Identifying appropriate prediction models for estimating hourly temperature over diverse agro-ecological regions of India

Abstract

The present study tests the accuracy of four models in estimating the hourly air temperatures in different agroecological regions of the country during two major crop seasons, kharif and rabi, by taking daily maximum and minimum temperatures as input. These methods that are being used in different crop growth simulation models were selected from the literature. To adjust the biases of estimated hourly temperature, three bias correction methods (Linear regression, Linear scaling and Quantile mapping) were used. When compared with the observed data, the estimated hourly temperature, after bias correction, is reasonably close to the observed during both kharif and rabi seasons. The bias-corrected Soygro model exhibited its good performance at 14 locations, followed by the WAVE model and Temperature models at 8 and 6 locations, respectively during the kharif season. In the case of rabi season, the bias-corrected Temperature model appears to be accurate at more locations (21), followed by WAVE and Soygro models at 4 and 2 locations, respectively. The pooled data analysis showed the least error between estimated (uncorrected and bias-corrected) and observed hourly temperature from 04 to 08 h during kharif season while it was 03 to 08 h during the rabi season. The results of the present study indicated that Soygro and Temperature models estimated hourly temperature with better accuracy at a majority of the locations situated in the agroecological regions representing different climates and soil types. Though the WAVE model worked well at some of the locations, estimation by the PL model was not up to the mark in both kharif and rabi seasons. Hence, Soygro and Temperature models can be used to estimate hourly temperature data during both kharif and rabi seasons, after the bias correction by the Linear Regression method. We believe that the application of the study would facilitate the usage of hourly temperature data instead of daily data which in turn improves the precision in predicting phenological events and bud dormancy breaks, chilling hour requirement etc.

Full text

1
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports
Identifying appropriate prediction
models for estimating hourly
temperature over diverse
agro‑ecological regions of India
Santanu Kumar Bal , V. P. Pramod , V. M. Sandeep , N. Manikandan
*, M. A. Sarath Chandran ,
A. V. M. Subba Rao , P. Vijaya Kumar , M. Vanaja & V. K. Singh
The present study tests the accuracy of four models in estimating the hourly air temperatures in
dierent agroecological regions of the country during two major crop seasons, kharif and rabi, by
taking daily maximum and minimum temperatures as input. These methods that are being used
in dierent crop growth simulation models were selected from the literature. To adjust the biases
of estimated hourly temperature, three bias correction methods (Linear regression, Linear scaling
and Quantile mapping) were used. When compared with the observed data, the estimated hourly
temperature, after bias correction, is reasonably close to the observed during both kharif and rabi
seasons. The bias‑corrected Soygro model exhibited its good performance at 14 locations, followed
by the WAVE model and Temperature models at 8 and 6 locations, respectively during the kharif
season. In the case of rabi season, the bias‑corrected Temperature model appears to be accurate at
more locations (21), followed by WAVE and Soygro models at 4 and 2 locations, respectively. The
pooled data analysis showed the least error between estimated (uncorrected and bias‑corrected) and
observed hourly temperature from 04 to 08 h during kharif season while it was 03 to 08 h during the
rabi season. The results of the present study indicated that Soygro and Temperature models estimated
hourly temperature with better accuracy at a majority of the locations situated in the agroecological
regions representing dierent climates and soil types. Though the WAVE model worked well at some
of the locations, estimation by the PL model was not up to the mark in both kharif and rabi seasons.
Hence, Soygro and Temperature models can be used to estimate hourly temperature data during both
kharif and rabi seasons, after the bias correction by the Linear Regression method. We believe that
the application of the study would facilitate the usage of hourly temperature data instead of daily
data which in turn improves the precision in predicting phenological events and bud dormancy breaks,
chilling hour requirement etc.
Temperature is a critical meteorological parameter for crop development and function both in the short and long
term1. High or low temperature, even for a short period, aects crop growth, especially in temperature-sensitive
crops like wheat. Very importantly, plants’ response to changes in day and night temperature (ermoperiodism)
aects the production of various enzymes and plant growth chemicals2. Further, an increase in temperature
increases the water vapour in the air exponentially at saturation, raising the vapour pressure decit (VPD) caus-
ing an enhancement in water loss from plants, causing a substantial reduction in vegetation productivity and
yield3. erefore, shis in long-term mean annual temperature and extreme temperature events will likely have
signicant impacts on crop production.
Biological development rates are linearly related to temperature. It is important to include the variations
in temperature in agricultural models which describe the crop phenology and development based on heat
accumulation4. Although daily mean temperature determines the growth and development of crop plants, the
day and night cycle/diurnal pattern of temperature is more important as it aects many plant morphological
characteristics like leaf, shoot orientation, plant height and internodes length etc.5 and disrupts the nutrient
balance6. erefore, analysing the response of crop plants to hourly temperature is more crucial than daily data.
OPEN
ICAR-Central Research Institute for Dryland Agriculture, Hyderabad, Telangana 500059, India. *email: manikandan.
narayanan@icar.gov.in
Content courtesy of Springer Nature, terms of use apply. Rights reserved

2
Vol:.(1234567890)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
Many studies revealed the need for sub-daily/hourly maximum and minimum temperatures to monitor the
crop phenological events7,8, dormancy breaks of temperate fruits9,10, chilling hour requirement for apple11–14,
forecasting of plant disease transmission15 and prediction of frost occurrence16.
Generally, meteorological observatories record daily maximum and minimum temperatures and hourly
temperature data is available at a few places17. e period for missing observational data can be replaced with
data generated by weather generators18. At locations, where Automatic Weather Stations (AWS) are installed
even record erroneous and uneven hourly/sub-hourly weather data due to malfunctioning of sensors/unknown
disruptions19. Moreover, the higher cost of installation and periodic maintenance of AWS makes it dicult to
increase its network, especially in developing/third-world countries.
As there is a paucity of hourly temperature data, oen daily maximum and minimum temperature data are
used to estimate the diurnal temperature curves20. e diurnal temperature curves have been in a variety of ways
that vary from simple curve-tting models based upon sine curves21–27 to more sophisticated techniques utilizing
Fourier analysis28 and complex energy balance models29–31. Even though modelling approaches are dierent32–35,
most models are based on temperature. Employing statistical tools to enhance the performance of these predictive
models/equations is a general practice in the research arena. Prior work with regard to the estimation of hourly
temperature values based on the equations in widely used crop simulation models gave unsatisfactory results.
is led to the use of bias correction technique to improve the model prediction ability in the present study.
With this background, the present study explores the accuracy of dierent models for estimating hourly
temperatures from daily maximum and minimum temperatures at places representing various climatic and soil
types. ree bias correction methods to improve the accuracy and usability of the estimated hourly temperature
data was also taken up in this study.
Results and discussion
e estimated hourly temperature from daily maximum and minimum temperature data using four dierent
models (WAVE, PL, Soygro and Temperature) indicated appreciable error between estimated and observed data.
To increase the accuracy of estimated hourly temperature data three bias correction methods (Linear Regression,
Linear Scaling and Quantile Mapping) were used and the results are furnished below.
Evaluation of bias correction methods. e heatmaps of performance metrics in terms of three e-
ciency criteria and two dierent measures for each of the 12 bias-corrected models at each location during
kharif (2012 and 2013) and rabi (2012–13 and 2013–14) are presented in Figs.1, 2, 3, 4 and 5. During the kharif
Figure1. Performance of bias-corrected models w.r.t R2 across the study locations during kharif (le) and rabi
(right).
Figure2. Performance of bias-corrected models w.r.t. NSE across the study locations during kharif (le) and
rabi (right).
Content courtesy of Springer Nature, terms of use apply. Rights reserved

3
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
season, the bias-corrected Soygro model exhibits higher R2, NSE and D-index values at 14 locations, followed
by the WAVE model and Temperature models at 8 and 6 locations, respectively. e results of Reicosky etal.36
indicated that the Soygro model was equally robust as the WAVE model in estimating hourly temperature from
daily maximum and minimum temperature in most circumstances. Across these 28 locations, bias correction
using Linear Regression was found to be more appropriate in estimating the hourly temperature. In the case
of dierence measures (nRMSE), Soygro model with Linear Regression as biascorrection appears to be most
accurate in estimating the hourly temperature at 14 locations, followed by the WAVE and Temperature models
at 8 and 6 locations, respectively, which is the same as that of the index measures. MAPE value for bias corrected
(Linear Regression) Temperature model was less at 12 locations, followed by the Soygro and WAVE models at 9
and 7 locations, respectively. Table1 shows the best of the bias-corrected models in terms of eciency criteria
and dierence measures across each of the study locations.
Variation among the models in dierent methods of error analysis was not consistent, especially with respect
to MAPE. erefore, a greater number of eciency criteria and dierent measures are chosen for error analysis
to nd out an appropriate bias-corrected model for estimating the hourly temperature at any particular location.
During the rabi season, the Temperature model with LR bias-correction was found to be accurate at more
locations (20), followed by WAVE and Soygro models at 5 and 2 locations, respectively with respect to both
Figure3. Performance of bias-corrected models w.r.t D-index across the study locations during kharif (le) and
rabi (right).
Figure4. Performance of bias-corrected models w.r.t nRMSE across the study locations during kharif (le) and
rabi (right).
Figure5. Performance of bias-corrected models w.r.t MAPE across the study locations during kharif (le) and
rabi (right).
Content courtesy of Springer Nature, terms of use apply. Rights reserved

4
Vol:.(1234567890)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
indices (R2, D-index and NSE) and dierence measures (nRMSE and MAPE). e study of Cesaraccio etal.7
also revealed that the estimated hourly temperature data by Temperature model was superior over PL, WAVE
and Wilkerson model37. Baker etal.38 also reported that all three methods (WAVE, PL and Linear model) per-
formed equally well in estimating hourly temperature data from daily maximum and minimum temperature
data. However, the above paper reported that all three methods performed well during summer when compared
to winter. e best of the bias-corrected models in terms of eciency criteria and dierent measures across the
study locations during rabi season is shown in Table2. It is to be noted that, LR was found to be more eective
in reducing the bias-correction of the appropriate model at each location. We used the LR criterion with an
assumption that there are no measurement errors in the observed data, as hourly data was collected from AWS.
Comparison of mean hourly temperature. To compare the appropriate method, with the observed
data, before and aer bias correction a line plot of mean hourly temperature for both kharif and rabi seasons was
plotted and presented in Fig.S1 and Fig.S2 (Supplementary le), respectively at each location. e estimated
hourly temperature with and without bias correction shows a clear dierence in estimating the hourly tempera-
ture, during both kharif and rabi seasons. e LR bias-correction method explicitly shows the improvement in
estimating the hourly temperature across each location. e estimated hourly temperature, aer bias correction,
is reasonably close to the observed values during both kharif and rabi seasons (Figs.1, 2, 3, 4, 5). McDonnel
etal.39 found LR method to be the most appropriate bias correction method for both air and soil temperatures,
which improved the air and soil temperature forecasts given by European Centre for Medium-Range Weather
Forecasts for Ireland. e magnitude of the errors with both uncorrected and bias-corrected models seems to
vary throughout the 24h at each location and is more distinctly noted by plotting the average hourly error, i.e.
the dierence between the estimated temperature, with and without bias-correction, and the observed tempera-
tures in Fig.6. e pooled data analysis showed that, during the kharif season, the dierence between estimated
(uncorrected and bias-corrected) and observed error is smallest during 04 to 08h as most of the models take
Tmin as input, whereas during the rabi season it is observed from 03 to 08h in the morning. Errors with the
uncorrected models at other times of the day are as large as − 1.2°C during kharif, and − 1.4 °C during rabi.
Reicosky etal.36 also observed the least variation between estimated and observed hourly temperature when
minimum temperature was recorded and the highest was observed during other times of the day. Further, they
reported that maximum temperature didn’t appear to aect the accuracy of the models employed to estimate
hourly temperature from daily data. Aer bias correction, the magnitude of error (dierence in model output
and observed) got reduced to ~ 0°C in kharif, whereas still underestimated by 0.2°C in rabi. is could be
attributed to the low diurnal variation in temperature that occurs during kharif season due to cloudy/overcast
conditions in most of the day. Whereas, rabi is the driest season of the year during which mostly clear days and
Table 1. Best of bias-corrected models for kharif season in terms of eciency criteria and dierence measures
across each of the study locations. S, Soygro; T, Temperature; W, Wave; LR, Linear Regression.
Locations
Eciency criteria Dierence
measures
ModeR2NSE D-Index nRMSE MAPE
Bahraich, Gonda, Gorakhpur, Kushinagar Madhubani, Pedavegi, Ram-
anathapuram and Ranga Reddy S-LR S-LR S-LR S-LR S-LR S-LR
Baghpat, Chhattarpur, Kendrapara, Nawada, Udaipur and Villupuram S-LR S-LR S-LR S-LR T-LR S-LR
East Sikkim, Kangra, Maharajganj, Nalgonda and Satna T-LR T-LR T-LR T-LR T-LR T-LR
Kinnaur T-LR T-LR T-LR T-LR S-LR T-LR
Aurangabad-M, Belgaum, Chintamani, Kinnaur, Lunglei, Mandi, Pune and
Uttarkashi W-LR W-LR W-LR W-LR W-LR W-LR
Sirmaur W-LR W-LR W-LR W-LR T-LR W-LR
Table 2. Best of the bias-corrected models for rabi season terms of eciency criteria and dierence measures
across each of the study locations. S, Soygro; T, Temperature; W, Wave; LR, Linear Regression.
Locations
Eciency criteria Dierence
measures
ModeR2NSE D-index nRMSE MAPE
Hamirpur S-LR S-LR S-LR S-LR S-LR S-LR
Nawada S-LR S-LR S-LR S-LR T-LR S-LR
Anantapur, Aurangabad-M, Lunglei and Namakkal W-LR W-LR W-LR W-LR W-LR W-LR
Alleppey, Aurangabad-B, Bilaspur, Chintamani, Golaghat, Gondia, Kangra, Kurnool, Nalgonda, Nandurbar, Pune-
Baramati, Ranga Reddy, Raipur, Satna, Sonepur, rissur, Udaipur and Villupuram T-LR T-LR T-LR T-LR T-LR T-LR
Ganjam and Jharsuguda T-LR T-LR T-LR T-LR S-LR T-LR
Kinnaur T-LR T-LR T-LR T-LR PL-LS T-LR
Content courtesy of Springer Nature, terms of use apply. Rights reserved

5
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
nights are observed. Reicosky etal.36 also found that predicted hourly temperature data from daily maximum
and minimum temperatures tted well during cloud-free days than cloudy days.
Suitability of models in various climatic and soil types during kharif and rabi seasons. Climate
type. During kharif season, Soygro model was found to be performing well in estimating the hourly tempera-
ture in hot sub-humid (7 locations) and hot semi-arid (7 locations) climates. However, in locations representing
warm per-humid/sub-humid to hot semi-arid climates WAVE and Temperature models performed better (Ta-
ble3). ese observations indicate a mixed performance of the models in dierent climates. Kharif is the main
rainy season of the year and prevailing cloudy conditions/overcast sky during the season leads to low diurnal
uctuation in temperature40. An overcast sky disturb/interfere with the incoming radiant energy during day
hours and especially energy loss during night hours in the form of longwave radiation. is leads to a change
in the diurnal pattern of air temperature i.e. reduction in the dierence between daytime and nighttime. It is
understood from the detail of the respective models that Soygro and Temperature models have divided 24h of a
day into three parts while WAVE and PL models divided the day into two parts (details in Materials and Methods
section). Soygro model could capture well the change in the diurnal pattern of temperature, as two out of the
three equations in the model consider data during midnight to sunrise hours and sunset to midnight hours. is
could be the reason for the better performance of Soygro model in many locations when compared to WAVE
and Temperature models.
Figure6. Average hourly temperature error calculated by comparing estimated and observed hourly
temperature during kharif and rabi seasons.
Table 3. Performance of models in predicting hourly temperature in dierent climates during kharif and rabi
seasons.
Climate type
Kharif season (28 locations) Rabi season (27 locations)
WAVE model PL model Soygro model Temperature
model WAVE model PL model Soygro model Temperature
model
Warm Per-
humid 1 – – – 1 – – –
Hot humid
and sub-
humid – – – 1 – – – 2
Warm sub-
humid 3 – – 2 – – 1 2
Hot sub-
humid – – 7 2 – – 1 9
Hot semi-arid 4 – 7 1 2 – – 8
Hot arid – – – – 1 – – –
Content courtesy of Springer Nature, terms of use apply. Rights reserved

6
Vol:.(1234567890)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
During rabi season, the Temperature model exhibited better performance in 21 out of 27 locations falling
under dierent AERs from hot per-humid & humid to hot semi-arid climates. It is observed that Soygro model
worked well only in two locations representing hot and warm sub-humid climates. WAVE model was found to
be best-suited for one per-humid, one arid and two hot semi-arid locations. Rabi season is the driest season of
the year characterised by low atmospheric humidity, cloud-free sky and a higher diurnal temperature range40.
e Temperature model, comprising two equations dealing with daylight hours and one equation for night
hours, probably captured the hourly march of temperature well during the rabi season. It was also observed that
the PL model could not perform better either during kharif or rabi seasons in any of the locations. One out of
two equations of the PL model, which deals with night hours, assumes temperature decrement from sunset to
sunrise at an exponential rate. Probably, this assumption can be attributed to the poor performance of PL model
across locations.
Soil type. Soil colour and texture play a predominant role in governing the diurnal pattern of soil temperature,
which in turn aects the atmospheric temperature through latent and sensible heat uxes41. e performance
of models in estimating the hourly temperature for locations having dierent soil types was looked at. e
results indicated that Soygro model performed better in locations having alluvium-derived soils, especially dur-
ing kharif season. However, Temperature and WAVE models did not show any specic pattern for soil types.
During rabi season, the hourly air temperature was well predicted by the Temperature model in all soil types. e
Temperature model worked well in 11 out of 27 locations represented by red, black, and lateritic soils (Table4).
Performance of the model was also good at 6 locations having alluvium soils and 2 locations each represented by
red loamy and brown forest podzolic soils. At the same time, the WAVE model performed well in red, black, lat-
eritic and red loamy soils, while Soygro model performed well in only two locations represented by alluvium and
brown forest soils. e study showed that Soygro and Temperature models worked well in most of the locations
during kharif and rabi seasons, respectively when compared to the WAVE model. However, the PL model’s per-
formance was not up to the mark, compared to the other three models in any of the soil types. It is understood
from the results that Soygro and Temperature models which have three dierent equations to deal with the day
and night hours helped for precise estimation of hourly data by these models.
As mentioned earlier, the Soygro model performed well in the locations with alluvium soils, especially during
kharif season and not during the rabi season. In general, the average soil moisture status of the soil is higher dur-
ing the kharif season than the rabi season and vice versa. During the kharif season, when soil moisture nears eld
capacity, it takes more time to heat up the soil and also the atmosphere later as the specic heat of wet sandy soil
is almost two times higher (0.4cal g−1 deg−1) than dry sandy soil (0.2cal g−1 deg−1)42. During the rabi season, as
soil is dry, it absorbs and releases the heat energy in less time and also the diurnal soil temperature range would
be greater than the kharif season. ough Soygro and Temperature models use three equations, Soygro model
consists of only one equation to deal with the daylight period while the Temperature model has two equations
for the daylight period. is could be the reason for the better performance of the Temperature model during
rabi season in most of the locations having dierent soil types.
Conclusions
Four models viz, WAVE, PL, Soygro and Temperature model were used in estimating the hourly temperature at
selected locations in dierent AERs of the country during two crop seasons (kharif and rabi). When compared
with the hourly observed data, the bias-corrected Soygro model exhibits higher values w.r.t three eciency
criteria (R2, NSE and D-index) at 14 locations, followed by the WAVE model and Temperature models in 8 and
6 locations, respectively during the kharif season. In the case of the rabi season, bias corrected Temperature
model appears to be accurate at more locations (20), followed by WAVE and Soygro models at 5 and 2 locations,
respectively. Bias correction was found to be more eective in reducing the error of the appropriate model at
each location with Linear Regression irrespective of the season. e magnitude of errors with both uncorrected
and bias-corrected models seems to be changing over the 24-h period of the day across each of the locations.
e performance of four dierent models over dierent agroecological regions of the country revealed the
better performance of the Soygro model during the kharif season at locations representing hot sub-humid and
semi-arid climates. Whereas, the Temperature model outperformed the other model during the rabi season at
most of the locations ranging from hot per-humid to hot semi-arid climates. Estimating the accuracy of hourly
Table 4. Performance of models in predicting hourly temperature in dierent soil types during kharif and rabi
seasons.
Soil type
Kharif season (28 locations) Rabi season (27 locations)
WAVE model PL model Soygro model Temperature
model WAVE model PL model Soygro model Temp erature
model
Alluvium
derived – – 11 2 – – 1 6
Red, black and
lateritic 4 – 2 2 3 – – 11
Red loamy 1 – 1 – 1 – – 2
Brown forest
podzolic 3 – – 2 – – 1 2
Content courtesy of Springer Nature, terms of use apply. Rights reserved

7
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
temperature in dierent soil types indicated that the Soygro model worked well during the kharif season at
the locations having alluvium-derived soils. At the same time, during the rabi season, the performance of the
Temperature model was better than other models in the agro ecological regions dominated by red, black and
lateritic soils. e smallest dierence between estimated (uncorrected and bias-corrected) and observed was
noticed from 04 to 08h during the kharif season when most of the models assume Tmin as input, while it was
from 03 to 08h in the morning during the rabi season. e results of the study strongly suggested that hourly
temperature during the kharif and rabi seasons can be estimated using the Soygro and Temperature models,
respectively aer the bias correction by the Linear Regression method, as these two models estimated hourly
temperature with better accuracy at a majority of the locations representing dierent climate and soil types.
Nevertheless, the WAVE model also can be used to estimate the hourly temperature data at some of the study
locations. However, the PL model did not perform satisfactorily at any of the locations. Hourly temperature
data in lieu of daily temperature (maximum and minimum) data would enhance the precision in predicting
phenological and other biological events.
Data and methods
Study area. Observed maximum and minimum temperatures, at daily and hourly scales, were collected from
the AWS of the AICRPAM-NICRA network. National Innovations in Climate Resilient Agriculture (NICRA), a
network project of the Indian Council of Agricultural Research (ICAR) aims to enhance the resilience of Indian
agriculture to climate change and climate vulnerability through strategic research and technology demonstra-
tion in the 100 most vulnerable districts of the country. e climatic variability is being assessed by the All India
Coordinated Research Project on Agrometeorology (AICRPAM) by installing AWS in each district under the
NICRA project43. e AWS records 6 meteorological parameters viz., temperature (maximum and minimum),
relative humidity (maximum and minimum), wind speed, wind direction, rainfall and solar direction. Depend-
ing on the availability of continuous hourly temperature (maximum and minimum) data over the study period,
44 locations were selected for the present study (Fig.7 and TableS1 of the Supplementary le). Out of 44 loca-
tions, the hourly temperature was estimated at 28 locations during the kharif season (2012 and 2013) and at 27
locations during the rabi season (2012–13 and 2013–14).
Methods of estimating hourly temperature. Four dierent methods for estimating hourly tempera-
ture were tested at dierent agro-ecological regions (AERs) of the country during two major crop seasons viz.,
the kharif (15-Jun to 15-Oct) and rabi (15-Oct to 15-Mar), by inputting the daily maximum and minimum
temperature. ese methods were taken from dierent crop growth simulation models. erefore, in the present
study, these methods are known by the name of their respective crop growth models or the sub-routines in which
they were employed. e details of each method are discussed hereunder.
WAVE model. e model was rst introduced by De Wit etal.44 and it was included in the subroutine WAVE
in ROOTSIMU V4.045. e model uses two dierent relations; formula one for estimating the hourly tempera-
ture from the time of minimum temperature (sunrise hour) to the time of maximum temperature (1400h) and
another for estimating from the time of maximum temperature to the time of the minimum temperature of the
next day. A cosine function is used in the model for both periods and is given by the following Eqs. (1) and (2).
For Sunrise Hour ≤ H ≤ 1400h
For 1400h < H < Sunrise Hour of next day
where T(H) is the temperature at hour H,
Tave =T
max
+T
min
2
;
Tamp =T
max
−Tmin
2
; Tmax and Tmin are the maximum
and minimum temperature, respectively. H’ = H-14 if H > 1400h and H’ = H + 10 if H < Sunrise Hour. For estimat-
ing the hourly temperature past 1400h, Tmin of the next day is considered. In the WAVE model, no site-specic
calibration is required.
Parton and Logan (PL) model. e model developed by Parton and Logan46 uses two dierent equa-
tions, like in the WAVE model, for estimating the hourly air temperature during daylight hours and night-time
hours. Parton-Logan’s model considers the sunrise hour to sunset hour as daylight hours and the time between
the sunset hour and sunrise hour of the next day as night-time hours. e model utilizes a truncated sine wave
at daylight hours (day-time) and an exponential decrease in temperature at night-time for estimating the hourly
temperature. e temperature at any given hour (T(H)) during the daylight hours is given by Eq.(3).
where Tmax and Tmin are the maximum and minimum temperature, respectively and Hmax and Hmin are the hour of
maximum and minimum temperatures, respectively. In the present study, Hmax is considered as 4h before sunset
hour (i.e. Hmax = Hss-4 where Hss is the sunset hour) and sunrise hour is considered as the Hmin. e temperature
at any given hour (T(H)) during the night-time hours is given by Eq.(4).
(1)
T(H)=Tave−Tamp ∗(Cos [π∗(H-Sunrise Hour)/(14-Sunrise Hour)])
(2)
T(H)
=T
ave
+T
amp
∗(Cos [π∗

H
′
/(10 +Sunrise Hour)]
)
(3)
T
(H)
=
Tmin
+
(Tmax
−
Tmin)
∗
Sin

π
2∗
(
H
−
H
min)
(Hmax −Hmin)
Content courtesy of Springer Nature, terms of use apply. Rights reserved

8
Vol:.(1234567890)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
where Tss is sunset hour temperature which can be determined using the daytime hour temperature relation,
b is the empirical constant (dimensionless), N is the time since sunset (s) and L is the night length (s). In the
present study, the empirical constant ‘b’ is taken as 2.20 across all the locations, as the parameter did not appear
to be strongly site-specic36.
(4)
T(H)=
T
min +
(T
ss −
T
min
)
∗
e
−
b*
N
L
1 - Western Himalayas,
cold arid ecoregions, with shallow skeletal soils
2 - Western Pl
ain, hot arid ecoregions with desert & saline soils
3 - Deccan Plateau, hot
arid ecoregions with red & black soils
4 - Northern Plain & Ce
ntral Highlands, hot semi-arid ecoregions with alluvium derived soils
5 - Central High lands, hot semi-arid ec
oregions with medium & deep black soils
6 - Deccan Plateau, hot semi-arid ecoregions with sh
allow & medium black soils
7 - Deccan Plateau & Eastern Ghats, hot semi-arid ecoregions with red &
medium black soils
8 - Ea
stern Ghats, Tamil Nadu Uplands & Deccan Plateau, hot semi-arid ecoregions with red loamy soils
9 - Northe
rn Plain, hot sub-humid ecoregions with alluvium derived soils
10- Central High lands, hot sub-hu
mid ecoregions with black & red soils
11- Ea
stern Plateau, hot sub-humid ecoregions with red & yellow soils
12- Ea
stern Plateau & Eastern Ghats, hot sub-humid ecoregions with red & lateritic soils
13- Ea
stern Plain, hot sub-humid ecoregions with alluvium derived soils
14- Western Himalayas, wa
rm sub-humid ecoregions with brown forest & podzolic soils
15- Beng
al & Assam Plain, hot sub-humid to humid ecoregions with alluvium derived soils
16- Ea
stern Himalayas, warm per-humid ecoregions with brown and red hill soils
17- North East
ern Hills, warm per-humid ecoregions with red and lateritic soils
18- Ea
stern Coastal Plain, hot sub-humid to semi-arid ecoregions with coastal alluvium derived soils
19- Western Gh
ats & Coastal Plain, hot humid-per-humid ecoregions with red, lateritic & alluvium derived soils
20- Islands of Andaman-Nicobar & Lakshadweep hot humid to per-humid island ecoregion with red loamy & sandy soils
Figure7. Study locations over dierent AER’s of the country (Numbers within each polygon represent dierent
AERs) (map generated using ArcMap 10.3; URL: https:// www. esri. com/ en- us/ arcgis/ produ cts/ arcgis- deskt op/
overv iew).
Content courtesy of Springer Nature, terms of use apply. Rights reserved

9
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
Soygro model. e model introduced by Wilkerson etal.37 estimates the hourly temperature by dividing
the day into three segments viz., midnight to sunrise + 2h; daylight hours and sunset to midnight. For each seg-
ment, the model uses three dierent Eqs. (5) to (14), which are given below.
For midnight to sunrise + 2h
For sunset to midnight
For daylight hours
where TAU, TLIN, SLOPE are temporary variables in calculations, T(H) is the temperature at hour H, n is the
current day of the year (1 to 365), RISE is the sunrise hour and SET is the sunset hour. e method assumes a
change from night to day temperature at sunrise + 2h, and the night temperatures are linear with time. It is to be
noted that, like the WAVE and Parton-Logan models, the Soygro model also does not consider any site-specic
constants.
Temperature model. e temperature model presented by Cesaraccio etal.7 is an empirical model for
estimating the hourly mean temperature. Like the Soygro model, the temperature model also divides the day
into three time periods i.e. from the sunrise hour (Hn) to the time of maximum temperature (Hx), from Hx to the
sunset hour (Ho) and from Ho to the sunrise hour for the next day (Hp). e model uses two sine-wave functions
in the daylight and a square-root decrease in temperature at night. e sunrise and sunset hours are determined
as a function of site latitude and the day of the year, whereas the hour of maximum temperature is assumed to
be 4h before sunset (Hx = Ho-4). Hp is calculated as Hp = Hn + 24. Tn and Tx are the minimum and maximum
temperature of the current day which occurs at Hn and Hx, respectively while the temperature during the sunset
hour (To) is determined using the below-mentioned Eq.(15).
where Tp is the minimum temperature of the following day and c is the empirical constant, which is obtained
by tting the equation to the observed hourly data set. For a given Tn, Tx, To and Tp, the Temperature model
estimates the temperature at any given hour (T(H)) for the three-time periods with the help of respect to three
dierent Eqs. (16) to (18).
For Hn < H ≤ Hx
For Hx < H < Ho
For Ho < H ≤ Hp
where
α
= Tx – Tn; R = Tx – To and b =
T
p
−T
o
√
H
p−
H
o
.
Bias correction methods. Researchers used dierent bias correction methods to reduce the errors and
improve the accuracy of prediction signicantly in dierent parts of the world47–50. In the present study also, to
(5)
TAU =(SETn−1−RISEn−1−2)/(SETn−1−RISEn−1)
(6)
TLIN =TMINn−1+(TMAXn−1−TMINn−1)∗Sin (TAU)
(7)
SLOPE =(TLIN −TMINn)/(24 −SETn−1+RISEn+2)
(8)
T(H)=TLIN −SLOPE (H+24−SETn−1)
(9)
TAU =(SETn−RISEn−2)/(SETn−RISEn)
(10)
TLIN =TMINn+(TMAXn−TMINn)∗Sin (TAU)
(11)
SLOPE =(TLIN −TMINn+1)/(24 −SETn+RISEn+1+2)
(12)
T(H)=TLIN −SLOPE (H−SETn)
(13)
TAU =(H−RISEn−2)/(SETn−RISEn)
(14)
T(H)=TMINn+(TMAXn−TMINn)∗Sin (TAU)
(15)
To=
T
x−
c

T
x−
T
p
(16)
T
(H)
=
Tn
+
α
∗
Sin
 H
−
H
n
Hx−Hnπ
2
(17)
T
(H)
=
To
+
R
∗
Sin

π
2+
H−Hx
4
π
2
(18)
T(H)=To+b√H−Ho
Content courtesy of Springer Nature, terms of use apply. Rights reserved

10
Vol:.(1234567890)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
reduce the biases and improve the accuracy of estimated hourly temperature, three bias correction methods were
used and the details of each are discussed below.
Linear regression. Linear Regression (LR) is simply a line of best t through the standard regression plot
of the observed against the estimated. Since temperature is well described by a normal distribution, a linear t is
sucient. e relative relationship of the values being compared is given by the slope value, whereas the inter-
cept indicates the lead or lag between the data. A slope of one and a y-intercept of zero show a perfect t between
simulated and observed data51 as mentioned in Eq.(19).
where Tcor,m,d,h and Test,m,d,h are the bias-corrected and estimated temperature (using either of the four models),
respectively for the ‘hth’ hour of ‘dth’ day and ‘mth’ month, mm(h) and cm(h) are the slope and intercepts of ‘hth’ hour
of ‘mth’ month, respectively.
Linear scaling. e Linear Scaling (LS) method aims to perfectly match the monthly mean of corrected
values with that of observed values52. It operates with monthly correction values worked out as the dierence
between observed and simulated data. In the present study, the bias correction for the estimated hourly tempera-
ture is given by Eq.(20).
where μ (Tobs,m(h)) and μ (Test,m(h)) are the mean value of observed and estimated temperature for the ‘hth’ hour
of ‘mth’ month.
Quantile mapping. Among the dierent bias correction methods, Quantile Mapping (QM) is considered
the most useful and popular. By applying a transfer function, QM corrects the systematic bias in the simulated
data so that it matches the distribution of the observational dataset53,54. For the estimated hourly temperature,
the QM bias correction is given by Eq.(21).
where Tcor,m,d,h and Test,m,d,h are the bias-corrected and estimated temperature (using either of the four models),
respectively for the ‘hth’ hour of ‘dth’ day and ‘mth’ month; CDF−1obs,m is inverse CDF of observed data set in the
validation period; CDFest,m is CDF of estimated data set in the validation period.
Methods of error analysis. Aer applying bias correction techniques (LR, LS and QM), the accuracy of
various models (WAVE, Parton-Logan, Soygro and Temperature) in estimating the hourly temperature was
tested by comparing them with the observed values at each location. e “goodness of t” of each model was
assessed using three eciency criteria (coecient of determination, coecient of eciency and index of agree-
ment) and two dierent measures (normalized root mean square error and mean absolute percentage error). e
bias-corrected model having more eciency criteria and fewer dierence measures is chosen as the appropriate
model for estimating the hourly temperature at a particular location. e details of each eciency criterion and
dierent measures are given below.
Coecient of determination. e coecient of determination (R2) is the square of Pearson’s product-
moment correlation coecient and describes the proportion of the total variance in the observed data that can
be explained by the model. R2 value ranges from 0 to 1, with higher values indicating better agreement and the
formula of R2 is given in Eq.(22).
where Oi and Si and are the observed and bias-corrected estimated values, Oavg and Savg are the average values of
observed and bias-corrected estimated values, respectively and n is the total number of observations.
Coecient of eciency. As correlation-based measures are more sensitive to outliers, the coecient of
determination measure leads to a bias towards the extreme events if employed in model evaluation. Nash and
Sutclie55 dened the coecient of eciency (NSE) as an improvement over the coecient of determination
for model evaluation purposes. Physically, it is the ratio of the mean square error to the variance in the observed
data, subtracted from unity (Eq.23).
e value of NSE ranges from − ∞ to 1, with higher values indicates perfect simulation.
(19)
Tcor,m,d,h =mm(h)∗Test,m,d,h +cm(h)
(20)
Tcor,m,d,h =
T
est,m,d,h +
µ

T
obs,(m(h)−
µ

T
est,m(h)
(21)
T
cor,m,d,h
=
CDF
−1
obs,m 
CDFest,m

Test,m,d,h

(22)
R
2=



n
i=1Oi−OavgSi−Savg 

n
i
=
1

Oi
−
Oavg

2

0.5

n
i
=
1

Si
−
Savg

2

0.5



2
(23)
NSE
=1−
n
i=1(Oi−Si)
2

n
i=1
O
i−
O
avg2
Content courtesy of Springer Nature, terms of use apply. Rights reserved

11
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
Index of agreement. In order to overcome the insensitivity of correlation-based measures to dierences
in the observed and model-simulated means, Willmott56 introduced the index of agreement (D-index), given
by Eq.(24).
Like R2, the value of D-index also varies from 0 to 1. e value of 1 indicates better agreement between model
simulated and observed values.
Normalized root mean square error. Root mean square error (RMSE) is increasingly being used in the
comparison and evaluation of simulation models and considered as the paramount measure of accuracy. It is
dened in the Eq.(25).
In terms of percentage error, root mean square error is given by normalized RMSE (nRMSE), which is given
by the Eq.(26).
Mean absolute percentage error. Mean Absolute Percentage Error (MAPE) is a measure of dierence
between two continuous variables, which is given by the Eq.(27).
MAPE is less sensitive to extreme values and therefore, it is intuitively more appealing than RMSE. However,
for evaluating the performance of model both RMSE and MAPE can be used as many researchers employed the
both indices50,57.
Data availability
e data used for the study are available from the corresponding author on reasonable request.
Received: 12 December 2022; Accepted: 25 April 2023
References
1. Moore, C. E. et al. e eect of increasing temperature on crop photosynthesis: From enzymes to ecosystems. J. Exp. Bot. 72(8),
2822–2844. https:// doi. org/ 10. 1093/ jxb/ erab0 90 (2021).
2. Patel, D. & Franklin, K. A. Temperature-regulation of plant architecture. Plant Signal. Behav. 47(7), 577–579 (2009).
3. Konings, A. G., Williams, A. P. & Gentine, P. Sensitivity of grassland productivity to aridity controlled by stomatal and xylem
regulation. Nat. Geosci. 10, 284–288 (2017).
4. VijayaKumar, P. et al. Algorithms for weather-based management decisions in major rainfed crops of India: Validation using data
from multi-location eld experiments. Agronomy J. 113, 1816–1830. https:// doi. org/ 10. 1002/ agj2. 20518 (2021).
5. Myster, J. & Moe, R. Eect of diurnal temperature alternations on plant morphology in some greenhouse crops—A mini review.
Sci. Hortic. 62(4), 205–215 (1995).
6. Inthichack, P., Nishimura, Y. & Fukumoto, Y. Diurnal temperature alternations on plant growth and mineral absorption in eggplant,
sweet pepper and tomato. Hortic. Environ. Biotechnol. 54, 37–43 (2013).
7. Cesaraccio, C., Spano, D., Duce, P. & Snyder, R. L. An improved model for determining degree-day values from daily temperature
data. Int. J. Biometeorol. 45, 161–169 (2001).
8. Bal, S. K. et al. Water demand of maize is projected to decrease under near-future climate in India. Sustainability https:// doi. org/
10. 3390/ su140 31419 (2022).
9. Anderson, J. L., Richardson, E. A. & Kesner, C. D. Validation of chill unit and ower bud phenology models for “Montmorency”
sour cherry. Acta Hortic. 184, 71–78 (1986).
10. Erez, A., Fishman, S., Linsley-Noakes, G. C. & Allan, P. e dynamic model for rest completion in peach buds. Acta Hortic. 276,
165–174 (1990).
11. Basannagari, B. & Kala, C. P. Climate change and apple farming in Indian Himalayas: A study of local perceptions and responses.
PLoS ONE 8(10), e77976. https:// doi. org/ 10. 1371/ journ al. pone. 007796 (2013).
12. Hartta, Y. S. Climate change and apple productions in Himachal Pradesh: A study of last two decades. Acad. Discourse 3(1), 75–81
(2014).
13. Pramanick, K. et al. Role of changing climate on chilling unit accumulation and yield for apple (Malus x Domestica Borkh) cultiva-
tion at Shimla, Himachal Pradesh, India. Int. J. Trop. Agric. 33(2), 1039–1044 (2015).
14. Sahu, N. et al. Why apple orchards are shiing to the higher altitudes of the Himalayas?. PLoS ONE 15(7), e0235041. https:// doi.
org/ 10. 1371/ journ al. pone. 02350 41 (2020).
15. Kang, W. S. et al. A web-based information system for plant disease forecast based on weather data at high spatial resolution. Plant
Pathol. J. 26(1), 37–48 (2010).
16. Bal, S. K. et al. Developing frost prediction models using multivariate statistical techniques for two diverse locations of Northern
India. eor. Appl. Climatol. 146, 1097–1110. https:// doi. org/ 10. 1007/ s00704- 021- 03786-8 (2021).
(24)
D-index
=1−
n
i=1(Oi−Si)
2

n
i=1

S
i
−O
avg 

+


O
i
−O
avg 
2
(25)
RMSE
=




n

i=1
(Si−Oi)2
n
(26)
nRMSE
=RMSE
O
avg
∗
100
(27)
MAPE =
n
i=1



Si−Oi
Oi



×
100
n
Content courtesy of Springer Nature, terms of use apply. Rights reserved

12
Vol:.(1234567890)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
17. Critcheld, H. J. General Climatology 4th edn, 453 (PHI Learning Pvt. Ltd, 2013).
18. Bal, S. K., Choudhury, B. U., Sood, A., Jalota, S. K. & Singh, H. Evaluation of climgen model to generate weather parameters in
dierent climatic situations in Punjab. J. Agrometeorol. 10(1), 73–79 (2008).
19. Shoaib, T. A. & Rasool, S. N. Correcting real time automatic weather stations data through quality checks and analysis. Vayu
Mandal. 41, 69–76 (2015).
20. Snyder, R. L., Spano, D., Cesaraccio, C. & Duce, P. Determining degree-day threshold from eld observations. Int. J. Biometeorol.
42, 177–182 (1999).
21. Allen, J. C. A modied sine wave method for calculating degree days. Environ. Entomol. 5(3), 388–396 (1976).
22. Hansen, J. E. & Driscoll, D. M. A mathematical model for the generation of hourly temperatures. J. Appl. Meteor. 16(9), 935–948
(1977).
23. Floyd, R. B. & Braddock, R. D. A simple method for tting average diurnal temperature curves. Agric. For. Meteorol. 32(2), 107–119
(1984).
24. Wann, M., Yen, D. & Gold, H. J. Evaluation and calibration of three models for daily cycle of air temperature. Agric. For. Meteorol.
34(2–3), 121–128 (1985).
25. De Gaetano, A. & Knapp, W. W. Standardization of weekly growing degree day accumulations based on dierences in temperature
observation and method. Agric. For. Meteorol. 66(1–2), 1–19 (1993).
26. Yin, X., Krop, M. J., McLaren, G. & Visperas, R. M. A non-linear model for crop development as a function of temperature. Agric.
For. Meteorol. 77, 1–16 (1995).
27. Roltsch, J. W., Zalom, F. G., Strawn, A. J., Strand, J. F. & Pitcairn, M. J. Evaluation of several degree day estimation methods in
California climates. Int. J. Biometeorol. 42, 169–176 (1999).
28. Carson, J. E. Analysis of soil and air temperatures by Fourier techniques. J. Geophys. Res. 68(8), 2217–2232 (1963).
29. Carson, J. E. & Moses, H. e annual and diurnal heat exchange cycle in upper layers of soil. J. Appl. Meteorol. 2(3), 397–406 (1963).
30. Brown, G. W. Predicting temperatures of small streams. Water Resour. Res. 5(1), 68–75 (1969).
31. Lemon, E., Steward, D. W. & Shawcra, R. W. e sun’s works in a corneld. Science 174(4007), 371–378 (1971).
32. Galán, C., Fuillerat, J. M., Comtois, P. & Dominguez-Vilches, E. Bioclimatic factors aecting daily Cupressaceae owering in
southwest Spain. Int. J. Biometeorol. 41, 95–100 (1998).
33. Hänninen, H. Modeling bud dormancy release in trees from cool and temperate regions. Acta. For. Fenn. 213, 47p (1990).
34. Kramer, K. Selecting a model to predict the onset of growth of Fagus sylvatica. J. Appl. Ecol. 31(1), 172–181 (1994).
35. Maak, K. & von Storch, H. Statistical downscaling of monthly mean air temperature to the beginning of owering of Galanthus-
nivalis L. in Northern Germany. Int. J. Biometeorol. 41, 5–12 (1997).
36. Reicosky, L. J., Winkelman, J. M., Baker, J. M. & Baker, D. G. Accuracy of hourly air temperatures calculated from daily minima
and maxima. Agric. For. Meteorol. 46(3), 193–209 (1989).
37. Wilkerson, G. G., Jones, J. W., Boote, K. J., Ingram, K. T. & Mishoe, J. W. Modeling soybean growth for crop management. Trans.
ASAE 26(1), 63–73 (1983).
38. Baker, J. M., Reicosky, D. C. & Baker, D. G. Estimating the time dependence of air temperature using daily maxima and minima:
A comparison of three methods. J. Atmos. Ocean. Technol. 5(6), 736–742 (1988).
39. McDonnell, J. et al. Verication and bias correction of ECMWF forecasts for Irish weather stations to evaluate their potential
usefulness in grass growth modelling. Meteorol. Appl. 25(2), 292–301 (2018).
40. Samui, R. P. & John, G. A simple approach in assessing the impact of weather on rice yield in two rice growing seasons at Pattambi,
Kerala. Mausam 54(2), 477–482 (2003).
41. Pan, H. L. & Mahrt, L. Interaction between soil hydrology and boundary-layer development. Bound. Layer Meteorol. 38, 185–202
(1987).
42. Rosenberg, N. J. Micro Climate: e Biological Environment 315 (Wiley-Interscience Publication, 1974).
43. VijayaKumar, P. et al. Network of Automatic Weather Stations: An AICRPAM-NICRA Initiative 40 (ICAR-C entral Research Institute
for Dryland Agriculture, 2018).
44. De Wit, C. T., Goudriaan, J. & VanLaar, H. H. Simulation of Assimilation, Respiration and Transpiration of Crops 148 (Centre for
Agricultural Publishing and Documentation, 1978).
45. Hoogenboom, G., Huck, M. G., ROOTSIMU v. 40. A Dynamic Simulation of Root Growth, Water Uptake, and Biomass Partitioning
in a So-Plant-Atmosphere Continuum: Update and Documentation 109th edn, 83 (Alabama Agr. Exp. Stn., 1986).
46. Parton, W. J. & Logan, J. A. A model for diurnal variation in soil and air temperature. Agric. Meteorol. 23, 205–216 (1981).
47. Piani, C., Haerter, J. O. & Coppola, E. Statistical bias correction for daily precipitation in regional climate models over Europe.
eor. Appl. Climatol. 99, 187–192 (2010).
48. Wilcke, R. A. I., Mendlik, T. & Gobiet, A. Multi-variable error correction of regional climate models. Clim. Change 120, 871–887.
https:// doi. org/ 10. 1007/ s10584- 013- 0845-x (2013).
49. Fang, G. H., Yang, J., Chen, Y. N. & Zammit, C. Comparing bias correction methods in downscaling meteorological variables for
a hydrologic impact study in an arid area in China. Hydrol. Earth Syst. Sci. 19(6), 2547–2559. https:// doi. org/ 10. 5194/ hess- 19-
2547- 2015 (2015).
50. Rao, A. V. M. S. et al. Evaluating area-specic adaptation strategies for maize under future climates of India. Sci. Total Environ.
836, 155511. https:// doi. org/ 10. 1016/j. scito tenv. 2022. 155511 (2022).
51. Moriasi, D. N. et al. Model evaluation guidelines for systematic quantication of accuracy in watershed simulations. Trans. ASABE
50(3), 885–900 (2007).
52. Lenderink, G., Buishand, A. & van Deursen, W. Estimates of future discharges of the river Rhine using two scenario methodolo-
gies: Direct versus delta approach. Hydrol. Earth Syst. Sci. 11(3), 1145–1159 (2007).
53. Déqué, M. et al. An intercomparison of regional climate simulations for Europe: Assessing uncertainties in model projections.
Clim. Change 81, 53–70 (2007).
54. Block, P. J., Souza-Filho, F. A., Sun, L. & Kwon, H. H. A stream-ow forecasting framework using multiple climate and hydrological
models. J. Am. Water Resour. Assoc. 45(4), 828–843 (2009).
55. Nash, J. E. & Sutclie, J. V. River ow forecasting through conceptual models-I. A discussion of principles. J. Hydrol. 10(3), 282–290
(1970).
56. Willmott, C. J. On the validation of models. Phys. Geogr. 2(2), 184–194 (1981).
57. Legates, D. R. & McCabe, G. J. Jr. Evaluating the use of goodness-of-t measures in hydrologic and hydroclimatic model validation.
Water Resour. Res. 35(1), 233–241 (1999).
Acknowledgements
e authors gratefully acknowledge All India Coordinated Research Project on Agrometeorology, Indian Council
of Agricultural Research, Government of India for supporting this research work.
Content courtesy of Springer Nature, terms of use apply. Rights reserved

13
Vol.:(0123456789)
Scientic Reports | (2023) 13:7789 | https://doi.org/10.1038/s41598-023-34194-9
www.nature.com/scientificreports/
Author contributions
S.K.B.: Conceptualization, Methodology, Investigation, Formal analysis, Writing, Reviewing, Editing V.P.P.: Data
curation, Formal analysis, Investigation, Writing V.M.S.: Reviewing & Editing N.M.: Investigation, Formal analy-
sis, Writing, Reviewing & Editing MAS: Writing, Reviewing & Editing A.V.M.S.: Methodology, Investigation,
Reviewing and Editing P.V.K.: Investigation, Reviewing & Editing M.V.: Investigation, Reviewing & Editing
V.K.S.: Reviewing, Editing and Supervision.
Competing interests
e authors declare no competing interests.
Additional information
Supplementary Information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 023- 34194-9.
Correspondence and requests for materials should be addressed to N.M.
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and
institutional aliations.
Open Access is article is licensed under a Creative Commons Attribution 4.0 International
License, which permits use, sharing, adaptation, distribution and reproduction in any medium or
format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the
Creative Commons licence, and indicate if changes were made. e images or other third party material in this
article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from
the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
© e Author(s) 2023
Content courtesy of Springer Nature, terms of use apply. Rights reserved

1.
2.
3.
4.
5.
6.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
apply.
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
not:
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
control;
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
writing;
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
content.
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
onlineservice@springernature.com