• agrometeorology;
  • Alps;
  • dew-point temperature


  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Unlike precipitation and temperature, humidity is not widely measured, fostering the development of algorithms that simulate air humidity using other measures. In humid temperate climates, atmospheric water vapour close to the ground often reaches saturation around the time of minimum temperature. This allows models of daily maximum dew-point temperature to be built from minimum air temperatures. Once the dew-point temperature has been estimated, hourly values can be interpolated by assuming that water content in the air remains unchanged during the day, relative humidity being the result of the modulation of air temperature on vapour pressure at saturation. This approach requires certain corrections in order to take into account seasonal and local features. The present work investigated and tested the application of algorithms to simulate relative humidity from minimum daily temperatures in 23 meteorological stations in an Italian alpine region. The basic model is corrected by decreasing dew-point temperature using temperature and precipitation measures, and also requires specific calibration. With respect to errors in the number of hours with high relative humidity, major biases may be generated at some sites. After correction, the number of sites where these techniques yield acceptable results ranges from about a quarter to a half of the total, the lower figure reflecting a stricter acceptance standard in the driest years. The simulation algorithms yield useful results for stations where site-specific calibration can be carried out, encouraging the use of simulated series from selected sites for climatic, meteorological and phytopathological modelling. Copyright © 2011 Royal Meteorological Society

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Relative humidity (RH) is a key factor in several aspects of the modelling of the atmospheric boundary layer. Measures of atmospheric humidity were included in Penman's original formulation of evapotranspiration (Penman, 1948), in the Food and Agriculture Organization's (FAO) reformulation of it for adoption as standard (Doorenbos and Pruitt, 1977) and again in the more advanced version known as the ‘Penman–Monteith method’(Allen et al., 1998).

Extensive use of RH can be found in simulation models of plant-pathogen interaction: humidity measures often serve as a substitute for a less common measure, that of leaf wetness duration (Sutton et al., 1984; Friesland and Schrödter, 1988; Huber and Gillespie, 1992; Hamada et al., 2008; Sentelhas et al., 2008; Kim et al., 2010). Important examples regard grapevine, a particularly valuable crop, where many efforts have been made to model downy mildew—Plasmopara viticola. Rossi and Caffi (2007) highlighted the role of humidity in oospore germination, and Hill (2000) and Rossi et al. (2008) have proposed models for downy mildew which make use of daily and hourly relative humidity, respectively. There has been interest in analysing the impacts of climate change on this pathogen, with future scenarios assumed only on the basis of climatic projections of temperature and precipitation (Salinari et al., 2006, 2007). Botrytis bunch rot caused by Botrytis cinerea Pers.:Fr. is one of the world's most destructive vine diseases and may cause severe losses when conditions are favourable to it. Infection models based on weather data have been developed for predicting disease risk (Broome et al., 1995) and to assess optimal timing of fungicide treatments in order to adequately control the disease. In the case of Botrytis bunch rot, disease risk is a function of wetness duration and temperature during the susceptible stages of grapevine growth. Therefore, changes in the climate, and especially in atmospheric humidity, may have a significant effect on this pathogen and possible future scenarios are of considerable interest to plant-pathogen modellers.

Climatic projections of atmospheric humidity are still difficult to make. Climatic downscaling of ground-level atmospheric humidity remains a challenge, given the many problems in processing atmospheric humidity measures close to the ground: the relatively sparse distribution of measurement sites, the generally limited length of series, the sensitivity of instruments to systematic biases (Fleming, 1998), insufficient attention to data quality, due also to the presence or succession of different measurement methods and standards (van Wijngaarden and Vincent, 2003) and, finally, the presence of local features that enhance microclimatic effects. Huth (2005) analysed the potential of direct climatic downscaling of humidity from the output of general circulation models (GCM) and detected the best atmospheric predictors of models, mainly atmospheric humidity fields aloft, but also stressed the limitations of such techniques (the variance explained by predictors did not exceed 65% for the best-performing humidity indices).

An alternative method of direct downscaling of atmospheric humidity is with humidity simulation models based on temperature and precipitation, the most commonly measured and investigated atmospheric variables, particularly in climate projections. This approach is also suitable for applications other than climate prognosis. In humid climates, such as the Alpine region, and more generally a large part of the temperate regions of middle latitudes, a reasonable hypothesis is that water vapour approaches saturation in the atmospheric layer closest to the ground at about the time of minimum night-time temperature. This is the basis of a methodology, developed in this work, aimed at simulating daily values of dew-point temperature from which the relevant hourly values of relative humidity can be calculated when hourly temperature values are known. The success of this algorithm may open the way to model applications requiring humidity values in absence of their direct measurement. This is especially the case with climate projections, in which, as already mentioned, straightforward downscaling techniques are rarely used for humidity, whereas simulations of future temperature and precipitation series are common. The objective of the present work is to assess the performance of a model simulating relative atmospheric humidity using minimum daily temperature and which includes corrections to the original algorithm that take into consideration the meteorological conditions affecting air humidity. The presence of a fairly dense network of stations in a limited area provides a good opportunity to test the ability of the proposed algorithms to represent relative humidity over an agricultural area, to highlight problems, and to infer possible performance patterns in relation to site-specific climatic features, with a view also to its possible use in climate prognosis.

2. Materials and methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

2.1. Geographic and climatic features of the target areas

The study area is in Trentino, a region in the eastern-central Italian Alps (Figure 1) which encompasses various climatic areas. This mountainous region contains a system of valleys converging on the largest and longest—the Adige Valley. The latter is often deep and has a flat bottom formed by alluvia from the River Adige. It slopes gently down to the Po valley, with an elevation decrease of about 50 m in 65 km.

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Figure 1. Location of the study area and the weather stations

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In general, Trentino has a humid, temperate, oceanic climate, particularly in the pre-alpine areas. Inner valleys have a cooler, drier and more continental-alpine climate. Precipitation is distributed over two maxima, in autumn (main) and in spring (secondary), although in some mountain areas rainfall peaks in the summer (Eccel and Saibanti, 2007).

2.2. Meteorological measures

Twenty three stations in Trentino were chosen for this study (Table I and Figure 1). They were all located in agricultural areas, for two reasons: the agrometeorological network is the only one in the area able to provide series of relative humidity of the required length, and the focus of the present work is mainly on simulations for use in plant pathology models. All stations measure temperature, precipitation and relative humidity at 1.5 m from the ground (Vaisala HMP45A Pt1000 thermometer and capacitive hygrometer, SIAP rain gauge UM7525). Hygrometer accuracy is ± 2% RH up to 90% and ± 3% RH for RH > 90%. Thermometer accuracy is ± 0.2 °C (at 20 °C). Maintenance is currently being carried out on sensors. However, a rather quick drift is a common feature of capacitive hygrometers. An overall survey of the network involved calibration with a hygrostatic chamber, which showed that instruments had a good response in the range 20 to 70–80%. Lower values were not often obtained, while there were some difficulties with a number of the instruments in correctly recording humidity values higher than 80%, including saturation. This led to the adoption of an automatic correction algorithm, which took the highest value obtained in the previous 6 months and set this value as saturation (100%). The auto-calibration algorithm applies a linear correction ranging from 0% (at measures = 70%) to the value necessary to reach 100% (at the highest measures actually recorded by the instrument).

Table I. Meteorological stations, their elevations, morphology, and aspect of the sites
Station IDNameElevation (m a.s.l.)MorphologyAspect
27S. Michele797Valley bottom
28Borgo V419Valley bottom
29Arco83Valley bottom
30Ala160Valley bottom
31Cles652Hill sideSE
32Trento Sud185Valley bottom
44Cembra548Hill sideSE
45Mezzocorona216Valley bottom
46Cognola344Hill sideSSW
48Pedersano462Hill sideESE
49Mori190Hill sideE
50Besagno379Hill sideNE
51Avio137Valley bottom
54Dro117Valley bottom
57Roveré d. Luna208Valley bottom
59Aldeno180Hill sideE
61Volano176Valley bottom
62Loppio213Valley bottom
63Serravalle150Valley bottom
64Marco159Valley bottom
65Mama d'Avio124Valley bottom
76Gardolo197Valley bottom
77Besenello190Valley bottom

A preliminary quality check on the meteorological data allowed deletion of individual wrong measures and to select a homogeneous period of measures (2001–2009). The number of sites, 23, resulted from a selection of instrumental series, which led to the exclusion of some stations from a more numerous, earlier group.

2.3. Models

2.3.1. Estimation of dew-point temperature

In order to estimate relative humidity from minimum air temperatures, two initial general assumptions are made:

  • 1.
    minimum temperature is a first-guess estimate of dew temperature;
  • 2.
    correction to this first-guess estimate can be carried out depending on either the presence/absence of precipitation or the water balance of the previous days.

Neither of the two statements above has general validity, but the proposed algorithm assumes that air humidity can be estimated with the simple measures of temperature and precipitation, those most commonly taken at weather stations.

Relative humidity can be expressed as the ratio between actual water vapour and saturation vapour, which is, in turn, a pure function of temperature:

  • equation image(1)

where e = actual water vapour pressure and es = saturation water vapour pressure. The latter can be calculated by a common empirical interpolation function (see, e.g., WMO, 1979; Holbo, 1981):

  • equation image(2)

It follows from the above-mentioned assumption 1 that when temperature is at its daily minimum (Tn) water vapour is saturated, that is, the temperature reaches dew point (Td):

  • equation image(3)

For humid temperate climates, as in Alpine agricultural areas, this is often an acceptable approximation under clear sky conditions with winds absent or light and, of course, in the case of ongoing or recent precipitation episodes. In such cases, the night-time decrease in temperature is slowed down after saturation has been reached, because of the release of latent heat following condensation. This is not the case during dry periods or cloudy or overcast nights with no recent rainfall, nor in the presence of wind.

2.3.2. Methodological procedures for Td correction

Td is a versatile measure of atmospheric humidity (Robinson, 1988; Gaffen and Ross, 1999). Nevertheless, converting humidity rates from one measure to another may give rise to errors, especially when these rates are low (New et al., 1999, 2002; Lin and Hubbard, 2004). The assumption of Equation (3) itself gives rise to a systematic positive bias in Td. This work considers, develops and compares two correction methods proposed in the literature, both of which decrease Td: one is the method proposed by the Numerical Terradynamic Simulation Group at the University of Montana ( in their MTCLIM model, the other is derived from a suggestion made in the FAO ‘Irrigation and Drainage Paper’.

Sboarina and Cescatti (2004) applied the MTCLIM model to a spatial interpolation of climatic data in Trentino, using series collected from the same area as the present study. Some of these series have been used in the present study. In this model, the corrected dew-point temperature (Td)MTCLIM is calculated by subtracting a temperature-dependent term from Tn, calibrated for every station:

  • equation image(4)

where k is the calibration coefficient, and Tday is the estimate of diurnal temperature, calculated from maximum (Tx) and mean (Tmean) daily temperatures:

  • equation image(5)

Tday can be interpreted as a weighted mean of maximum and mean temperature, where the weights are 0.45 and 0.55, respectively. The coefficient k in Equation (4) accounts for the site-specific tendency for relative humidity to remain below 100%.

The second correction method originates from the adjustments suggested by the FAO (Allen et al., 1998—Annex 6) for calculating evapotranspiration at sites where the meteorological conditions are often arid, preventing Tn from lowering to Td. FAO Paper 56 suggests leaving the Equation (3) unaltered for humid and sub-humid climates, and introducing a correction of − 2 °C to Td for arid and semi-arid climates. This is a straightforward but rather crude method, designed for water balance calculations. Nevertheless, it suggests a link between the local source of humidity in the soil and its availability for evaporation, and where this is the case, condensation in the air. As the climate in the study area is classifiable as ‘humid’, the original formulation of the algorithm would not require any correction to Td. On the other hand, preliminary inspection ascertained that correction is necessary to represent properly humidity conditions in the target area, especially if the high-humidity hourly band is to be correctly simulated.

2.3.3. Proposed improvements to the model

The MTCLIM algorithm suggests coefficients for generally decreasing Td. Because the presence of rainfall generally leads to vapour saturation, and given that rainfall has a typically seasonal pattern, an attempt to improve the correction skill was made by calibrating k by month and by wet/dry days separately, a wet day being one with a recorded rainfall of at least 1 mm. Extension of the classification ‘wet’ to the day following precipitation was also considered, given that maximum humidity is often reached in the early hours of the day. Model skill was also evaluated in absence of site-specific calibration in order to simulate the case where no calibration is possible (stations with no humidity measures) by averaging the coefficients over all stations and applying them to individual sites. Post-processing derived from the MTCLIM model will be referred to as ‘MTCLIM correction’.

Concerning the FAO approach to the correction of Td, this was carried out for ‘temporarily non-humid’ conditions, giving the term a meteorological, rather than a climatological value. The occurrence of conditions for applying a correction was set as a function of a simple ‘drought daily index’ Id, given by:

  • equation image(6)

where i is the day, Z is the period (days) of calculation of Id, P is the amount of precipitation and ETr is the reference evapotranspiration calculated by Hargreaves' formula (Allen et al., 1998):

  • equation image(7)

where Rg0 is the extra-atmospheric radiation and L is the latent heat of vapourization. Rg0 values were calculated on a monthly basis and considered equal for all the stations, given the short distances between them.

The daily differences measured between Tn and Td (a raw bias) were correlated with Id for every station. To devise an analytical formulation of this link, the fits of two types of curves were tested: first and second degree, each assessed for a variable length of the period of calculation of Id (from 6 to 30 days). The curves were forced to yield null corrections when Id ≥ 3. This approach also yields a corrected value of Td, expressed as an Id-dependent decrease of Tn:

  • equation image(8)

Post-processing according to FAO's suggestions will be referred to as the ‘FAO correction’.

The result of the correction of Td, whether calculated by Equation (4) or by Equation (8), is that e values are lower, since Equation (2) is calculated with a lower temperature than Tn. Equation (1) then yields the daily maximum, corrected, values of RH.

2.3.4. Production of hourly values of relative humidity

There is a third hypothesis regarding hourly interpolation of relative humidity: values within a day result from changes in temperature only, and not from changes in the absolute moisture content of air. That is, relative humidity is the result of the change in the saturation vapour pressure es and not in vapour pressure e, which is a reasonable assumption. In the USA, Gaffen and Ross (1999) found that, on average, Td differs by about 0.5 K between day and night. The same assumption is made for arid and semi-arid climates in the models presented by Castellví et al. (1996), who proposed corrections for the warmest hours. From Equation (1), vapour pressure e can be calculated as:

  • equation image(9)

The vapour saturation value es changes according to the daily modulation of temperature (Equation (2)), and the application of Equation (1) gives back the value of relative humidity for every hour of the day. Because the maximum values of humidity correspond to the lowest temperatures in the day, normally occurring in the earliest hours, an option was considered to split the hourly interpolation of humidity within a day in two, with the aim of keeping the range of hours that are interpolated from a constant, daily value of e as close as possible to the time of calculation (about 0600 h). The hourly interpolations were therefore made in two different ways: with e values constant from 0000 to 2400 h of the current day, or from 1800 h of the previous day to 1800 h of the current day.

2.3.5. Assessment of the models

Several error metrics were considered to take into account the different aspects of the interpolation algorithms. Errors were calculated for both daily and hourly applications. Daily errors included:

  • mean error (bias) on both maximum and minimum daily relative humidity values;

  • standard deviation on both maximum and minimum daily relative humidity values, and,

  • Root-Mean-Squared Errors (RMSE) on both maximum and minimum daily relative humidity values, also splitting the series into ‘wet’ and ‘dry’ days.

All these data took into account several options: either the ‘raw’ model (assuming Tn = Td with no corrections) or the model with ‘MTCLIM corrections’ or ‘FAO corrections’, either average or site-specific calibration of the correction coefficient k (Equation (4)), considering the day after rainfall as either ‘wet’ or ‘not wet’, and either for the whole year or for the ‘summer’ period only (May to August). Particular attention was paid to the latter period of the year, when vegetation is in its full developmental stage. In these months grape vines are especially prone to attacks of pathogens, such as Botrytis cinerea.

The choice of the best model can, in fact, change according to purpose, so that the uncorrected (‘raw’) model may behave better than a corrected model under certain conditions, e.g. on wet days, while the contrary is true for dry days. Knowing that for many phytopathological applications (Gleason et al., 1994; Rao et al., 1998; Sentelhas et al., 2004, 2008; Wichink Kruit et al., 2004) the relevant requirement for a model is the number of hours with relative humidity above a minimum threshold, the error in the hourly simulated values was also calculated, that is, for ‘very humid’ hours (values ≥ 90%) or ‘not very humid’ hours (values ⩽55%). The availability of hourly errors allows more indices to be assessed, namely the percentages of errors in the number of hours above a fixed threshold, which is the discriminatory information used in many models of grapevine infection. Hourly errors were calculated according to different scenarios:

  • according to the ‘raw’ model (assuming that Td = Tn), or according to the ‘MTCLIM’ or ‘FAO’ corrections for Td, or to averages of the ‘raw’ model with both types of correction;

  • for the whole year or for the critical season (May to August), and,

  • with reference to either all the hours, or to the ‘very humid’ hours only, or to the ‘not very humid’ hours only.

To calculate hourly errors, a ‘leave-one-out’ cross-validation was carried out on years, which involved building as many models as years of the series (9) and leaving out 1 year in each turn. Errors were calculated for each model on the excluded year, yielding nine matrices of errors. This approach allowed consideration of errors in single years and extraction of some statistics, such as mean annual errors or highest absolute values over the cross-validation years.

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Selection of the possible model options in the humidity simulation was made on the basis of the daily series, with the poorly performing options dropped in the subsequent hourly simulations. Table II reports the performance of the ‘raw’model (no corrections on Td) in terms of errors. A preliminary calculation was made on the number of cases where air attained saturation (allowing a 3% bias corresponding to sensor precision). On average, this condition is satisfied in about 21% of the daily cases, with seasonal differences: the maximum is in autumn (35%), the minimum in spring (only 13%). There are also large differences between stations. This first result alone demonstrates the necessity for correction and also for a site-specific evaluation of the goodness of the ‘raw’ model.

Table II. Performance of the ‘raw’ model (no correction implemented on Td)
 Mean75th percentileMax
  1. ‘ME’, mean error; ‘SD’, standard deviation; ‘RMSE’, Root-mean-squared error; ‘RH max’ (‘RH min’), error refers to the maximum (minimum) daily value of RH; ‘Wet days’, ‘Dry days’, days with rainfall ≥ 1 mm or < 1 mm, respectively.

  2. Reference period: May to August. All figures in %RH.

  3. Statistics over the stations: means, 75th percentile values and maximum values.

ME—RH max12.015.020.1
SD—RH max9.310.413.2
ME—RH min8.310.615.7
SD—RH min7.98.49.0
RMSE—RH max15.218.323.2
Wet days only7.29.211.2
Dry days only17.420.826.5
RMSE—RH min11.613.018.0
Wet days only10.611.515.7
Dry days only12.013.618.8

Table II and the following tables summarize the errors calculated over the 23 stations: the mean, the 75th percentile and the maximum over stations (conversely, the 25th percentile and the minimum if errors are negative). The mean error on the maximum daily values of RH is 12%, the maximum is 20%. Obviously, the raw model systematically overestimates maximum humidity by assuming daily attainment of atmospheric saturation. Errors in minimum daily values are considerably lower, as are their standard deviations. Another general outcome is that errors are higher on dry days than on wet (rainy) days when air humidity is generally higher.

There were no evident improvements when the option of considering the day following a rainy one as ‘wet’ was implemented, so the simplest option was chosen for subsequent simulations (days were considered wet only if precipitation ≥ 1 mm).

Table III reports the performances of the two correction methods for Td when the corrections are applied with both site-specific calibration and with calibration values averaged over all the sites. In the former case, the calibration trial must be carried out on every single meteorological station where a simulation will be carried out, while in the latter case it is necessary only for sites where no humidity record is specifically available. This is commonly the case with sites where only temperature and precipitation but not direct air humidity measurements are taken. As expected, the mean error is similar in the two cases (especially with the ‘FAO’ correction). When the models are applied in site-specific mode, the ‘FAO’ correction seems to perform slightly better than the ‘MTCLIM’, at least in some cases.

Table III. Performance of correction models (‘FAO’ and ‘MTCLIM’) of RH, according to the type of estimation of correction coefficients (site-specific vs. averages over the sites)
 Site-specific correctionsAverage corrections
 Mean75th (25th) percentileMax (min)Mean75th (25th) percentileMax (min)
  1. ‘ME’, mean error; ‘SD’, standard deviation; ‘RMSE’, Root-mean-squared error;

  2. ‘RH max’ (‘RH min’), error refers to the maximum (minimum) daily value of RH;

  3. ‘corr. FAO’, ‘corr. MTCLIM’: type of correction on Td.

  4. Reference period: May to August. All figures in %RH.

  5. Statistics over the stations: means, 75th percentiles (when mean values are negative: 25th percentiles) and maxima (when mean values are negative: minima).

ME—RH max—corr. MTCLIM− 1.2− 1.5− 2.7− 1.7− 4.9− 11.2
SD—RH max—corr. MTCLIM8.69.712.59.29.812.2
ME—RH max—corr. FAO− 0.2− 0.3− 0.4− 0.3− 3.1− 8.1
SD—RH max—corr. FAO8.08.810.68.38.810.6
ME—RH min—corr. MTCLIM2.
SD—RH min—corr. MTCLIM8.
ME—RH min—corr. FAO2.
SD—RH min—corr. FAO7.
RMSE—RH max—corr. MTCLIM8.79.712.810.612.214.5
 Wet days only4.
 Dry days only9.911.114.612.114.116.7
RMSE—RH max—corr. FAO8.08.810.69.510.312.4
 Wet days only4.
 Dry days only9.09.912.010.811.814.2
RMSE—RH min—corr. MTCLIM8.48.910.
 Wet days only8.
 Dry days only8.28.710.
RMSE—RH min—corr. FAO8.
 Wet days only8.
 Dry days only8.

Two examples of hourly simulation of relative humidity according to the two correction models are given in Figures 2 and 3. While the first represents a trend typical for the summer period, the second highlights the potential effects of underestimating the number of ‘very humid’ hours due to the occurrence of periods in which atmospheric humidity is above the 90% threshold, while hourly generation of values from the daily (constant) simulated Td leads to a shorter ‘very humid’ period during the day.

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Figure 2. Example of relative humidity simulation, station no. 77, 3–8 July 2007. Thick solid line: measures. Thin solid grey line: ‘raw model’ simulation. Thin dotted grey line: ‘MTCLIM’ corrected model averaged with ‘raw model’. The 90% relative humidity line is marked

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Figure 3. Measured (solid black) and simulated (dotted grey) values of relative humidity during a sample period. Station no. 76, 24–28 August 2006

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Hourly validation of the models gave some interesting indications. In this case, the stricter results of cross-validation are given. With its two alternative corrections, the model apparently functions properly, even though non-negligible biases were found in the estimation of minimum values of humidity in the case of the ‘raw model’, and in the estimation of maximum values in the case of the ‘MTCLIM’ and ‘FAO’ corrected models (Table IV). Corrections seem to improve the estimates of mean values, but not the maximum or minimum daily values, but the most interesting results come from the evaluation of errors in the number of hours above a high threshold of 90%. Although errors in the maximum values seem under control, especially in the ‘raw model’, the number of hours above the threshold is considerably overestimated. On the other hand, the corrected models, which act by decreasing the daily value of Td, both show highly negative biases. To counterbalance this behaviour, two averaged models were considered, where Td is the result of the average of the ‘raw’ model and either the ‘MTCLIM’ or ‘FAO’ corrected models. The result is positive, with negligible mean errors. Results for the error indices based on the number of hours exceeding the threshold value of 90% are shown in Table V. Both corrections are able to bring the mean errors in hours down to extremely low values. Nevertheless, figures close to zero are the result of averages of single values which may be high, as can be seen from the column reporting the maximum errors in the cross-validation years. Boxplots of errors for every station (Figure 4, for both averaged corrected models) highlight how the error scattering at some stations is much larger than at others.

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Figure 4. Errors in the number of very humid hours (RH > 90%). Error bands ± 10% and ± 30% are drawn. Stations with errors within the two bands (respectively, mean and IQR) are marked. (a) Average (‘raw model’—‘MTCLIM’ correction). (b) Average (‘raw model’—‘FAO’ correction)

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Table IV. Crossvalidation errors (% RH) for hourly models (‘raw’, ‘FAO’, and ‘MTCLIM’ corrections)
 Mean on crossvalidation years 2001–2009Maximum on crossvalidation years 2001–2009
 Mean75th (25th) percentileMax (min)Mean75th (25th) percentileMax (min)
  1. ‘Raw’, no corrections implemented on Td; ‘corr. FAO’, ‘corr. MTCLIM’ type of correction on Td;

  2. ‘RH [UPWARDS ARROW]’ (‘RH [DOWNWARDS ARROW]’): only records with relative humidity ≥ 90% (⩽55%), respectively.

  3. Statistics over the stations: means, 75th percentiles (when mean values are negative: 25th percentiles) and maxima (when mean values are negative: minima).

Mean error—all year      
Corr. FAO− 2.1− 2.9− 5.5− 4.1− 5.4− 8.6
Corr. MTCLIM0.
Raw—RH [UPWARDS ARROW]− 2.6− 3.5− 5.0− 3.5− 4.2− 6.6
Corr. FAO—RH [UPWARDS ARROW]− 10.2− 10.8− 11.6− 11.6− 12.4− 14.1
Corr. MTCLIM—RH [UPWARDS ARROW]− 9.3− 9.9− 12.5− 12.2− 13.1− 18.0
Raw—RH [DOWNWARDS ARROW]15.617.224.119.321.335.2
Corr. MTCLIM—RH [DOWNWARDS ARROW]8.510.111.812.112.626.8
Mean error—May to August      
Corr. FAO− 1.0− 1.6− 4.6− 4.0− 5.9− 7.3
Corr. MTCLIM− 0.7− 1.2− 4.7− 1.9− 4.8− 8.1
Raw—RH [UPWARDS ARROW]− 1.1− 2.4− 3.4− 1.8− 4.0− 5.0
Corr. FAO—RH [UPWARDS ARROW]− 9.3− 10.2− 11.0− 11.4− 12.6− 13.8
Corr. MTCLIM—RH [UPWARDS ARROW]− 10.3− 11.7− 15.3− 13.2− 15.1− 20.4
Raw—RH [DOWNWARDS ARROW]10.512.818.614.116.521.6
Table V. Crossvalidation errors for hourly models (‘raw’, ‘FAO’, and ‘MTCLIM’ corrections): percentages of errors on hours with measured RH ≥ 90% (unit: % hours | 1.0 = 100%)
 Mean on crossvalidation yearsMaximum on crossvalidation yearsYear 2003
 MeanNr. stations ⩽0.1MeanNr. stations ⩽0.3MeanNr. stations ⩽0.1
  1. Legend—lines:

  2. ‘Raw’ no corrections on Td.

  3. ‘Corr. FAO’, ‘corr. MTCLIM’: type of correction on Td.

  4. ‘Average (raw—FAO)’, ‘average (raw—MTCLIM)’, average between ‘raw’ model and either FAO- or MTCLIM- corrected models, respectively.

  5. Legend—columns:

  6. ‘Mean’ mean value over the 23 stations; ‘nr. stations err. < 0.1 (0.3)’, number of stations with errors on the number of very humid hours in the band ± 10% ( ± 30%). Period: May to August.

Corr. FAO− 0.50− 0.70− 0.50
Corr. MTCLIM− 0.70− 0.90− 0.80
Average (raw—FAO)0.090.450.37
Average (raw—MTCLIM)0.080.440.27

4. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Comparison between Figure 4(a) and (b) shows there is no reason to prefer one correction method over the other. The number of stations that positively fit expectations regarding error is subjective. For example, if the double criterion is assumed to have a mean cross-validation error within ± 10% and an inter-quartile range (IQR) within ± 30%, this number is nine in both the ‘MTCLIM’ and ‘FAO’ averaged models, with most of the well-performing stations meeting the requirements for both methods. The number of stations with the double criterion satisfied for at least one model among the ‘raw’, the average (‘raw’, ‘MTCLIM’), and the average (‘raw’, ‘FAO’) is 12, about half the total number of stations. Six of these stations have a 95% confidence limit within the 30% error band for both correction methods.

Table V also reports the number of stations with percent errors in hours lower than the two above-mentioned thresholds (10% on means and 30% on maxima). While the requirement on mean errors is attained at two stations only for the ‘raw model’ and at none for the ‘MTCLIM’ and ‘FAO’ correction models, results improve significantly for both the ‘averaged corrected models’. A special case is that of summer 2003, a useful benchmark as it was an exceptionally hot and dry period in large parts of Europe, including northern Italy and the Alps in general (for a review: García-Herrera et al., 2010). Given its special characteristics, summer 2003 can be considered a paradigm of possible summer conditions in the coming decades, due to the expected climatic warming associated with a reduction of rainfall over the whole Mediterranean region (van der Linden and Mitchell, 2009). So, it would be useful to compare the performances of models in this year and to assess whether 2003 coincides with the year of maximum error in the models. The performance of the corrected models in 2003 is fairly good: while there is a non-negligible, and expected, mean positive bias (20–30%), the number of stations with error percentages below the threshold is good, only slightly lower than the average on all the cross-validation years. This is a good result and it supports the confidence in the corrected models, even in particularly anomalous years. If a more restrictive standard is adopted on the evaluation of results, that is, one which takes into account simultaneous satisfaction of the mean, the IQR, and the 2003-only test trials, only 7 out of the 23 sites considered are fully responsive (six, if instead of the IQR the 30% error band is taken as the limit for the 95% percentile of errors).

Enforceability of the algorithm is restricted to stations for which it is possible to reproduce humidity reliably. Regarding estimation of the number of very humid hours in the period of interest (May to August), one result of the analysis of errors in the simulations is that, despite an apparently low bias in the ‘raw’ model (Table IV), the relevant errors in the number of very humid hours is almost always high (Table V). However, application of the correction algorithms and averaging in the ‘raw’ model considerably lowers the errors, even though the error in the sample of very humid hours increases. This can be explained if it is recalled that the error in relative humidity is calculated on the sample filtered by the measurements (values ≥ 90% only), whereas the error in the percentage number of hours above the threshold is calculated by counting hours after separate filtering by model estimations and by measures.

Humidity estimates of both the raw and the corrected models seem to have a typical range of errors, within which the relevant error in the percentage of very humid hours is satisfactory. This relation is represented in Figure 5, where acceptability of the error in hours is in the range of ± 10%. As expected, there is a significant link between errors in very humid hours and errors in relative humidity: Pearson's R2 = 0.37 (p = 0.002) for the ‘raw’ model and 0.34 (p = 0.004) for the average (‘raw’—‘MTCLIM corrected’) model [results were similar for the average (‘raw’—‘FAO corrected’) model]. More interestingly, mean hourly errors for very humid hours can be statistically related to mean humidity rates at the stations. Relative humidity is better suited to being modelled at the more humid sites, which seem to be more frequent in the higher and the more northerly part of Trentino, while the sites with larger errors (stations 30, 49, 51, 54 and 63 in Figure 4) are all in the southernmost part and at low elevations (Figure 1 and Table I). The latter area, contiguous to the pre-alpine region, generally has a comparatively drier and warmer climate and is well ventilated, which checks stagnation of humidity in the soil and the air close to the ground. The importance of the corrections in the ‘raw’ model is evident from Figure 6, as is the close dependence of the error on the mean relative humidity of stations, but if the ‘raw’ model functions better at humid stations, as expected, as the model assumes vapour saturation to be attained every night, the corrected models give better results for less humid sites. More generally, while the ‘raw’ model seems totally unreliable for sites whose summer mean relative humidity is outside a very narrow band of values, the correction algorithms allow us to consider stations with a mean relative humidity within a much broader range, roughly from 58 to 67%. The Person's R2 values are 0.59 (p = 2.1 × 105) for the ‘raw’ model, and 0.28 (p = 0.008) for the average (‘raw’—‘MTCLIM corrected’) model [results were similar for the average (‘raw’—‘FAO corrected’) model]. However, while the correlation between mean summer relative humidity and model skill is high, it is not striking and does not support the use of this index alone to infer the ability of models to simulate humidity with no instrumental measurements.

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Figure 5. Relationship between error in the number of very humid hours and mean error in RH values (May to August). The ± 10% band is marked. (a) All values. (b) Detail around the ± 10% band. Key: (○) ‘raw’ model, R2 = 0.37 (p = 0.002)—(●) average (‘MTCLIM’—‘raw’ model), 0.34 (p = 0.004)

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Figure 6. Relationship between error in the number of very humid hours and mean RH (May to August). (a) All stations. (b) Detail around the ± 10% band. Key: (○) ‘raw’ model, R2 = 0.59, p = 2.1 × 105—(●) average (‘MTCLIM’—‘raw’ model), R2 = 0.28, p = 0.008

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5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

In this work, the use of algorithms to estimate relative humidity using measures of minimum temperature corrected by rainfall measurements is proposed. The main assumptions forming the basis of these algorithms are that water vapour frequently reaches saturation at night and that relative humidity over a day is the simple result of the modulation of temperature at constant air water content. However, the role of correction algorithms is fundamental. These have been designed to correct dew-point temperature, which in turn depends either on the presence of precipitation (‘MTCLIM’ correction) or on the water balance over the previous weeks (‘FAO’ correction).

The correction algorithms yielded a satisfactory simulation of atmospheric humidity in a number of sites (25–50% of the stations, according to the strictness of the acceptance standard). A test carried out on the extremely hot and dry summer of 2003 confirmed the positive results. Model performance was found to have a non-exclusive dependence on average humidity at the station. Nevertheless, a site-specific calibration is required in order to assess station fitness for a proper simulation of relative humidity from temperature and precipitation measures.

Despite this important caveat, the study showed that some sites do indeed reproduce well the dynamics that underpin the basic assumptions of the proposed models. For selected sites, this finding permits the models to be used for simulating relative humidity in contexts where measures are not available, such as for generating humidity series from the more commonly available projected series of temperature and precipitation from climate model outputs.


  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References

This study was carried out in the frame of the project ENVIROCHANGE, funded by the Autonomous Province of Trento. Thanks to Ilaria Pertot, Piero Cau and Fabio Zottele (Fondazione Edmund Mach) and to Riccardo de Filippi (Fondazione Bruno Kessler) for their collaboration.


  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results
  6. 4. Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
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