Medium-term hydrologic forecast uncertainty is strongly dependent on the forecast quality of meteorological variables. Of these variables, the influence of precipitation has been studied most widely, while temperature, radiative forcing and their derived product potential evapotranspiration (PET) have received little attention from the perspective of hydrological forecasting. This study aims to fill this gap by assessing the usability of potential evaporation forecasts for 10-day-ahead streamflow forecasting in the Rhine basin, Europe. In addition, the forecasts of the meteorological variables are compared with observations.
Streamflow reforecasts were performed with the daily wflow_hbv model used in previous studies of the Rhine using the ECMWF 20-year meteorological reforecast dataset. Meteorological forecasts were compared with observed rainfall, temperature, global radiation and potential evaporation for 148 subbasins. Secondly, the effect of using PET climatology versus using observation-based estimates of PET was assessed for hydrological state and for streamflow forecast skill.
We find that (1) there is considerable skill in the ECMWF reforecasts to predict PET for all seasons, and (2) using dynamical PET forcing based on observed temperature and satellite global radiation estimates results in lower evaporation and wetter initial states, but (3) the effect on forecasted 10-day streamflow is limited. Implications of this finding are that it is reasonable to use meteorological forecasts to forecast potential evaporation and use this is in medium-range streamflow forecasts. However, it can be concluded that an approach using PET climatology is also sufficient, most probably not only for the application shown here, but also for most models similar to the HBV concept and for moderate climate zones.
As a by-product, this research resulted in gridded datasets for temperature,
radiation and potential evaporation based on the Makkink equation for the
Rhine basin. The datasets have a spatial resolution of
Hydrologic forecasting has the aim of predicting the future state of
important hydrologic fluxes, most notably streamflow. Throughout the process
of forecasting, from model setup via initial state estimation to forecast
run, meteorological forcing is a key component. Precipitation is known to be
the main driver of hydrological processes, and most of the forecast
uncertainty is attributed to inaccurate precipitation forcing
Evaporation is a result of the interaction between meteorological forcing and
physical and physiological processes at the land surface. Meteorological
forcing provides the potential energy (potential evaporation or PET) for
evaporative processes to take place. There are many formulas to estimate the
potential energy available for evaporation, which can be divided in three
types of formulas based on their data requirements
Constraints on data availability have led to additional approximations for
potential evaporation. A common approximation is the calculation of a monthly
potential evaporation climatology or PET demand curves
Hydrological models have proven to be insensitive to the difference between
variable potential evaporation forcing and climatological monthly potential
evaporation forcing with respect to the model's potential to estimate
streamflow after calibration
As mentioned above, there has been little attention to the forecast skill of the secondary forcing variables temperature and radiation in the hydrological context of potential evaporation. Furthermore, there is an easy and often used practice of avoiding potential evaporation forecasts by using a potential evaporation climatology. Therefore, the objective of this study is to assess to what extent potential evaporation forecasts can contribute to streamflow forecast skill.
This question is evaluated for the Rhine basin in Europe
(Fig.
Several studies already directly addressed some aspects of operational
ensemble flow forecasts in the Rhine.
To answer the research question, model experiments are performed, but first the data and hydrological model are presented (Sect. 2). Second, the model experiments are described, which also partitions the main question into three subquestions (Sect. 3) which are subsequently answered (Sect. 4). The paper concludes with a discussion on the results in the wider context of evaporation modeling in hydrologic forecasting and the conclusions (Sect. 5).
Map of the Rhine basin, Europe. Black lines delineate 148 subbasins used in the analysis of the meteorological forecast skill. Square markers show the locations used for forecast skill analysis.
Observational data have been preprocessed for use with a grid-based
hydrological model. The data were
processed with hourly time resolution, on a
For this study the precipitation dataset from
Temperature observations (1996–2016) are interpolated on the same
To calculate temperature
Second, interpolate the measured temperature
The final temperature estimate for grid cell
The availability of solar radiation measurements at the surface has proven to
be spatially and temporally inadequate for many applications, with remotely
sensed solar radiation products having the largest potential to remedy this
For this study, downward shortwave radiation is resampled and merged from the
EUMETSAT Surface Incoming Solar Radiation (SIS)
In earlier research it has been shown that LSA-SAF (2005–current) and CM-SAF
(1983–2005) can consistently be merged into one time series
There are different approaches in making use of remotely sensed data to
calculate evapo(transpi)ration. One branch of research aims to calculate
actual evapotranspiration directly from satellite imagery
For operational use, PET estimates can be derived from satellite data only,
or from a combination of satellite imagery and ground measurements.
A disadvantage of using satellites such as MODIS is their temporal coverage
which is restricted to a single overpass at a set time each day giving one
instantaneous value. This can be resolved by assuming a sinusoidal
development of PET over the day
Here, potential evaporation is calculated from geostationary satellite
radiation estimates and ground observations of temperature with the method
proposed by
The reasons for choosing the Makkink equation are that (1) it only needs
radiation and temperature, for which gridded estimations are available, and
that (2) the Makkink equation is used by the Royal Netherlands Meteorological
Institute (KNMI), so that the work presented here is compatible with ongoing
local research
The potential evaporation is calculated based on air
temperature
Difference between climatology and near-real-time potential
evaporation. Shown for the year 2004 for grid cell
The European Center for Medium-Range Weather Forecasts (ECMWF) issues
hindcasts produced with the current model cycle for certain days for the last
20 years. The reforecast obtained for this study was produced with model
cycle 43r1
Forecasted Makkink potential evaporation (PET
wflow is a modular hydrological modeling framework that allows for easy
implementation and prototyping of regular grid hydrological model concepts in
python-pcraster
The analysis consists of a meteorological part and a hydrological part
(Fig.
Flow chart of the model experiment. Blue boxes represent data products. Green boxes depict modeling activities. Arrows represent the flow of data for historical runs (blue lines) and forecast runs (black). The red boxes indicate the areas for analysis of the results, each box targeting a research subquestion.
In this analysis we aim to answer the following question. What is the forecast skill of temperature, radiation and potential evaporation compared to precipitation?
For this purpose the observations and forecasts are spatially averaged over
148 subbasins (Fig.
The mean continuous ranked probability score (CRPS) is an overall measure of
forecast quality and is calculated by
The limits of the mean CRPS vary depending on the basin and season, and it is
therefore difficult to compare between basins and season. For this reason the
CRPS is translated into the continuous ranked probability skill score, which
measures the performance of a forecasting system relative to a reference
forecast. The reference forecast here is seasonal climatology. As such the
CRPSS equals 1 for a perfect forecast and 0 when the forecast ensemble does
not score a better CRPS than the CRPS calculated for the climatological
distribution.
The above scores are calculated with the Ensemble Verification System (EVS),
a software package to calculate ensemble verification metrics
In this second part of the analysis we aim to answer the following questions.
To what extent are initial states affected by the use of climatological
versus near-real-time potential evaporation? To what extent can potential evaporation forecasts contribute to
streamflow forecast skill?
To answer the first question, the wflow_hbv model is consecutively forced
with PET
Streamflow gauges for analysis were selected such that
only gauges were chosen for which the model was deemed behavioral as
expressed by a KGE score threshold of 0.5; only one gauge was selected for each stream in the basin, except for the
Rhine River itself, for which two additional gauges were chosen. If multiple
gauges in the same stream were present, the gauge most downstream was chosen.
The gauge “most downstream” was selected by sorting on mean yearly
discharge and picking the highest; and from the then remaining list, the largest 20 streams were selected for analysis.
The streamflow locations are shown in Fig.
The forecast skill is assessed for all catchments and for each season.
Seasons are Northern Hemisphere seasons spring (MAM), summer (JJA),
autumn (SON), and winter (DJF). Figure
Continuous ranked probability skill score (CRPSS) for the four
forcing variables benchmarked against sample climatology for the 148 HBV
subbasins. CRPSSs are aggregated into mean (solid), 10th and 90th percentiles
(dashed). Note that the CRPSS at
Continuous ranked probability score (CRPS) for the four forcing
variables for the 148 HBV subbasins for the whole year. CRPS is aggregated
into mean (solid), 10th and 90th percentiles (dashed). Note that the CRPS at
There is no skill in the ECMWF forecast beyond 10 days for daily
precipitation. This is consistent with the 9-day lead time in streamflow
forecasts found by
There is more skill in the forecast for the variables temperature and
incoming shortwave radiation. Likewise, there is considerable skill remaining
in the potential evaporation forecast. For temperature the 1-day forecast is
close to perfect for autumn and spring. The skill in temperature forecast is
similar for spring, summer and autumn but worse during winter. The spread,
the difference in skill between basins, is also largest during winter and
spring. The RME shows that there is a small negative bias in the temperature
forecasts. The RME for winter is largest; however, it should be noted that
the RME is the mean difference weighed by the mean of the observations
(Eq.
Relative mean error (RME) for the four forcing variables for the
148 HBV subbasins for the whole year. RME is aggregated into mean (solid),
10th and 90th percentiles (dashed). Note that the CRPSS at
For radiation there is already quite a considerable loss in skill after 1
day, but then the CRPSS remains quite stable for longer forecasts, notably
during spring and autumn. There is a larger decline in skill for summer and
for extreme low radiation values in winter. In absolute terms, the CRPS is
related to the magnitude of the average radiation for each season, with the
smallest absolute errors for winter and the largest during summer
(Fig.
The skill of the potential evaporation forecast is closely tied to the skill in radiation forecast, both because Makkink potential evaporation is directly proportional to radiation and because of the larger uncertainty in the radiation forecast. The forecast skill has the same properties as those found for the radiation forecast. A small difference is that part of the forecast skill in temperature is found back in a slightly improved forecast skill after 10 days for PET compared to radiation in summer.
Overall, there is relatively little spread in skill between basins, with the
10th and 90th percentiles close to the mean and following the same
trajectory. The difference in skill between the different seasons is larger
than the spread between basins, especially for the variables temperature,
radiation and potential evaporation. This difference in skill between seasons
is partly misleading. For example, the forecast skill for radiation in winter
(Fig.
Likewise, high temperatures receive higher skill scores than low season
temperatures. This is even more distinct in the radiation forecasts. This
does, however, not mean that the forecasts of such rare events are more
accurate: both RME (Fig.
Dynamic potential evaporation leads to lower actual evaporation (AET). The
difference is largest for summer and spring (Fig.
Seasonal mean difference in calculated actual evaporation (AET) for each season. Actual evaporation includes evaporation from interception.
The lower evaporation with dynamic PET forcing cascades through the different
model storages, accumulating in a mostly wetter lower zone (LZ) storage under
dynamic forcing. Finally, the lower evaporation results in higher discharge
throughout the Rhine basin (see Figs. S2–S7).
Exceptions are the high Rhine during spring and to a lesser extent during
autumn, and several areas during winter when there is very little effect
overall. The wetter conditions also result in higher peak discharges. As
these higher discharges are a result of the temporal dynamics of the
potential evaporation input, we expect to find a similar effect on forecasted
discharges. As will be shown later (Fig.
The CRPSS for streamflow forecast is hardly influenced by potential
evaporation forcing type. At first sight, the skill scores obtained with
dynamic or climatological PET are identical. Small differences only become
visible when taking a close-up of the differences by subtracting one from the
other (Fig.
CRPSS for forecast runs (forecasted PET, climatological PET) and
their difference benchmarked against model output for the 20 largest
sub-catchments in the Rhine basin. CRPSSs are aggregated into mean (solid),
10th and 90th percentiles (dashed). Note that the CRPSS at
RME for forecast runs (forecasted PET, climatological PET) and their
difference for the 20 largest streams in the Rhine basin. RME scores are
aggregated into mean (solid), 10th and 90th percentiles (dashed). Note that
the CRPSS at
Analyzed for each season separately, there is a little more to discover about the role of potential evaporation forecasts and the sensitivity of forecast skill to the meteorological forecast in general. The contribution of the meteorological forecast to streamflow forecast uncertainty is largest for summer, as shown by the largest decrease in CRPSS for the 10-day forecast in summer compared to the other seasons. The CRPSS especially “dips” for the most extreme discharges, which is not as strong for spring and autumn, and especially compared to the flat response of the CRPSS for the highest 30 % of discharges in winter.
In terms of the effect of potential evaporation climatology versus forecasted potential evaporation, the influence is largest (but still quite small) for summer and spring. This is tied to the potential evaporation being of larger magnitude; there is hardly a response for winter, where there is the lowest potential evaporation.
The influence of PET forecasts on low flow prediction is further examined by
calculating the scores for different levels of non-exceedance
CRPSS for forecast runs (forecasted PET, climatological PET) and
their difference benchmarked against model output for the 20 largest streams
in the Rhine basin. CRPSSs are aggregated into mean (solid), 10th and
90th percentiles (dashed). Note that the CRPSS at
This paper presented a simple and straightforward investigation with an operational forecasting practice perspective. First, observation data were preprocessed for use in the gridded wflow_hbv model. Second, the wflow_hbv model was subjected to dynamical and climatological PET forcing. Three aspects were analyzed: (1) the skill in meteorological forecast, (2) the effect of PET forcing on initial states and (3) the effect of PET forcing on forecast skill.
Nine to 10 days is the upper limit on forecast lead time for daily precipitation for the ECMWF forecast in the Rhine basin, with only very little skill remaining compared to climatology. There is considerable skill in daily temperature, radiation and potential evaporation forecasts, also after 10 days. Variable PET forcing resulted in lower evaporation and in wetter initial states and higher modeled discharges.
The main result of this study is that potential evaporation forecasts
improved streamflow forecasts only slightly. This confirms earlier results
that the influence of random errors on estimated streamflow was generally not
measurable when comparing model runs directly, needing a 20% systematic bias
in PET to influence model outcomes significantly
There is a wider discussion on evaporation modeling in hydrological models
Further limitations are that only one model was tested (wflow_hbv) and for one climate zone (moderate temperate). The model was calibrated originally on a different PET climatology than studied here and was not recalibrated. The latter is not seen as a limitation. Deliberately not recalibrating the model enabled us to focus on the changes in modeled processes instead of comparably vague assessments based on model performance expressed in efficiencies, with the effects brought forward by the PET forcing hidden somewhere in the parameter space.
In the analysis, forecasting metrics were calculated over subsets of
observation–forecast pairs conditioned on the observations. Alternatively,
the subsets could have been conditioned on the mean of the forecasts. This
would present more intuitive information for a forecaster at the time of a
forecast when the observation is by definition not yet known
The idea to look at potential evaporation forecast was instigated as part of a program to improve forecasts of low flows. Indeed, it is a recurring hypothesis that potential evaporation forecasts should aid especially in making low flow predictions. The uniform response of several skill scores for different subsets of observed discharge does not support this idea; there is no special gain for low flows.
Instead, from our model results it follows that the correct prediction of a drought is firstly dependent on a correct forecast of no rain. Low flow recession is subsequently determined, in the absence of further feedback mechanisms, solely by the storage–discharge relationship of, in this case, the lower zone representing the saturated zone as well as the routing of surface water.
The follow-up question then is the following. Is this true in reality, or is this a model deficiency? Should we rethink hydrological modeling to incorporate more feedbacks on evaporation? Certainly there are models with more complex representation of evaporative processes. These are valid and important questions, especially in the light of hydrologic response to change in climate drivers. However, from the results presented here, it should not be expected that a better understanding of evaporative processes and feedbacks will result directly in a significant increase in 10-day predictive skill for streamflow.
Gridded precipitation, temperature, radiation and potential
evaporation used in this study are available through the 4TU data center; see
The supplement related to this article is available online at:
BvO prepared the data, performed the analyses and wrote the article. RU contributed to improving the article and experimental setup. AW supplied part of the scripts used in the analysis and contributed in preprocessing steps of the forecasts as well as contributing to the design of the model experiments and final article text.
The authors declare that they have no conflict of interest.
This work is partly supported by the IMPREX project funded by the European
Commission under the Horizon 2020 framework program (grant 641811) and partly
by the Dutch Ministry of Infrastructure and the Environment. Part of the work
was conducted as an in-kind contribution to Netherlands Organisation for
Scientific Reasearch project “SWM-EVAP: Smart Water Management in a complex
environment: improving the monitoring and forecasting of surface evaporation” (ALWTW.2016.049).
Meteorological data for this research have been gratefully received from the Deutscher
Wetterdienst Climate Data Center; KNMI Data Centrum; Météo France;
Federal Office of Meteorology and Climatology MeteoSwiss; Administration de
la gestion de l'eau du Grand-Duché de Luxembourg; and Service Publique de
Wallonie Département des Etudes et de l'Appui à la Gestion. Discharge
data have been gratefully received from SCHAPI (Service Central
d'Hydrométéorologie et d'Appui àla Prévision des Inondations)
through Banque HYDRO; Bundesamt für Umwelt BAFU; Bundesanstalt für
Gewässerkunde (BfG); Administration de la gestion de l'eau du
Grand-Duché de Luxembourg; Bavarian Environment Agency,