing the decision-makers to evaluate the effective risk of having water deficit for a specific storage in a specific month, are shown (from May to August) in figure 12.

Fig. 12. Monthly risk of having failures and deficit percentage with respect to demand (from May to August).

## **5. Drought indices**

214 Evapotranspiration – Remote Sensing and Modeling

September, while for the month of April a meteorological index was chosen, since owing to the rules adopted for dam management, at the end of March the dam level is not a significant index. For the month of April an analysis was carried out relating the yearly irrigation deficit to the 6 month-SPI calculated in March (considering in this way the first six months of the hydrologic year, from October to March). In the selection of the threshold values a rule was followed considering that, if the multicriteria analysis provides more

The first objective of the ACP is the definition of indices and their thresholds for univocally establishing the beginning of an emergency situation. Since the hydrologic analysis in April shows that the water demand is always less than the water availability in the Farneto del Principe Dam, and that every year the volume stored increases during this month, the thresholds are selected starting from May, choosing as an index, such as in the AMP, the volume stored in the dam. Furthermore, since using the 1000-year series of generated meteorological data the application of the two previous Plans determined a very high temporal reliability of the system (98.7%), it is not useful to evaluate the emergency thresholds considering the few residual years. Hence, the adopted approach was based on a

probabilistic analysis of the system failures and deficit percentage of the demand.

Specifically, hypothesizing that all the short-term measures were already adopted, the 1000 year series of generated meteorological data, for every month and for different fixed initial volumes stored, were used to assess the probability of having failures in fulfilling demand either in the same month or in the subsequent irrigation period, and the deficit percentage with respect to demand. The results, allowing the decision-makers to evaluate the effective risk of having water deficit for a specific storage in a specific month, are shown (from May

Fig. 12. Monthly risk of having failures and deficit percentage with respect to demand (from

optimal solutions, the one with the lowest irrigation deficit is selected.

**4.5 Applying the Agricultural Contingency Plan**

to August) in figure 12.

May to August).

Drought indices are tools necessary at all levels of the planning process: as it was shown in the previous sections, in the Strategic Plan they are used to identify the zones most exposed to drought risk in the analyzed areas, whereas in the Management Plan and in the Contingency Plan they are used to define trigger values for the activation of the measures for impact prevention or mitigation.

Most of the proposed methodologies for the characterization and the monitoring of drought phenomena are based on drought indices with the capability of synthetically summarizing drought conditions in a specific moment for a particular area. Nevertheless, drought is difficult to represent through a single index, hence frequently more indices or aggregate indices are used.

In rainfed agriculture meteorological indices are particularly suitable, because they give the opportunity of establishing a direct spatial correlation between the drought event and the agricultural production, allowing drought risk maps to be drawn.

Many authors provide lists describing the characteristics of the main drought indices (e.g. Ntale & Gan, 2003; Tsakiris et al., 2007a). Among them, the most widely used are the Palmer Drought Severity Index (PDSI; Palmer, 1965), the most "classical" drought index formulated to evaluate prolonged periods of both abnormally wet and abnormally dry weather conditions, and the Standardized Precipitation Index (SPI; McKee et al., 1993), a meteorological drought index based on the precipitation amount in a period of n months. Since SPI just needs precipitation data to be calculated, it has found widespread application. Guttman (1998) shows that the PDSI has a complex structure with an exceptionally long memory, while the SPI is an easily interpreted, simple moving average process. Hayes et al. (1999) describe the three main advantages in using SPI: the first and primary is its simplicity, the second is its variable time scale, and the third is its standardization. Nevertheless, the SPI is a meteorological index unable to take into account the effects of aquifers, soil, land use characteristics, crop growth and temperature anomalies, which influence agricultural and hydrological droughts.

Besides SPI, in the process of drought identification the MEDROPLAN Guidelines (Tsakiris et al., 2007a) suggest using also: the Reconnaissance Drought Index (RDI, Tsakiris et al., 2007b), also accounting for temperature anomalies (therefore for an eventual excessive evapotranspiration); deciles (Gibbs & Maher, 1967), used by the Australian Drought Watch System, which compare monthly observed precipitation values with the quantiles corresponding to the not exceeded frequencies of 10%, 20%,… 100% achieved from a long enough monthly precipitation series; the Surface Water Supply Index (SWSI, Shafer & Dezman, 1982), aggregating information about precipitation, runoff, volumes stored in the reservoirs and snowpack, and expressing drought conditions in a standardized way. Furthermore, owing to their diffusion, other two indices are recalled: the run method (Yevjevich, 1967), based on the comparison between the time series of the analyzed hydrological index and a representative threshold of "normal" conditions, and the Palmer Hydrological Drought Index (Karl, 1986), a modified version of the PDSI for real-time monitoring.

An interesting way to account for soil and land use effects (in some respects, the way followed by Palmer to calculate PDSI) is to derive the drought indices starting from hydrological modeling. These indices can be called "comprehensive" drought indices, because they allow a more comprehensive picture of the water cycle and its elements (Niemeyer, 2008). A typical example of comprehensive drought index is the Groundwater Resource Index (GRI) derived by Mendicino et al. (2008a) using the monthly water balance model shown in figure 1. For each single element where the model was applied (5 km regular cell), the monthly values of groundwater detention (i.e. the storage *D*) were standardized (for almost all the cells and months the skewness test of normality showed that the series were normally distributed) through the following equation:

$$\text{GRT}\_{y,m} = \frac{D\_{y,m} - \mu\_{y,m}}{\sigma\_{y,m}} \tag{2}$$

where *GRIy,m* and *Dy,m* are respectively the values of the index and of the groundwater detention for the year *y* and the month *m*, while *D,m* and *D,m* are respectively the mean and the standard deviation of groundwater detention values *D* simulated for the month *m* in a defined number of years (at least 30). This simple index, but based on several pieces of information provided by the water balance model, allows assessment of the deviation from the mean values of the available groundwater in a spatially-distributed way for the whole territory where the model is applied. Figure 13 shows the maps of the GRI distribution in northern Calabria for the months of April from 1979 to 2006. Examining the maps immediately the years with lower GRI values (the driest years, with brighter colors) are recognizable, as are the wettest years (darkest colors).

Fig. 13. Boundaries of the selected study area in Calabria and GRI distribution in northeastern Calabria for the months of April from 1979 to 2006 (from Mendicino et al., 2008a).

Other comprehensive indices were developed by Narasimhan & Srinivasan (2005), who using the Soil and Water Assessment Tool (SWAT) model, derived two drought indices

(Niemeyer, 2008). A typical example of comprehensive drought index is the Groundwater Resource Index (GRI) derived by Mendicino et al. (2008a) using the monthly water balance model shown in figure 1. For each single element where the model was applied (5 km regular cell), the monthly values of groundwater detention (i.e. the storage *D*) were standardized (for almost all the cells and months the skewness test of normality showed that

*D*

where *GRIy,m* and *Dy,m* are respectively the values of the index and of the groundwater

the standard deviation of groundwater detention values *D* simulated for the month *m* in a defined number of years (at least 30). This simple index, but based on several pieces of information provided by the water balance model, allows assessment of the deviation from the mean values of the available groundwater in a spatially-distributed way for the whole territory where the model is applied. Figure 13 shows the maps of the GRI distribution in northern Calabria for the months of April from 1979 to 2006. Examining the maps immediately the years with lower GRI values (the driest years, with brighter colors) are

Fig. 13. Boundaries of the selected study area in Calabria and GRI distribution in northeastern Calabria for the months of April from 1979 to 2006 (from Mendicino et al., 2008a).

Other comprehensive indices were developed by Narasimhan & Srinivasan (2005), who using the Soil and Water Assessment Tool (SWAT) model, derived two drought indices

, ,

(2)

*D,m* are respectively the mean and

, *y m y m*

*D,m* and

*y m*

the series were normally distributed) through the following equation:

detention for the year *y* and the month *m*, while

recognizable, as are the wettest years (darkest colors).

,

*GRI*

*y m*

for agricultural drought monitoring, the Soil Moisture Deficit Index (SMDI) and the Evapotranspiration Deficit Index (ETDI), based respectively on weekly soil moisture and evapotranspiration (ET) deficit. Also Matera et al. (2007) derived a new agricultural drought index, called DTx, based on the daily transpiration deficit calculated by a water balance model.

In the few last years the possibility of using long data series coming from remote sensing has opened new and promising perspectives to satellite-derived drought indices, which have the advantage of being intrinsically spatially distributed. Anderson et al. (2007) provide a brief presentation of TIR-based drought indices, while a list of many NOAA-AVHRR images-derived drought indices is presented by Bayarjargal et al. (2006). Zhang et al. (2005) exploit the capabilities of the MODerate resolution Imaging Spectroradiometer (MODIS) for monitoring and forecasting crop production using a satellite-based Climate-Variability Impact Index.

Several remote sensing-derived drought indices depend on the ratio *ET*/*PET*, where *ET* is actual evapotranspiration and *PET* potential evapotranspiration (e.g. Crop Water Stress Index (CWSI), Jackson et al., 1981; Drought Severity Index (DSI), Su et al., 2003; Evaporative Drought Index (EDI), Anderson et al., 2007; Yao et al., 2010). While *PET* is generally calculated by means of ground based measurements, *ET* is easily estimated through "residual" methods (e.g. SEBAL, Bastiaanssen et al., 1998; and Bastiaanssen, 2000; SEBI, Menenti & Choudhury, 1993; S-SEBI, Roerink et al., 2000; SEBS, Su, 2002; TSEB, Norman et al., 1995; DisAlexi, Anderson et al., 1997; METRIC, Allen et al., 2007), where the evapotranspirative term is the residual term of the energy balance equation:

$$
\lambda \mathcal{E} = \mathcal{R}\_n - G - H \tag{3}
$$

with *Rn* net radiation, *G* soil heat flux, *H* sensible heat flux and *E* latent heat flux, from which *ET* is derived.

Even though at this stage very seldom they are used as operational tools, remote sensingderived indices are potentially very useful because they intrinsically provide space-time variation of drought phenomena, and the ratio *ET*/*PET* can be reasonably related to soil water content. For instance, the relative evaporation *r* can be directly linked to the soil degree of saturation /*<sup>s</sup>* (Su et al., 2003). As an example, figure 14 shows the space-time evolution of the DSI, derived from SEBS and MODIS images, during summer 2006 in Northern Calabria. DSI is equal to 1 - *E* / *Ewet* (where *Ewet* is the latent heat flux estimated for the so-called "wet" pixel), hence higher DSI values indicate low actual evapotranspiration. A graph shown at the top of the figure provides information about precipitation in a micrometeorological station placed almost in the middle of the area (these data are only roughly representative, owing to the extension of the whole area). Figure 14 shows that the maps with the highest DSI values (e.g. July 20, but also September 4 and October 31), indicating drought stress conditions, are related to some of the most distant days from antecedent significant precipitation events.

To complete this brief review, a much-discussed issue is mentioned, i.e. the possibility of using the drought indices (especially SPI) to forecast stochastically the possible evolution of an ongoing drought (Cancelliere et al., 1996; Lohani et al., 1998; Bordi et al., 2005; Cancelliere et al., 2007). Several studies are also aimed at explaining and predicting possible drought conditions through the analysis of sea surface temperature (SST) and atmospheric circulation patterns (e.g. Wilby et al., 2004; Kim et al., 2006; Cook et al., 2007).

Fig. 14. Evolution of the DSI derived from SEBS in northern Calabria, from May 22 to October 31 2006. Top graph shows precipitation events on the representative micrometeorological station, placed approximately in the middle of the analyzed area.

However, when dealing with complex systems, where irrigated agriculture assumes a greater importance, one single index is often not able to capture the different features of drought and to take in account the effects of human activities (use of irrigation, water from reservoirs, wells, etc.) on the hydrological cycle. On the other hand, it is more practical to declare drought condition considering only one indicator. Thus, there is a growing interest in aggregating more indices. Keyantash & Dracup (2004) use an Aggregate Drought Index that considers all relevant variables of the hydrological cycle through Principal Component Analysis (but they do not include groundwater in the suite of variables); instead Steinemann & Cavalcanti (2006) use the probabilities of different indicators of drought and shortage, selecting the trigger levels on the basis of the most severe level of the indicator or the level of the majority of the indicators.

## **6. Future scenarios**

The most critical scenarios discussed in the previous paragraphs could become "normal" circumstances if global climate change increases the prolonged and intense drought periods. At the end of the proposed analysis, it is useful to hypothesize some future climatic scenarios, with the aim of steering decision makers towards suitable water management policies, as it is suggested by the European Commission (COM, 2009).

The methodology usually followed to assess the hydrological consequences of climate change basically consists of a three-step process (Xu et al., 2005): (1) the development and use of general circulation models (GCMs) to provide future global climate scenarios under the effect of increasing greenhouse gases, (2) the development and use of downscaling techniques (both statistical methods and nested regional climate models, RCMs, which are being continuously improved) for "downscaling" the GCM output to the scales compatible

Fig. 14. Evolution of the DSI derived from SEBS in northern Calabria, from May 22 to

micrometeorological station, placed approximately in the middle of the analyzed area.

However, when dealing with complex systems, where irrigated agriculture assumes a greater importance, one single index is often not able to capture the different features of drought and to take in account the effects of human activities (use of irrigation, water from reservoirs, wells, etc.) on the hydrological cycle. On the other hand, it is more practical to declare drought condition considering only one indicator. Thus, there is a growing interest in aggregating more indices. Keyantash & Dracup (2004) use an Aggregate Drought Index that considers all relevant variables of the hydrological cycle through Principal Component Analysis (but they do not include groundwater in the suite of variables); instead Steinemann & Cavalcanti (2006) use the probabilities of different indicators of drought and shortage, selecting the trigger levels on the basis of the most severe level of the indicator or the level of

The most critical scenarios discussed in the previous paragraphs could become "normal" circumstances if global climate change increases the prolonged and intense drought periods. At the end of the proposed analysis, it is useful to hypothesize some future climatic scenarios, with the aim of steering decision makers towards suitable water management

The methodology usually followed to assess the hydrological consequences of climate change basically consists of a three-step process (Xu et al., 2005): (1) the development and use of general circulation models (GCMs) to provide future global climate scenarios under the effect of increasing greenhouse gases, (2) the development and use of downscaling techniques (both statistical methods and nested regional climate models, RCMs, which are being continuously improved) for "downscaling" the GCM output to the scales compatible

policies, as it is suggested by the European Commission (COM, 2009).

October 31 2006. Top graph shows precipitation events on the representative

the majority of the indicators.

**6. Future scenarios**

with hydrological models, and (3) the development and use of hydrological models to simulate the effects of climate change on hydrological regimes at various scales. However, uncertainties within this framework have to be taken into account such as the internal variability of the climate system, model structure and parameterizations at different spatial and temporal scales, the downscaling techniques and bias correction methods and the choice of future climate scenarios. Several different approaches were chosen for providing operational solutions to these drawbacks (Xu et al., 2005). However, numerous GCM simulations show almost univocal trends for global climate evolution. Giorgi & Lionello (2008) highlight a robust and consistent description specifically for the Mediterranean area, with a significant reduction in precipitation, mainly in summertime. In the same area, according to Giorgi (2006), a major increase in climatic variability is also expected.

Below, some results obtained by Senatore et al. (2011) are shown related to future water availability in the main basin of northern Calabria (Crati River Basin, 1332 km2, Fig. 15) at the end of the XXI century. Future scenarios were made by applying the outputs of three Regional Climate Models (RCMs) RegCM, HIRHAM and COSMO-CLM to the newly developed Intermediate Space Time Resolution Hydrological Model (In-STRHyM). The analysis was performed using two time slices (1961–1990 and 2070–2099) with the SRES A2 (GCM HAD3AM) and A1B (GCM ECHAM5/MPI-OM) scenarios. Observed biases in simulated precipitation and temperature fields during the control period (1961-1990) were corrected before using meteorological outputs from each RCM as input for In-STRHyM.

 It has a relatively simple structure and is suitable for long period simulations to be undertaken within acceptable time frames. Specifically, In-STRHyM calculates separately transpiration and evaporation, depending on a remote sensing-derived vegetation fraction. Both transpiration and bare soil evaporation are estimated through the crop coefficient approach suggested by Allen et al. (1998), considering a water stress coefficient of the canopy depending on soil moisture conditions, and the reference values calculated through the Priestley & Taylor (1972) equation.

The RCMs predict an increase in mean annual temperature from 3.5 °C to 3.9 °C, and a decrease in mean annual precipitation from 9% to 21%. The effects of the changes in the forcing meteorological variables are relevant for all the hydrological output variables. Here we highlight results achieved for actual evapotranspiration (*ET*). This variable tends to decrease with reduced precipitation, but it increases with higher temperatures. Lower decrease in precipitation predicted by HIRHAM, together with the higher temperatures, leads to an average year *ET* increase of +2.5%, while for RegCM and CLM the annual mean reduction is equal to -5.1% (Fig. 15) and -8.3%, respectively. However, in the summer period, that is the irrigation period, in all cases an *ET* reduction is achieved (from -1.0% with HIRHAM to -9.1% with RegCM, Fig. 15), indicating a decrease in water availability for plants and soil. This water stress is better highlighted when considering simulated root zone soil moisture. For this variable a reduction is predicted, differently from *ET*, during the whole year (-20.7%±1.9%, -12.8%±1.9% and -17.6%±1.8% with RegCM, HIRHAM and CLM, respectively). Figure 16 shows as an example the daily changes computed using RegCM (the behavior considering the other RCMs is similar): they are less relevant in winter and spring, but the reduction is dramatic in summer and early autumn, due to the increased evaporative demand (up to -40% with RegCM).

Fig. 15. Location of the Crati River Basin (left) and spatially distributed percentage changes in annual actual evapotranspiration (middle) and in actual evapotranspiration during the April–September irrigation period (right) simulated using RegCM (2070-2099 vs 1961-1990) (adapted from Senatore et al., 2011).

Fig. 16. Daily changes in root zone soil moisture computed using RegCM. RCM values are rescaled over 360 days, with the first day being October the 1st (readapted from Senatore et al., 2011).

## **7. Summary and conclusions**

Evapotranspiration deeply affects the water resources availability in Calabria (average annual actual evapotranspiration estimated equal to almost 60% of the average cumulated annual rainfall). Highest water requirements come from agriculture, where losses due to evapotranspiration demand have to be re-equilibrated by huge amounts of water, mainly in the summer hot and dry period. The analysis of the comparison between the available water resource and the water demand was carried out considering both the "normal" conditions due to meteorological forcing, and the most critical derived by intense and prolonged drought periods. In the first case, neglecting the very conservative constraints proposed by the Regional Basin Authority for the minimum flow requirements, specific issues are not observed, the residual water availability being sufficient. Several problems arise instead when drought conditions occur: in these cases the development of guidelines is essential to define operative aspects about the individuation of the water use priorities, to characterize different drought levels, to individuate the main objectives of water management related to these levels, and to determine and apply the mitigation measures.

The proposed example of water resource management under shortage conditions in the agricultural area of the Sibari Plain shows the benefits that a proactive approach may provide with respect to the classical approaches based on emergency measures, which are usually expensive and not efficient. Within a proactive approach, specific care should be taken into account for reducing evapotranspiration losses through appropriate agronomic techniques. This action has to be considered as a strategic measure, with an impact on water scarcity reduction comparable to the effect of structural measures.

The review of drought indices showed that evapotranspiration could provide useful insights: i) when adopted within comprehensive indices, considering the effects of the whole water balance, and not only of some components, on water resources availability; ii) and mainly, when dealing with optical remote sensing techniques, because these allow to estimate in a relatively easy way the spatially distributed actual evapotranspiration over a specific area, and then they can relate this quantity to soil moisture and to the incoming of drought events.

Finally, applying some future scenarios with different GCMs and RCMs, it was observed that in Calabria the issues related to water resource management under shortage conditions in the next few years will be more frequent and intense, affecting wider areas. Evapotranspiration will be "tied down" by reduced precipitation (reducing its magnitude) and by higher temperatures (providing an opposite effect). It will not clearly increase or decrease on an annual basis, but in any case it will contribute to reduce useable water from the soil, needed for agricultural purposes. The hypothesized scenarios of climate change, though subject to uncertainty, have to be intended as an important part of knowledge for the planning of future interventions on the water resource by the Public Authorities, and for defining the optimal criteria to evaluate the amount of public investments.

## **8. References**

220 Evapotranspiration – Remote Sensing and Modeling

Fig. 15. Location of the Crati River Basin (left) and spatially distributed percentage changes in annual actual evapotranspiration (middle) and in actual evapotranspiration during the April–September irrigation period (right) simulated using RegCM (2070-2099 vs 1961-1990)

Fig. 16. Daily changes in root zone soil moisture computed using RegCM. RCM values are rescaled over 360 days, with the first day being October the 1st (readapted from Senatore et

Evapotranspiration deeply affects the water resources availability in Calabria (average annual actual evapotranspiration estimated equal to almost 60% of the average cumulated annual rainfall). Highest water requirements come from agriculture, where losses due to evapotranspiration demand have to be re-equilibrated by huge amounts of water, mainly in the summer hot and dry period. The analysis of the comparison between the available water resource and the water demand was carried out considering both the "normal" conditions due to meteorological forcing, and the most critical derived by intense and prolonged drought periods. In the first case, neglecting the very conservative constraints proposed by the Regional Basin Authority for the minimum flow requirements, specific issues are not observed, the residual water availability being sufficient. Several problems arise instead when drought conditions occur: in these cases the development of guidelines is essential to define operative aspects about the individuation of the water use priorities, to characterize different drought levels, to individuate the main objectives of water management related to

these levels, and to determine and apply the mitigation measures.

(adapted from Senatore et al., 2011).

**7. Summary and conclusions**

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## **Guidelines for Remote Sensing of Evapotranspiration**

Christiaan van der Tol and Gabriel Norberto Parodi *University of Twente, Faculty of ITC The Netherlands*

## **1. Introduction**

226 Evapotranspiration – Remote Sensing and Modeling

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This chapter describes the possibilities, the limitations and the future of remote sensing of evapotranspiration (ET). The principles behind the techniques of remote sensing of ET are presented systematically. The mathematical formulations of the key equations are used to highlight the critical parts and the variables that remote ET is most sensitive to. The focus will be on the input data. Which input data do we definitively need, and with what accuracy? How can we select the best methodology to estimate ET spatially? A number of new developments will be introduced, and priorities for the near future formulated.

There is no global, validated ET product available today. We can find products of other components of the terrestrial water cycle, like rainfall and soil moisture, but not of ET. This means that remote estimation of ET is custom made, and that it requires specific skills. At first glance, this is surprising, because the idea of remote sensing of evapotranspiration is more than three decades old (Jackson et al., 1977; Jackson et al., 1987; Seguin, 1988). In this chapter we hope to clarify the reasons why the operational dissemination of remote sensing evapotranspiration products lags behind.

The one fundamental problem with estimating ET is that it cannot be measured directly. This is well illustrated by borrowing an allegory from the evangelist Billy Graham: "I've seen the effects of the wind but I've never seen the wind". This quote is certainly true, in a literal sense, for evapotranspiration. Evapotranspiration affects the water and energy balances, and it is these effects of evapotranspiration which are observed. For example, evapotranspiration reduces soil moisture content and its cools the land surface. By studying changes in soil moisture with lysimeters, or by studying patterns in land surface temperature with remote sensing, ET is estimated. The problem is that ET is not the only factor affecting the water and energy budgets of the surface. Other processes and physical properties play important roles as well. For this reason, quite a large number of input variables are needed to achieve reasonably accurate estimates of ET; estimates that are at least better than rule-of-thumb a priori estimates. This is the case for field techniques, and even more so for remote techniques. In remote sensing an additional issue is that the input data are not from just one source. Often data of different satellite platforms are needed in conjunction with meteorological data from ground stations.

In the process of collecting the data, the user faces practical and scientific problems. The practical problems of the user include the data collection, merging the data in a GIS database, and programming the algorithm for the calculation of evapotranspiration. Each of these steps requires expertise and access to dedicated GIS software packages, because most algorithms are not available 'on the shelf'. The scientific problem is that the procedure requires merging of data measured at different time and spatial scales. The merging of data for the calculation of evapotranspiration is a typical example of a data assimilation problem. Ideally, both the accuracy and the representativeness of each of the input data are taken into account in the calculation of the final product: the spatial map of evapotranspiration. Although algorithms for the calculation of evapotranspiration are available in the literature and on the internet, there is no consistent data assimilation procedure attached that calculates the accuracy and reliability of the final product.

In recent years there have been a number of initiatives to build global products of evapotranspiration (Vinukullu et al., 2011; www.wacmos.org), addressing the above mentioned issues. The priorities for the near future are to establish a consistent way of merging the input data, improve the data assimilation techniques and to validate algorithms. In addition, new sources of data may be introduced. A promising tool is the use of satellite based laser altimetry for surface roughness estimation (Rosette et al., 2008).

It is the aim of this chapter to focus on principles that the algorithms have in common, and on the input data. Reviews of the history of remote sensing of ET can be found in the scientific literature (Courault et al., 2005; Glenn et al., 2007; Gowda et al., 2007; Kalma et al., 2008). In addition to these reviews, we would like to provide some anchor points and guidelines for the selection of a methodology for estimating ET in basin hydrology. We will quantify and evaluate the error of each of the input data, and show how this error propagates into the final result. For this analysis we will use theoretical considerations, a remote sensing model, and a selection of field data.

## **2. Principles of remote sensing algorithms for evapotranspiration**

Although remote sensing of evapotranspiration has evolved since the first initiatives in the 1970's, the fundamental principle has remained the same. All remote sensing based evapotranspiration estimates make use of the thermal and visible bands and the formulation of the energy balance of the surface. The instantaneous latent heat flux of evaporation is calculated as a residual of the energy balance, and this latent heat flux is in turn converted into an evapotranspiration rate after time integration. An inherent problem of this approach is that the errors in the various terms of the energy balance are affecting the latent heat flux in a manner that is difficult to predict. For this reason it is necessary to evaluate the different terms of the energy balance individually.

In the evaluation of the remote sensing algorithms presented in this section, we will discuss the terms, and indicate at what spatial and temporal resolution the data can be collected. It will become clear that the land surface temperature is the most important state variable. It plays a crucial role in sensible heat flux, ground heat flux and the balance of long wave radiation. Apart from the collection of accurate land surface temperature data, important selection criteria for a methodology are the heterogeneity of the land cover, the topography and the spatial resolution (sampling) of the remote data.

Neglecting the energy used in the process of photosynthesis, the instantaneous energy balance equation (EBE) over crops reads:

$$
\mathcal{R}\_n = \mathcal{G} + \mathcal{H} + \mathcal{\lambda}E \tag{1}
$$

*R*n is the net radiation remaining in the system, *G* the ground heat flux, *H* the sensible heat flux and *E* is the latent heat flux that is the energy consumed in evapotranspiration (all in W m-2). Radiation fluxes are positive when directed towards the land surface, the other fluxes are positive when pointed away from the surface. The partition of energy between the terms is largely controlled by the availability of water or moisture in the system. When moisture is not restricted, λ*E* reaches a maximum and *H* is small.

In order to estimate ET, Eq. 1 is solved for λ*E*. When applied to remote sensor retrievals, *R*<sup>n</sup> is solved entirely from a combination of radiation counting at sensor level and few ground information. Ground or soil heat flux is a minor component in densely vegetated areas, but a large term in non-vegetated or sparsely vegetated areas (Heusinkveld et al., 2004). The importance of a better evaluation of the soil heat flux is gaining attention, mainly to ensure the EBE closure in such areas. The evaluation of *H* is the major difficulty. There are several models and approaches to solve for *H* (SEB models) and a number of parameters and assumptions are still under debate. The remote sensing models for ET mainly differ in the way *H* is treated.

In the following sections, the individual terms of the EBE (Eq. 1) will be discussed in further detail. A theoretical description is presented for each term in the EBE, in combination with a discussion on the feasibility of data acquisition from remote and ground sources.

#### **2.1 Net radiation**

228 Evapotranspiration – Remote Sensing and Modeling

these steps requires expertise and access to dedicated GIS software packages, because most algorithms are not available 'on the shelf'. The scientific problem is that the procedure requires merging of data measured at different time and spatial scales. The merging of data for the calculation of evapotranspiration is a typical example of a data assimilation problem. Ideally, both the accuracy and the representativeness of each of the input data are taken into account in the calculation of the final product: the spatial map of evapotranspiration. Although algorithms for the calculation of evapotranspiration are available in the literature and on the internet, there is no consistent data assimilation procedure attached that

In recent years there have been a number of initiatives to build global products of evapotranspiration (Vinukullu et al., 2011; www.wacmos.org), addressing the above mentioned issues. The priorities for the near future are to establish a consistent way of merging the input data, improve the data assimilation techniques and to validate algorithms. In addition, new sources of data may be introduced. A promising tool is the use of satellite based laser altimetry for surface roughness estimation (Rosette et al., 2008). It is the aim of this chapter to focus on principles that the algorithms have in common, and on the input data. Reviews of the history of remote sensing of ET can be found in the scientific literature (Courault et al., 2005; Glenn et al., 2007; Gowda et al., 2007; Kalma et al., 2008). In addition to these reviews, we would like to provide some anchor points and guidelines for the selection of a methodology for estimating ET in basin hydrology. We will quantify and evaluate the error of each of the input data, and show how this error propagates into the final result. For this analysis we will use theoretical considerations, a

calculates the accuracy and reliability of the final product.

remote sensing model, and a selection of field data.

terms of the energy balance individually.

balance equation (EBE) over crops reads:

and the spatial resolution (sampling) of the remote data.

**2. Principles of remote sensing algorithms for evapotranspiration**

Although remote sensing of evapotranspiration has evolved since the first initiatives in the 1970's, the fundamental principle has remained the same. All remote sensing based evapotranspiration estimates make use of the thermal and visible bands and the formulation of the energy balance of the surface. The instantaneous latent heat flux of evaporation is calculated as a residual of the energy balance, and this latent heat flux is in turn converted into an evapotranspiration rate after time integration. An inherent problem of this approach is that the errors in the various terms of the energy balance are affecting the latent heat flux in a manner that is difficult to predict. For this reason it is necessary to evaluate the different

In the evaluation of the remote sensing algorithms presented in this section, we will discuss the terms, and indicate at what spatial and temporal resolution the data can be collected. It will become clear that the land surface temperature is the most important state variable. It plays a crucial role in sensible heat flux, ground heat flux and the balance of long wave radiation. Apart from the collection of accurate land surface temperature data, important selection criteria for a methodology are the heterogeneity of the land cover, the topography

Neglecting the energy used in the process of photosynthesis, the instantaneous energy

*R GH E <sup>n</sup>*

*R*n is the net radiation remaining in the system, *G* the ground heat flux, *H* the sensible heat flux and *E* is the latent heat flux that is the energy consumed in evapotranspiration (all in

(1)

Net radiation *R*n is the dominant term in the EBE, since it represents the source of energy that must be balanced by the thermodynamic equilibrium of the other terms. The net radiation can also be expressed as an electromagnetic balance of all incoming and outgoing radiation reaching and leaving a flat horizontal and homogeneous surface as:

$$R\_n = S\downarrow - S\uparrow + L\downarrow - L\uparrow \tag{2}$$

Where *S* is the shortwave radiation, nominally between 0.25 to 3m and *L* is the long wave radiation, nominally between 3 to 100 m. The arrows show the direction of the flux entering '' or leaving '' the system.

Equation 2 is very convenient from the data acquisition point of view since each term can either be obtained from available models, or directly from instruments at ground stations or remote platforms. As remote sensors are positioned looking to Earth, they measure outgoing radiation only. The incoming fluxes must be either modelled or derived through alternative methodologies.

The instantaneous incoming shortwave radiation (also called global radiation), *S*, is commonly measured at ground stations by means of pyranometers or solarimeters. These instruments usually work in the shortwave broadband range (usually 0.305 - 2.4 m). This range comprises almost 96% of the spectral interval of the solar irradiance. Recently there are remote sensing products and clearinghouses that account for the incoming and outgoing shortwave and long wave radiation. The use of them may reduce the need of permanently operational ground radiometers.

The outgoing shortwave radiation is the portion of the shortwave reflected back to the atmosphere. It is characterized by the albedo. The reflectance is the ratio between the reflected and the incoming radiation in a certain wavelength over an arbitrary horizontal plane. The integrated value over all visible bands defines the albedo, *r*0. Since albedo is a reflective property of the material, it can be evaluated from remote sensors multi-spectral bands, and the integration to full shortwave range is approached by a linear model that might include the atmospheric correction. The shortwave radiation balance reads:

$$
\Delta S = S \downarrow - S \uparrow = (1 - r\_0) \cdot S \downarrow \tag{3}
$$

For all bodies, the total incident radiation is either reflected by the body, absorbed by it or transmitted through. This is expressed by the Kirchoff's law:

$$1 = \rho\_{\lambda} + \tau\_{\lambda} + \alpha\_{\lambda} \tag{4}$$

where is the reflectivity, the transmissivity and the absorptivity. A blackbody is defined as a body that absorbs all the radiation that receives. A blackbody is a physical abstraction that does not exist in nature. To keep a body temperature constant, it should emit the same radiation that absorbs. As a consequence a property of blackbodies, the absorptivity, is equal to the emissivity, and both are equal to 1, while reflectivity and transmissivity are equal to zero.

Terrestrial materials behave more as grey bodies, meaning that part of the received radiation is reflected back to the atmosphere, or in other words, not all the energy that receives is absorbed. In order to keep the temperature constant, the absorbed radiation should equal the emission, so again emissivity is equal to absorptivity. Because the reflectivity is not zero, emissivity of real bodies is smaller than 1.

The longwave radiation terms are calculated with Planck's equation extended to real bodies. A blackbody having a kinetic temperature *T*0 [K] emits in a single wavelength a radiation that corresponds to:

$$L\_{\lambda}^{bb} = \frac{3.74 \cdot 10^8}{\lambda^5} \cdot \frac{1}{\left[ \exp\left(\frac{1.44 \cdot 10^4}{\lambda \cdot T\_0}\right) - 1 \right]}\tag{5}$$

Where *L* bb is the blackbody energy emission [W m-2 m-1] and is the wavelength [m]. The kinetic temperature is the temperature as it would be measured by a standard thermometer in contact with the surface of the body. Emissivity ελ at a chosen wavelength is the ratio of the radiation emitted by a real body at temperature *T*0 to the radiation emitted by a blackbody at the same temperature. By definition, a blackbody has a constant emissivity equal to one for all wavelengths, whereas the real emissivity varies with wavelength. For natural bodies, the thermal emission can then be written as:

$$L\_{\vec{\lambda}}(T\_0) = \varepsilon\_{\vec{\lambda}} \cdot L\_{\vec{\lambda}}^{bb}(T\_0) \tag{6}$$

Integration of *L* over all wavelengths leads to:

$$L(T\_0) \uparrow = \bigcap\_{0}^{\omega} \varepsilon\_{\lambda} \cdot L\_{\lambda}^{bb}(T\_0) \cdot d\lambda = \sigma \cdot \varepsilon\_0 \cdot T\_0^4 \tag{7}$$

where = 5.67 x10-8 W m-2 K-4 is the Stefan-Boltzmann constant and 0 is a broadband surface emissivity. A remote sensor working within a spectral range of the thermal channels measures only a portion of *L*(*T*0). The outgoing longwave radiation at any sensor channel is calculated by integration over the spectral range of the sensor:

$$L\_i^{sat}(T\_0) \uparrow = \int\_i \boldsymbol{\varepsilon}\_{\lambda} \cdot L\_{\lambda}^{bb}(T\_0) \cdot d\lambda \tag{8}$$

For all bodies, the total incident radiation is either reflected by the body, absorbed by it or

defined as a body that absorbs all the radiation that receives. A blackbody is a physical abstraction that does not exist in nature. To keep a body temperature constant, it should emit the same radiation that absorbs. As a consequence a property of blackbodies, the absorptivity, is equal to the emissivity, and both are equal to 1, while reflectivity and

Terrestrial materials behave more as grey bodies, meaning that part of the received radiation is reflected back to the atmosphere, or in other words, not all the energy that receives is absorbed. In order to keep the temperature constant, the absorbed radiation should equal the emission, so again emissivity is equal to absorptivity. Because the reflectivity is not zero,

The longwave radiation terms are calculated with Planck's equation extended to real bodies. A blackbody having a kinetic temperature *T*0 [K] emits in a single wavelength a radiation

5 4

The kinetic temperature is the temperature as it would be measured by a standard thermometer in contact with the surface of the body. Emissivity ελ at a chosen wavelength is the ratio of the radiation emitted by a real body at temperature *T*0 to the radiation emitted by a blackbody at the same temperature. By definition, a blackbody has a constant emissivity equal to one for all wavelengths, whereas the real emissivity varies with

0 0 () () *bb LT L T*

0 0 0 0

surface emissivity. A remote sensor working within a spectral range of the thermal channels measures only a portion of *L*(*T*0). The outgoing longwave radiation at any sensor channel is

0 0 () () *sat bb*

*i L T LT d*

() () *bb LT L T d T*

0

4

(7)

*T*

1.44 10 exp 1

8

bb is the blackbody energy emission [W m-2 m-1] and

wavelength. For natural bodies, the thermal emission can then be written as:

0

calculated by integration over the spectral range of the sensor:

*i*

= 5.67 x10-8 W m-2 K-4 is the Stefan-Boltzmann constant and

3.74 10 1

the transmissivity and

1

transmitted through. This is expressed by the Kirchoff's law:

*bb L*

is the reflectivity,

transmissivity are equal to zero.

that corresponds to:

Where *L*

where

emissivity of real bodies is smaller than 1.

Integration of *L* over all wavelengths leads to:

where  <sup>0</sup> *SS S r S* (1 ) (3)

(4)

the absorptivity. A blackbody is

(5)

is the wavelength [m].

(6)

(8)

0 is a broadband

The surface temperature *T*0 is retrieved from Eq (8), once the surface emissivity in the considered thermal channel is estimated. Once '*T*0' is obtained and 0 estimated*, L* is retrieved from Eq 7. Before the application of Eq (8), an atmospheric correction process is needed to derive Li sur(*T*0) at the surface, because *L*<sup>i</sup> sat(*T*0) as measured at the satellite sensor is affected by atmospheric interference. Atmospheric correction in the thermal range and in the shortwave is out of the scope of this chapter. We only mention that Li sur(*T*0) can be obtained from Li sat(*T*0) and using atmospheric correction model, in which water vapour and aerosol concentrations are the main input variables.

The incoming long wave radiation cannot be derived directly from remote sensors. It can either be determined from ground data or derived after atmospheric modelling. It varies with cloudiness (water vapour), air temperature and atmospheric constituents. For clear skies, the notion of effective thermal infrared emissivity of the atmosphere or apparent emissivity of the atmosphere ( ' *a* ) introduces an overall emission value for all constituents. If the air temperature *T*a at screen level is available, *L* is estimated as:

$$L \cdot \mathbb{L} = \sigma \cdot \boldsymbol{\varepsilon}\_a^\cdot \cdot \boldsymbol{T}\_a^4 \tag{9}$$

There are several models simple to evaluate ' *a* . The apparent emissivity of the atmosphere is usually estimated with equations based on vapour pressure and temperature at standard meteorological stations. For clear skies a common formulation, among others, is (Brutsaert, 1975):

$$
\omega\_a^\circ = \mathbf{1.24} \left( \frac{e\_a}{T\_a} \right)^{\frac{1}{7}} \tag{10}
$$

Where *T*a is the air temperature [K] and *e*a is the vapour pressure [mbar], everything measured at screen level. A portion *L* reaching the Earth surface is reflected back to the atmosphere. Since the surface is opaque the transmissivity is zero, the reflection of *L*↓ can be evaluated with Kirchoff law. As 0 describes the emissivity of a body in the thermal range, (1- 0) accounts for the reflection. The final expression for *R*n becomes:

$$R\_n = (1 - r\_o) \cdot S \stackrel{\downarrow}{\rightsquigarrow} + \varepsilon\_a^{\uparrow} \cdot \sigma \cdot T\_a^4 - (1 - \varepsilon\_0) \cdot \varepsilon\_a^{\uparrow} \cdot \sigma \cdot T\_a^4 - \varepsilon\_0 \cdot \sigma \cdot T\_0^4 \tag{11}$$

Eq. 11 is valid for instantaneous observations. The conversion to a daily value is briefly discussed in Sect 2.4.

It is not always necessary to carry out the calculations of Eqs 3-11 manually. Some organizations provide atmospherically corrected components of the radiation platforms directly. For example LandSaf (landsaf.meteo.pt) provides MeteoSat Second Generation (MSG) products of atmospherically corrected *S* and *L* with a 15 minute resolution and daily albedo for South America, Africa and Europe. An emissivity product will be released soon. Validation over ground based measurements for a site in Spain over sparse vegetation shows that these products are rather reliable (Fig 1.).

As an alternative to the use of satellite data, a computation of the radiation terms from synoptic weather stations is also possible. The recommendations by the FAO (Doorenbos and Pruitt, 1977; Allen et al., 1998) could be followed. The daily short wave radiation *S*↓day [MJm-2day-1], is measured at agrometeorological stations with pyranometers and integrated to daytime hours. In most areas in the world, only sunshine hours are measured with periheliometers. In that case, the daily incoming shortwave radiation *S*↓day can be obtained from the following empirical relationship:

$$S\_{\rm day} \cdot \downarrow = (a\_s + b\_s \cdot \frac{m}{N}) \cdot S\_{0,\rm day} \cdot \downarrow \tag{12}$$

where *a*s is the fraction of the extraterrestrial radiation reaching the ground in a complete overcast day (when *n*=0), *a*s + *b*s the fraction of the extraterrestrial radiation reaching the ground in a complete clear day (*n*=*N*), *n* the duration of bright sunshine per day [hours], *N* the total daytime length [hours], *S*0, day is the terrestrial radiation [MJm-2 day-1]. Local instrumentation can be used to calibrate *a*s and *b*s for local conditions.

Fig. 1. Comparison between MeteoSat Second Generation radiation products (symbols) with 5-minute interval ground based measurements (lines) for a pixel with sparse vegetation in central Spain, for 5 July 2010.

The net daily shortwave radiation *S*day is estimated as in Eq. (3), assuming an average daily (sun hours only) albedo *r*0day. The daily longwave radiation exchange between the surface and the atmosphere is very significant. Since on average the surface is warmer than the atmosphere and 0>a', there is usually a net loss of energy as thermal radiation from the ground. The daily net shortwave radiation *L*day [W m-2] between vegetation and soil on the one hand, and atmosphere and clouds on the other, can be represented by the following radiation law:

$$
\Delta L\_{\text{day}} = -f \cdot \varepsilon\_{a,\text{day}}^{\text{'}} \cdot \sigma \cdot \left(T\_{a,\text{mean}} + 273.15\right)^{4} \tag{13}
$$

periheliometers. In that case, the daily incoming shortwave radiation *S*↓day can be obtained

day 0,day ( ) *s s <sup>n</sup> S ab S*

where *a*s is the fraction of the extraterrestrial radiation reaching the ground in a complete overcast day (when *n*=0), *a*s + *b*s the fraction of the extraterrestrial radiation reaching the ground in a complete clear day (*n*=*N*), *n* the duration of bright sunshine per day [hours], *N* the total daytime length [hours], *S*0, day is the terrestrial radiation [MJm-2 day-1]. Local

Fig. 1. Comparison between MeteoSat Second Generation radiation products (symbols) with 5-minute interval ground based measurements (lines) for a pixel with sparse vegetation in

The net daily shortwave radiation *S*day is estimated as in Eq. (3), assuming an average daily (sun hours only) albedo *r*0day. The daily longwave radiation exchange between the surface and the atmosphere is very significant. Since on average the surface is warmer than the

ground. The daily net shortwave radiation *L*day [W m-2] between vegetation and soil on the one hand, and atmosphere and clouds on the other, can be represented by the following

day ,da ,mean ( 273.15) *Lf T ay a*

a', there is usually a net loss of energy as thermal radiation from the

(13)

' 4

instrumentation can be used to calibrate *a*s and *b*s for local conditions.

*N*

(12)

from the following empirical relationship:

central Spain, for 5 July 2010.

0>

atmosphere and

radiation law:

Where '*a*,day [-] is the daily net emissivity between the atmosphere and the ground, *f* a cloudiness factor and *T*a,mean is the mean daily air temperature at screen level [°C]. Parameter '*a,*day can be estimated from data from meteorological stations as:

$$
\stackrel{\circ}{\varepsilon\_{a,\text{day}}} = a\_{\varepsilon} + b\_{\varepsilon} \cdot \sqrt{\stackrel{\varepsilon\_{d,\text{mean}}}{10}} \tag{14}
$$

Where *a*e is a correlation coefficient (ranging from 0.34 to 0.44, with a default of 0.34), *b*e a correlation coefficient (ranging from -0.14 to –0.25 with a default of -0.14), *e*d,mean the average vapour pressure at temperature [mbar]. If true *e*d,mean is not available, then it can be calculated from daily average relative humidity *RH*mean and mean air temperature *T*a,mean [°C]:

$$e\_{d, \text{mean}} = \frac{RH\_{\text{mean}}}{100} \cdot e\_{s, \text{mean}} \text{ and } \ e\_{s, \text{mean}} = 6.108 \cdot \exp\left|\frac{17.27 \cdot T\_{\text{o,mean}}}{T\_{\text{o,mean}} + 237.15}\right|\tag{15}$$

The cloudiness factor *f* is equal to 1 in case of a perfect clear day and 0 in a complete overcast day. In case the station has solar radiation data from pyranometers *f* can be calculated as:

$$f = a\_c \cdot \frac{S \downarrow\_{\text{day}}}{S \downarrow\_{\text{clear,day}}} + b\_c \cdot \text{or} \cdot f = a\_c \cdot \frac{S \downarrow\_{\text{day}}}{(a\_s + b\_s \cdot) \cdot S\_0 \downarrow\_{\text{day}}} + b\_c \tag{16}$$

Where *as*, *bs*, *a*c and *i*c are calibration values to be estimated through specialized local studies which involve measuring longwave radiation values. Average values for *a*c and *b*c in arid and humid environments can be found in Table 1:

Table 1. Typical values the coefficients *a*c, *b*c, *a*s and *b*s for arid and humid climates (Maidment, 1992).

If only data on sunshine hours data are available, then:

$$f = \left(a\_c \cdot \frac{b\_s}{a\_s + b\_s}\right) \cdot \frac{n}{N} + \left(b\_c + \frac{a\_s}{a\_s + b\_s} \cdot a\_c\right) \tag{17}$$

#### **2.2 Sensible heat flux**

The sensible heat flux (*H*) is the exchange of heat through air as a result of a temperature gradient between the surface the atmosphere. Since the surface temperature during the day is usually higher than the air temperature, the sensible heat flux is normally directed upwards. During the night the situation may be reversed. Close to the surface, the sensible heat transport takes place mostly by diffusive processes, whereas at some distance away from the surface turbulent transport becomes more important.

The mathematical formulation of the sensible heat flux is based on the theory of mass transport of heat and momentum between the surface and the near-surface atmospheric environment (surface boundary layer). All existing remote sensing algorithms for turbulent sensible heat flux use the analogy of Ohm law of resistance driven by a gradient of temperature:

$$H = \rho\_a \cdot c\_p \cdot \frac{T\_s - T\_a}{r\_{\text{ah}}} \tag{18}$$

where a is the density of moist air [kg m-3], *c*p is the air specific heat at constant pressure [J kg-1 K-1], *r*ah is the aerodynamic resistance to heat transport between the surface and the reference level [s m-1] and *T*s – *T*a is the driving temperature gradient between the surface (with temperature *T*s) and the reference height (with temperature *T*a).

Equation 18 shows that the estimation of sensible heat flux has two main elements: a temperature difference between two heights and the corresponding resistance. As a first approximation we can conclude that the error in the sensible heat is linearly proportional to the error in the temperature gradient, and linearly proportional to the error in the inverse of the resistance. Equation 1 shows that this error (W m-2) is directly transferred to the latent heat flux. We will now show that this is only approximately true, because the equation is not linear and the aerodynamic resistance itself depends on the temperature gradient. We will show that because of this, *r*ah can only be solved iteratively.

Understanding the physical concepts involved in the calculation of sensible heat flux, and in particular the aerodynamic resistance, is essential for an evaluation of remote sensing techniques. The evaluation of *r*ah is the most complicated issue of all in the whole EBE procedure for AET estimates. It is our experience that lack of or incomplete knowledge of the entire formulation, image pre-processing and atmospheric correction processes leads to severe flaws in the intermediate and final outputs. Many researchers are still seeking for alternatives, procedures and methods to improve the accuracy of ET estimates form the EBE – RS approach. The actual parameterization is not optimal in the sense that some sensitive information can only be strictly evaluated under controlled experimental research, and not in a routine fashion.

Near the ground two phenomena take place simultaneously in the transfer of heat between the surface and the atmosphere: free convection produced by temperature gradient *T*s-*T*<sup>a</sup> and forced convection by the dragging forces of the wind. Then, the estimation of the turbulent heat fluxes requires a description of the turbulent wind profile near the surface. The starting point of the analysis is the wind profile in a neutral atmosphere (no convection, and *T*s=*T*a). In this situation and for an open site, the horizontal wind speed *u* [m s-1] varies logarithmically with height above the ground *z* [m]:

$$
\ln(z) = A \cdot \ln(z) + B \tag{19}
$$

*B* is usually replaced by *A* .ln (zom) where *z*0m is the aerodynamic roughness length of the surface for momentum transport and represents the value of *z* for which Eq 19 predicts *u*(*z*) = 0 (see also Fig 2):

$$
\mu(z) = A \cdot \ln \left( \frac{z}{z\_{0\text{m}}} \right) \tag{20}
$$

In Eq 20, *A* must have the dimension of velocity and it should be independent of *z* since the profile description is given by the logarithmic term. Over plant communities of uniform height *h*, the turbulent boundary layer behaves as if the vertically distributed elements of the community were located at a certain distance *d* from the ground. Parameter *d* is called

sensible heat flux use the analogy of Ohm law of resistance driven by a gradient of

kg-1 K-1], *r*ah is the aerodynamic resistance to heat transport between the surface and the reference level [s m-1] and *T*s – *T*a is the driving temperature gradient between the surface

Equation 18 shows that the estimation of sensible heat flux has two main elements: a temperature difference between two heights and the corresponding resistance. As a first approximation we can conclude that the error in the sensible heat is linearly proportional to the error in the temperature gradient, and linearly proportional to the error in the inverse of the resistance. Equation 1 shows that this error (W m-2) is directly transferred to the latent heat flux. We will now show that this is only approximately true, because the equation is not linear and the aerodynamic resistance itself depends on the temperature gradient. We will

Understanding the physical concepts involved in the calculation of sensible heat flux, and in particular the aerodynamic resistance, is essential for an evaluation of remote sensing techniques. The evaluation of *r*ah is the most complicated issue of all in the whole EBE procedure for AET estimates. It is our experience that lack of or incomplete knowledge of the entire formulation, image pre-processing and atmospheric correction processes leads to severe flaws in the intermediate and final outputs. Many researchers are still seeking for alternatives, procedures and methods to improve the accuracy of ET estimates form the EBE – RS approach. The actual parameterization is not optimal in the sense that some sensitive information can only be strictly evaluated under controlled experimental research, and not

Near the ground two phenomena take place simultaneously in the transfer of heat between the surface and the atmosphere: free convection produced by temperature gradient *T*s-*T*<sup>a</sup> and forced convection by the dragging forces of the wind. Then, the estimation of the turbulent heat fluxes requires a description of the turbulent wind profile near the surface. The starting point of the analysis is the wind profile in a neutral atmosphere (no convection, and *T*s=*T*a). In this situation and for an open site, the horizontal wind speed *u* [m s-1] varies

*B* is usually replaced by *A* .ln (zom) where *z*0m is the aerodynamic roughness length of the surface for momentum transport and represents the value of *z* for which Eq 19 predicts *u*(*z*)

( ) ln *<sup>z</sup> uz A*

In Eq 20, *A* must have the dimension of velocity and it should be independent of *z* since the profile description is given by the logarithmic term. Over plant communities of uniform height *h*, the turbulent boundary layer behaves as if the vertically distributed elements of the community were located at a certain distance *d* from the ground. Parameter *d* is called

0m

*z*

(with temperature *T*s) and the reference height (with temperature *T*a).

show that because of this, *r*ah can only be solved iteratively.

logarithmically with height above the ground *z* [m]:

ah *s a a p T T H c*

(18)

*uz A z B* ( ) ln( ) (19)

(20)

*r*

a is the density of moist air [kg m-3], *c*p is the air specific heat at constant pressure [J

temperature:

in a routine fashion.

= 0 (see also Fig 2):

where  the zero plane displacement or displacement height level of the flow. It acts as a correction to the level where *z*=0, and thus *z* in Eqs 19 and 20 should be directly replaced by *z*-*d* in vegetated areas:

shift *z zd* (21) <sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> 2.5 3 3.5 4 u (m s-1) ln (z)

Fig. 2. Example plot of mean wind speed *u* against ln(*z*), measured above a 31 m tall forest in The Netherlands in August 2009. The intercept with the vertical axis leads to *z*0m+*d* = 17.9 m.

The displacement height *d* is usually rather large: it ranges between 60 to 80 percent of the plant community height. Common values for well developed wheat are found in Verma and Bartfield (1979). A relation *d*= 0.67*h* is usually adopted for other vegetation types (Allen et al., 1998). An exact estimation can be carried out when a wind speed measurements at three or more heights are available.  Strictly speaking, *d* also depends on plant density; for sparse vegetation, *d* is often neglected. In many occasions, insufficient data are available to accurately predict its values for discrete crop canopies (Verma and Bartfield, 1979). If no valid field data are present, then it is suggested to leave *d* out of the equations altogether.

The logarithmic wind profile in neutral conditions forms the basis for calculating the aerodynamic resistance for heat transport (and transport of water vapour) by mechanical turbulence. To include thermal turbulence (or convection or buoyancy), the Monin-Obukhov theory is needed in addition (Obukhov, 1946). We will now summarize the equations leading to the aerodynamic resistance of mechanical transport, followed by the modification for non-neutral conditions, when convection plays a role.

The transfer of momentum in the direction of the flux takes place through molecular and turbulent eddy activity. Random vertical movements of the air cause air with different horizontal wind speeds to mix. This causes a momentum sink at the surface in a form of shear stress, . For convenience the shear stress is expressed as a function of a scalar *u*\*, usually called eddy velocity or friction velocity [m s-1]:

$$
\pi = \rho\_d \mu\_\*^2 \tag{22}
$$

Since wind is produced by turbulent eddy motion, it is postulated that *A* in Eq 20 is proportional to the speed of the internal eddies. Then it can be demonstrated that:

$$A = \frac{\mu\_\*}{k} \tag{23}$$

Where *k* is Von Kármán's constant, experimentally found to be 0.41. The final expression of the wind profile under neutral atmosphere is:

$$
\mu(z) = \frac{\mu\_\*}{k} \cdot \ln\left(\frac{z}{z\_{0\text{m}}}\right) \tag{24}
$$

Then the gradient of wind speed with height can be expressed as:

$$\frac{d\mathbf{u}}{dz} = \frac{\mathbf{u} \cdot \mathbf{s}}{k \cdot z} \tag{25}$$

In the theory of estimating the aerodynamic resistance from the wind profile, only vertical transport is considered. In the atmosphere the steepest gradients of heat, wind speed and humidity are found in the vertical direction. Horizontal variation is present in the order of tens of kilometres (Brutsaert, 2005), but these are considered negligible. This implies that horizontal advection effects (for example between pixels) are not considered in the remote sensing approach, a serious restrictions in patchy (wet and dry) environments.

In analogy to horizontal wind speed, heat and water vapour also have vertical profiles near the surface. Vertical mixing then causes a transport of heat and vapour too, resulting in vertical fluxes of sensible and latent heat. The three fluxes, of momentum (*F*u), heat (*F*h) and vapour (*F*v), can be expressed as the covariance of vertical wind speed (*w*') and concentration of the admixture (*u*', *T*' and *q*'):

$$\begin{aligned} F\_u &\equiv -\tau = \rho \cdot \overline{w' \cdot u'}\\ F\_h &\equiv -H = \rho \cdot c\_p \cdot \overline{w' \cdot T'}\\ F\_v &\equiv -\lambda E = \rho \cdot \overline{w' \cdot q'} \end{aligned} \tag{26}$$

These equations can be linked with the approach of electrical analogy (Eq 18) by approximating the covariance to simply the product of the vertical gradient of the quantities at two different heights (Brutsaert, 2005). A dimensionless parameter *C* is needed to fit the equality. This can be done for all three quantities. For example, for heat:

$$
\overline{w' \cdot T'} = \mathcal{C}\_h \cdot \left(\overline{\mu\_2} - \overline{\mu\_1}\right) \cdot \left(\overline{T\_4} - \overline{T\_3}\right) \tag{27}
$$

In this case, *Ch* will depend on the heights 1, 2, 3 and 4. It is convenient to choose the heights 4 and 3 equal to 2 and 1:

$$\overline{w' \cdot T'} = \mathbb{C}\_h \cdot \left(\overline{u\_2} - \overline{u\_1}\right) \cdot \left(\overline{T\_2} - \overline{T\_1}\right) \tag{28}$$

Similarly, for momentum transport (shear stress):

$$
\overline{uw'u'} = \mathbb{C}\_d \cdot \left(\overline{\mu\_2} - \overline{\mu\_1}\right)^2 \tag{29}
$$

The coefficient *Cd* can be calculated by combining Eqs 22, 24, 26 and 29. Using *z*1=*z*0m, and considering that at *z*= *z*0m , the wind speed is zero:

*<sup>u</sup>*\* *<sup>A</sup>*

Where *k* is Von Kármán's constant, experimentally found to be 0.41. The final expression of

\*

*u z*

sensing approach, a serious restrictions in patchy (wet and dry) environments.

*u*

*v*

equality. This can be done for all three quantities. For example, for heat:

*h p*

These equations can be linked with the approach of electrical analogy (Eq 18) by approximating the covariance to simply the product of the vertical gradient of the quantities at two different heights (Brutsaert, 2005). A dimensionless parameter *C* is needed to fit the

In this case, *Ch* will depend on the heights 1, 2, 3 and 4. It is convenient to choose the heights

The coefficient *Cd* can be calculated by combining Eqs 22, 24, 26 and 29. Using *z*1=*z*0m, and

2

*F wu F H c wT F E wq*

Then the gradient of wind speed with height can be expressed as:

( ) ln *u z*

\* *du u*

In the theory of estimating the aerodynamic resistance from the wind profile, only vertical transport is considered. In the atmosphere the steepest gradients of heat, wind speed and humidity are found in the vertical direction. Horizontal variation is present in the order of tens of kilometres (Brutsaert, 2005), but these are considered negligible. This implies that horizontal advection effects (for example between pixels) are not considered in the remote

In analogy to horizontal wind speed, heat and water vapour also have vertical profiles near the surface. Vertical mixing then causes a transport of heat and vapour too, resulting in vertical fluxes of sensible and latent heat. The three fluxes, of momentum (*F*u), heat (*F*h) and vapour (*F*v), can be expressed as the covariance of vertical wind speed (*w*') and

' '

' '

' '

*wT C u u T T* ' ' *<sup>h</sup>* 21 43 (27)

*wT C u u T T* ' ' *<sup>h</sup>* 21 21 (28)

2 1 ' ' *wu C u u <sup>d</sup>* (29)

*k z*

0m

the wind profile under neutral atmosphere is:

concentration of the admixture (*u*', *T*' and *q*'):

Similarly, for momentum transport (shear stress):

considering that at *z*= *z*0m , the wind speed is zero:

4 and 3 equal to 2 and 1:

*<sup>k</sup>* (23)

*dz k z* (25)

(24)

(26)

$$\mathbf{C}\_d = \left[ k \sqrt{\ln \left( \frac{z\_2}{z\_{0\text{m}}} \right)} \right]^2 \tag{30}$$

In neutral conditions it can be assumed that *C*h=*C*v=*C*d, and thus:

$$H = -\rho \cdot c\_p \mathbb{C}\_d \cdot \mu\_2 \cdot \left(\overline{T\_2} - \overline{T(z\_{0m})}\right) \tag{31}$$

The appearance of the average temperature at height *z*0m in Eq 31 is inconvenient. It can be eliminated by assuming a logarithmic wind profile for temperature too, by defining a scalar roughness height for heat transfer *z*0h at which the extrapolated temperature profile fitted through *T*2 and 0 *T z*( ) *<sup>m</sup>* becomes *T*0, i.e. the kinematic surface temperature. Using this we finally express the aerodynamic resistance *rah* in neutral conditions as:

$$r\_{\rm ah} = \frac{\ln\left(\frac{z\_2}{z\_{0\rm m}}\right)\ln\left(\frac{z\_2}{z\_{0\rm h}}\right)}{k^2 \cdot \nu} = \frac{\ln\left(\frac{z\_2}{z\_{0\rm h}}\right)}{k\nu\_\*}\tag{32}$$

The roughness height, *z*0h, changes with surface characteristics, atmospheric flow and thermal dynamic state of the surface (Blümel, 1999; Massman, 1999). It can be shown that:

$$z\_{0h} = z\_{0m} \;/\exp\left(kB^{-1}\right) \tag{33}$$

where *B*-1 is the inverse Stanton number, a dimensionless heat transfer coefficient.

Free convection might alter the forced convective eddies generated by wind turbulence. During daytime or when temperature decreases with height, convection amplifies the vertical eddy motions (unstable condition). During the night or when inversion conditions occur, and temperature increases with height, the horizontal eddy motions are enhanced (stable conditions).

Mechanical turbulence and buoyancy coexists in a form of a hybrid regime known as mixconvection. Monin and Obukhov showed that these conditions eventually lead to an alteration of the wind and temperature profiles (Brutsaert, 1982). The Monin-Obukhov similarity theory uses dimensional analysis to correct the wind profile produced by buoyancy effects in such conditions. A non-dimensional correction factor for momentum transfer m() is introduced to correct the wind profile gradient for conditions different from neutral, in which is the ratio of thermal to mechanical turbulence:

$$\frac{du}{dz} = \frac{u\_\*}{kz} \cdot \varphi\_m\left(\xi\right) \tag{34}$$

They introduced semi-empirical functions to correct the wind profile depending on the stability, based on dimensional analysis, of the form:

$$
\mu\_\* = \frac{\overline{u(z)}}{k} \cdot \left[ \ln \left( \frac{z - d\_0}{z\_{0\text{m}}} \right) - \Psi\_m \left( \frac{z - d\_0}{L} \right) + \Psi\_m \left( \frac{z\_{0\text{m}}}{L} \right) \right] \tag{35}
$$

$$H = \frac{T\_s - \overline{T(z)}}{k \cdot \mu\_\* \cdot \rho \cdot c\_p} \cdot \left[ \ln \left( \frac{z - d\_0}{z\_{0\text{h}}} \right) - \Psi\_h \left( \frac{z - d\_0}{L} \right) + \Psi\_h \left( \frac{z\_{0\text{h}}}{L} \right) \right] \tag{36}$$

Where *L* is defined as the Monin-Obukhov length (*L* = *z* ) [m], calculated as:

$$L = -\frac{\rho\_a \cdot \mathbb{C}\_p \cdot u\_\*^{\overline{3}} \cdot T(z)}{k \cdot \mathbb{g} \cdot H} \tag{37}$$

Where *g* is the gravity constant (9.81 m s-2). Semi-empirical expressions for the stability corrections *<sup>h</sup>* and *m* can be found in the literature, for example Paulson (1970) and Brutsaert (1982). It is important to realize that *L* depends on air temperature and sensible heat flux, while sensible heat flux and air temperature in turn depend on *L*. For this reason, an iterative procedure is needed to calculate *L*, *u\** and *H* using Eqs 35-37.

#### **2.3 Ground heat flux**

The ground heat flux has received relatively little attention compared to the other terms. This is often justified, because ground heat flux is usually the smallest of all terms. Moreover, the 24-hour sum of ground heat flux is close to zero, because the heat absorbed during the day is released during the night.